id,prompt,label,reasoning,graph_id,story_id,rung,query_type,formal_form
0,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 42%. For people who drink coffee, the probability of ringing alarm is 51%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.51
0.51 - 0.42 = 0.09
0.09 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 42%. For people who drink coffee, the probability of ringing alarm is 51%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.51
0.51 - 0.42 = 0.09
0.09 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 42%. For people who drink coffee, the probability of ringing alarm is 51%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.51
0.51 - 0.42 = 0.09
0.09 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 8%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 41%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 86%. For people who do not drink coffee, the probability of alarm set by wife is 74%. For people who drink coffee, the probability of alarm set by wife is 24%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.08
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.41
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.74
P(V2=1 | X=1) = 0.24
0.24 * (0.54 - 0.08)+ 0.74 * (0.86 - 0.41)= -0.23
-0.23 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
6,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 8%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 41%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 86%. For people who do not drink coffee, the probability of alarm set by wife is 74%. For people who drink coffee, the probability of alarm set by wife is 24%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.08
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.41
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.74
P(V2=1 | X=1) = 0.24
0.74 * (0.86 - 0.41) + 0.24 * (0.54 - 0.08) = 0.32
0.32 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
9,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 79%. For people who do not drink coffee, the probability of ringing alarm is 42%. For people who drink coffee, the probability of ringing alarm is 51%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.79
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.51
0.79*0.51 - 0.21*0.42 = 0.49
0.49 > 0",mediation,alarm,1,marginal,P(Y)
11,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 79%. The probability of not drinking coffee and ringing alarm is 9%. The probability of drinking coffee and ringing alarm is 40%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.79
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.40
0.40/0.79 - 0.09/0.21 = 0.09
0.09 > 0",mediation,alarm,1,correlation,P(Y | X)
15,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 26%. For people who drink coffee, the probability of ringing alarm is 76%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.76
0.76 - 0.26 = 0.50
0.50 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. For people who do not drink coffee, the probability of ringing alarm is 26%. For people who drink coffee, the probability of ringing alarm is 76%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.76
0.77*0.76 - 0.23*0.26 = 0.64
0.64 > 0",mediation,alarm,1,marginal,P(Y)
30,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 50%. For people who drink coffee, the probability of ringing alarm is 64%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.64
0.64 - 0.50 = 0.13
0.13 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
33,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 17%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 64%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 51%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 98%. For people who do not drink coffee, the probability of alarm set by wife is 72%. For people who drink coffee, the probability of alarm set by wife is 27%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.17
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.51
P(Y=1 | X=1, V2=1) = 0.98
P(V2=1 | X=0) = 0.72
P(V2=1 | X=1) = 0.27
0.27 * (0.64 - 0.17)+ 0.72 * (0.98 - 0.51)= -0.21
-0.21 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
35,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 17%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 64%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 51%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 98%. For people who do not drink coffee, the probability of alarm set by wife is 72%. For people who drink coffee, the probability of alarm set by wife is 27%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.17
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.51
P(Y=1 | X=1, V2=1) = 0.98
P(V2=1 | X=0) = 0.72
P(V2=1 | X=1) = 0.27
0.72 * (0.98 - 0.51) + 0.27 * (0.64 - 0.17) = 0.34
0.34 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
38,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 76%. The probability of not drinking coffee and ringing alarm is 12%. The probability of drinking coffee and ringing alarm is 48%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.48
0.48/0.76 - 0.12/0.24 = 0.13
0.13 > 0",mediation,alarm,1,correlation,P(Y | X)
40,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
42,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 20%. For people who drink coffee, the probability of ringing alarm is 68%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.68
0.68 - 0.20 = 0.49
0.49 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
43,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 20%. For people who drink coffee, the probability of ringing alarm is 68%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.68
0.68 - 0.20 = 0.49
0.49 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
45,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 20%. For people who drink coffee, the probability of ringing alarm is 68%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.68
0.68 - 0.20 = 0.49
0.49 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
46,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 3%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 48%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 47%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 95%. For people who do not drink coffee, the probability of alarm set by wife is 37%. For people who drink coffee, the probability of alarm set by wife is 45%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.03
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.45
0.45 * (0.48 - 0.03)+ 0.37 * (0.95 - 0.47)= 0.04
0.04 > 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
50,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 82%. For people who do not drink coffee, the probability of ringing alarm is 20%. For people who drink coffee, the probability of ringing alarm is 68%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.68
0.82*0.68 - 0.18*0.20 = 0.59
0.59 > 0",mediation,alarm,1,marginal,P(Y)
54,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
59,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 41%. For people who drink coffee, the probability of ringing alarm is 47%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.47
0.47 - 0.41 = 0.06
0.06 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
60,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 11%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 60%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 46%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 92%. For people who do not drink coffee, the probability of alarm set by wife is 61%. For people who drink coffee, the probability of alarm set by wife is 1%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.11
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.92
P(V2=1 | X=0) = 0.61
P(V2=1 | X=1) = 0.01
0.01 * (0.60 - 0.11)+ 0.61 * (0.92 - 0.46)= -0.29
-0.29 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
61,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 11%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 60%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 46%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 92%. For people who do not drink coffee, the probability of alarm set by wife is 61%. For people who drink coffee, the probability of alarm set by wife is 1%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.11
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.92
P(V2=1 | X=0) = 0.61
P(V2=1 | X=1) = 0.01
0.01 * (0.60 - 0.11)+ 0.61 * (0.92 - 0.46)= -0.29
-0.29 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
65,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 66%. For people who do not drink coffee, the probability of ringing alarm is 41%. For people who drink coffee, the probability of ringing alarm is 47%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.47
0.66*0.47 - 0.34*0.41 = 0.44
0.44 > 0",mediation,alarm,1,marginal,P(Y)
67,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 66%. The probability of not drinking coffee and ringing alarm is 14%. The probability of drinking coffee and ringing alarm is 31%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.31
0.31/0.66 - 0.14/0.34 = 0.06
0.06 > 0",mediation,alarm,1,correlation,P(Y | X)
72,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 26%. For people who drink coffee, the probability of ringing alarm is 71%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.71
0.71 - 0.26 = 0.45
0.45 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
73,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 26%. For people who drink coffee, the probability of ringing alarm is 71%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.71
0.71 - 0.26 = 0.45
0.45 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
74,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 3%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 45%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 94%. For people who do not drink coffee, the probability of alarm set by wife is 49%. For people who drink coffee, the probability of alarm set by wife is 53%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.03
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.94
P(V2=1 | X=0) = 0.49
P(V2=1 | X=1) = 0.53
0.53 * (0.50 - 0.03)+ 0.49 * (0.94 - 0.45)= 0.02
0.02 > 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
79,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 88%. For people who do not drink coffee, the probability of ringing alarm is 26%. For people who drink coffee, the probability of ringing alarm is 71%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.71
0.88*0.71 - 0.12*0.26 = 0.66
0.66 > 0",mediation,alarm,1,marginal,P(Y)
80,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 88%. The probability of not drinking coffee and ringing alarm is 3%. The probability of drinking coffee and ringing alarm is 63%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.63
0.63/0.88 - 0.03/0.12 = 0.45
0.45 > 0",mediation,alarm,1,correlation,P(Y | X)
82,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
85,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 51%. For people who drink coffee, the probability of ringing alarm is 49%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.49
0.49 - 0.51 = -0.03
-0.03 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
86,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 51%. For people who drink coffee, the probability of ringing alarm is 49%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.49
0.49 - 0.51 = -0.03
-0.03 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
93,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. For people who do not drink coffee, the probability of ringing alarm is 51%. For people who drink coffee, the probability of ringing alarm is 49%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.49
0.77*0.49 - 0.23*0.51 = 0.50
0.50 > 0",mediation,alarm,1,marginal,P(Y)
97,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how drinking coffee correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
99,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 27%. For people who drink coffee, the probability of ringing alarm is 90%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.90
0.90 - 0.27 = 0.63
0.63 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 27%. For people who drink coffee, the probability of ringing alarm is 90%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.90
0.90 - 0.27 = 0.63
0.63 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 6%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 56%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 100%. For people who do not drink coffee, the probability of alarm set by wife is 48%. For people who drink coffee, the probability of alarm set by wife is 79%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 1.00
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.79
0.48 * (1.00 - 0.56) + 0.79 * (0.50 - 0.06) = 0.50
0.50 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. For people who do not drink coffee, the probability of ringing alarm is 27%. For people who drink coffee, the probability of ringing alarm is 90%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.90
0.77*0.90 - 0.23*0.27 = 0.76
0.76 > 0",mediation,alarm,1,marginal,P(Y)
108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 6%. The probability of drinking coffee and ringing alarm is 70%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.70
0.70/0.77 - 0.06/0.23 = 0.63
0.63 > 0",mediation,alarm,1,correlation,P(Y | X)
109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 6%. The probability of drinking coffee and ringing alarm is 70%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.70
0.70/0.77 - 0.06/0.23 = 0.63
0.63 > 0",mediation,alarm,1,correlation,P(Y | X)
110,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 42%. For people who drink coffee, the probability of ringing alarm is 66%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.66
0.66 - 0.42 = 0.24
0.24 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 42%. For people who drink coffee, the probability of ringing alarm is 66%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.66
0.66 - 0.42 = 0.24
0.24 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 42%. For people who drink coffee, the probability of ringing alarm is 66%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.66
0.66 - 0.42 = 0.24
0.24 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 11%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 63%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 99%. For people who do not drink coffee, the probability of alarm set by wife is 59%. For people who drink coffee, the probability of alarm set by wife is 35%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.11
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.99
P(V2=1 | X=0) = 0.59
P(V2=1 | X=1) = 0.35
0.35 * (0.63 - 0.11)+ 0.59 * (0.99 - 0.49)= -0.13
-0.13 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 11%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 63%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 99%. For people who do not drink coffee, the probability of alarm set by wife is 59%. For people who drink coffee, the probability of alarm set by wife is 35%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.11
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.99
P(V2=1 | X=0) = 0.59
P(V2=1 | X=1) = 0.35
0.59 * (0.99 - 0.49) + 0.35 * (0.63 - 0.11) = 0.37
0.37 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 79%. For people who do not drink coffee, the probability of ringing alarm is 42%. For people who drink coffee, the probability of ringing alarm is 66%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.79
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.66
0.79*0.66 - 0.21*0.42 = 0.61
0.61 > 0",mediation,alarm,1,marginal,P(Y)
123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 79%. The probability of not drinking coffee and ringing alarm is 9%. The probability of drinking coffee and ringing alarm is 53%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.79
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.53
0.53/0.79 - 0.09/0.21 = 0.24
0.24 > 0",mediation,alarm,1,correlation,P(Y | X)
129,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 34%. For people who drink coffee, the probability of ringing alarm is 68%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.68
0.68 - 0.34 = 0.34
0.34 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 7%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 53%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 94%. For people who do not drink coffee, the probability of alarm set by wife is 58%. For people who drink coffee, the probability of alarm set by wife is 40%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.07
P(Y=1 | X=0, V2=1) = 0.53
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.94
P(V2=1 | X=0) = 0.58
P(V2=1 | X=1) = 0.40
0.40 * (0.53 - 0.07)+ 0.58 * (0.94 - 0.50)= -0.08
-0.08 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 7%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 53%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 94%. For people who do not drink coffee, the probability of alarm set by wife is 58%. For people who drink coffee, the probability of alarm set by wife is 40%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.07
P(Y=1 | X=0, V2=1) = 0.53
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.94
P(V2=1 | X=0) = 0.58
P(V2=1 | X=1) = 0.40
0.58 * (0.94 - 0.50) + 0.40 * (0.53 - 0.07) = 0.42
0.42 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 74%. For people who do not drink coffee, the probability of ringing alarm is 34%. For people who drink coffee, the probability of ringing alarm is 68%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.74
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.68
0.74*0.68 - 0.26*0.34 = 0.59
0.59 > 0",mediation,alarm,1,marginal,P(Y)
139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how drinking coffee correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 58%. For people who drink coffee, the probability of ringing alarm is 61%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.61
0.61 - 0.58 = 0.03
0.03 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 58%. For people who drink coffee, the probability of ringing alarm is 61%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.61
0.61 - 0.58 = 0.03
0.03 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 13%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 62%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 97%. For people who do not drink coffee, the probability of alarm set by wife is 91%. For people who drink coffee, the probability of alarm set by wife is 24%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.13
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.97
P(V2=1 | X=0) = 0.91
P(V2=1 | X=1) = 0.24
0.91 * (0.97 - 0.50) + 0.24 * (0.62 - 0.13) = 0.35
0.35 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
150,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 76%. The probability of not drinking coffee and ringing alarm is 14%. The probability of drinking coffee and ringing alarm is 47%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.47
0.47/0.76 - 0.14/0.24 = 0.03
0.03 > 0",mediation,alarm,1,correlation,P(Y | X)
151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 76%. The probability of not drinking coffee and ringing alarm is 14%. The probability of drinking coffee and ringing alarm is 47%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.47
0.47/0.76 - 0.14/0.24 = 0.03
0.03 > 0",mediation,alarm,1,correlation,P(Y | X)
153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how drinking coffee correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 44%. For people who drink coffee, the probability of ringing alarm is 75%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.75
0.75 - 0.44 = 0.30
0.30 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 8%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 51%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 92%. For people who do not drink coffee, the probability of alarm set by wife is 85%. For people who drink coffee, the probability of alarm set by wife is 60%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.08
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.92
P(V2=1 | X=0) = 0.85
P(V2=1 | X=1) = 0.60
0.60 * (0.51 - 0.08)+ 0.85 * (0.92 - 0.49)= -0.10
-0.10 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 8%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 51%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 92%. For people who do not drink coffee, the probability of alarm set by wife is 85%. For people who drink coffee, the probability of alarm set by wife is 60%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.08
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.92
P(V2=1 | X=0) = 0.85
P(V2=1 | X=1) = 0.60
0.60 * (0.51 - 0.08)+ 0.85 * (0.92 - 0.49)= -0.10
-0.10 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 8%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 51%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 92%. For people who do not drink coffee, the probability of alarm set by wife is 85%. For people who drink coffee, the probability of alarm set by wife is 60%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.08
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.92
P(V2=1 | X=0) = 0.85
P(V2=1 | X=1) = 0.60
0.85 * (0.92 - 0.49) + 0.60 * (0.51 - 0.08) = 0.41
0.41 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
162,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 84%. For people who do not drink coffee, the probability of ringing alarm is 44%. For people who drink coffee, the probability of ringing alarm is 75%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.75
0.84*0.75 - 0.16*0.44 = 0.70
0.70 > 0",mediation,alarm,1,marginal,P(Y)
164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 84%. The probability of not drinking coffee and ringing alarm is 7%. The probability of drinking coffee and ringing alarm is 62%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.62
0.62/0.84 - 0.07/0.16 = 0.30
0.30 > 0",mediation,alarm,1,correlation,P(Y | X)
167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how drinking coffee correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 50%. For people who drink coffee, the probability of ringing alarm is 55%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.55
0.55 - 0.50 = 0.05
0.05 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 9%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 55%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 42%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 86%. For people who do not drink coffee, the probability of alarm set by wife is 90%. For people who drink coffee, the probability of alarm set by wife is 30%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.90
P(V2=1 | X=1) = 0.30
0.30 * (0.55 - 0.09)+ 0.90 * (0.86 - 0.42)= -0.27
-0.27 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 9%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 55%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 42%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 86%. For people who do not drink coffee, the probability of alarm set by wife is 90%. For people who drink coffee, the probability of alarm set by wife is 30%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.90
P(V2=1 | X=1) = 0.30
0.90 * (0.86 - 0.42) + 0.30 * (0.55 - 0.09) = 0.31
0.31 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 9%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 55%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 42%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 86%. For people who do not drink coffee, the probability of alarm set by wife is 90%. For people who drink coffee, the probability of alarm set by wife is 30%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.90
P(V2=1 | X=1) = 0.30
0.90 * (0.86 - 0.42) + 0.30 * (0.55 - 0.09) = 0.31
0.31 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 69%. The probability of not drinking coffee and ringing alarm is 15%. The probability of drinking coffee and ringing alarm is 38%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.69
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.38
0.38/0.69 - 0.15/0.31 = 0.05
0.05 > 0",mediation,alarm,1,correlation,P(Y | X)
180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 10%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 55%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 52%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 96%. For people who do not drink coffee, the probability of alarm set by wife is 65%. For people who drink coffee, the probability of alarm set by wife is 22%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.10
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.96
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.22
0.22 * (0.55 - 0.10)+ 0.65 * (0.96 - 0.52)= -0.19
-0.19 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 10%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 55%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 52%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 96%. For people who do not drink coffee, the probability of alarm set by wife is 65%. For people who drink coffee, the probability of alarm set by wife is 22%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.10
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.96
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.22
0.65 * (0.96 - 0.52) + 0.22 * (0.55 - 0.10) = 0.41
0.41 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 71%. For people who do not drink coffee, the probability of ringing alarm is 39%. For people who drink coffee, the probability of ringing alarm is 62%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.62
0.71*0.62 - 0.29*0.39 = 0.55
0.55 > 0",mediation,alarm,1,marginal,P(Y)
204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 78%. For people who do not drink coffee, the probability of ringing alarm is 56%. For people who drink coffee, the probability of ringing alarm is 66%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.78
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.66
0.78*0.66 - 0.22*0.56 = 0.64
0.64 > 0",mediation,alarm,1,marginal,P(Y)
205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 78%. For people who do not drink coffee, the probability of ringing alarm is 56%. For people who drink coffee, the probability of ringing alarm is 66%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.78
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.66
0.78*0.66 - 0.22*0.56 = 0.64
0.64 > 0",mediation,alarm,1,marginal,P(Y)
214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 10%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 95%. For people who do not drink coffee, the probability of alarm set by wife is 24%. For people who drink coffee, the probability of alarm set by wife is 77%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.10
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.24
P(V2=1 | X=1) = 0.77
0.77 * (0.54 - 0.10)+ 0.24 * (0.95 - 0.55)= 0.23
0.23 > 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 10%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 95%. For people who do not drink coffee, the probability of alarm set by wife is 24%. For people who drink coffee, the probability of alarm set by wife is 77%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.10
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.24
P(V2=1 | X=1) = 0.77
0.24 * (0.95 - 0.55) + 0.77 * (0.54 - 0.10) = 0.44
0.44 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 81%. For people who do not drink coffee, the probability of ringing alarm is 21%. For people who drink coffee, the probability of ringing alarm is 86%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.86
0.81*0.86 - 0.19*0.21 = 0.74
0.74 > 0",mediation,alarm,1,marginal,P(Y)
220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 81%. The probability of not drinking coffee and ringing alarm is 4%. The probability of drinking coffee and ringing alarm is 70%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.70
0.70/0.81 - 0.04/0.19 = 0.65
0.65 > 0",mediation,alarm,1,correlation,P(Y | X)
222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 41%. For people who drink coffee, the probability of ringing alarm is 52%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.52
0.52 - 0.41 = 0.12
0.12 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 7%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 42%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 86%. For people who do not drink coffee, the probability of alarm set by wife is 72%. For people who drink coffee, the probability of alarm set by wife is 24%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.07
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.72
P(V2=1 | X=1) = 0.24
0.72 * (0.86 - 0.42) + 0.24 * (0.54 - 0.07) = 0.33
0.33 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 7%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 42%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 86%. For people who do not drink coffee, the probability of alarm set by wife is 72%. For people who drink coffee, the probability of alarm set by wife is 24%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.07
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.72
P(V2=1 | X=1) = 0.24
0.72 * (0.86 - 0.42) + 0.24 * (0.54 - 0.07) = 0.33
0.33 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 46%. For people who drink coffee, the probability of ringing alarm is 77%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.77
0.77 - 0.46 = 0.30
0.30 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 6%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 99%. For people who do not drink coffee, the probability of alarm set by wife is 94%. For people who drink coffee, the probability of alarm set by wife is 50%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.99
P(V2=1 | X=0) = 0.94
P(V2=1 | X=1) = 0.50
0.50 * (0.49 - 0.06)+ 0.94 * (0.99 - 0.54)= -0.19
-0.19 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 6%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 99%. For people who do not drink coffee, the probability of alarm set by wife is 94%. For people who drink coffee, the probability of alarm set by wife is 50%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.99
P(V2=1 | X=0) = 0.94
P(V2=1 | X=1) = 0.50
0.94 * (0.99 - 0.54) + 0.50 * (0.49 - 0.06) = 0.50
0.50 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 6%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 99%. For people who do not drink coffee, the probability of alarm set by wife is 94%. For people who drink coffee, the probability of alarm set by wife is 50%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.99
P(V2=1 | X=0) = 0.94
P(V2=1 | X=1) = 0.50
0.94 * (0.99 - 0.54) + 0.50 * (0.49 - 0.06) = 0.50
0.50 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 11%. The probability of drinking coffee and ringing alarm is 59%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.59
0.59/0.77 - 0.11/0.23 = 0.30
0.30 > 0",mediation,alarm,1,correlation,P(Y | X)
251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how drinking coffee correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 39%. For people who drink coffee, the probability of ringing alarm is 59%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.59
0.59 - 0.39 = 0.20
0.20 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 13%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 58%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 46%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 89%. For people who do not drink coffee, the probability of alarm set by wife is 57%. For people who drink coffee, the probability of alarm set by wife is 31%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.13
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.89
P(V2=1 | X=0) = 0.57
P(V2=1 | X=1) = 0.31
0.57 * (0.89 - 0.46) + 0.31 * (0.58 - 0.13) = 0.32
0.32 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 10%. For people who drink coffee, the probability of ringing alarm is 69%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.69
0.69 - 0.10 = 0.59
0.59 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 0%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 45%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 41%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 89%. For people who do not drink coffee, the probability of alarm set by wife is 22%. For people who drink coffee, the probability of alarm set by wife is 58%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.00
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.41
P(Y=1 | X=1, V2=1) = 0.89
P(V2=1 | X=0) = 0.22
P(V2=1 | X=1) = 0.58
0.22 * (0.89 - 0.41) + 0.58 * (0.45 - 0.00) = 0.42
0.42 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. For people who do not drink coffee, the probability of ringing alarm is 10%. For people who drink coffee, the probability of ringing alarm is 69%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.69
0.77*0.69 - 0.23*0.10 = 0.55
0.55 > 0",mediation,alarm,1,marginal,P(Y)
277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 2%. The probability of drinking coffee and ringing alarm is 53%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.53
0.53/0.77 - 0.02/0.23 = 0.59
0.59 > 0",mediation,alarm,1,correlation,P(Y | X)
280,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 38%. For people who drink coffee, the probability of ringing alarm is 60%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.60
0.60 - 0.38 = 0.22
0.22 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 0%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 48%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 36%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 80%. For people who do not drink coffee, the probability of alarm set by wife is 79%. For people who drink coffee, the probability of alarm set by wife is 54%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.00
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.36
P(Y=1 | X=1, V2=1) = 0.80
P(V2=1 | X=0) = 0.79
P(V2=1 | X=1) = 0.54
0.54 * (0.48 - 0.00)+ 0.79 * (0.80 - 0.36)= -0.12
-0.12 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 0%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 48%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 36%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 80%. For people who do not drink coffee, the probability of alarm set by wife is 79%. For people who drink coffee, the probability of alarm set by wife is 54%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.00
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.36
P(Y=1 | X=1, V2=1) = 0.80
P(V2=1 | X=0) = 0.79
P(V2=1 | X=1) = 0.54
0.79 * (0.80 - 0.36) + 0.54 * (0.48 - 0.00) = 0.33
0.33 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 70%. For people who do not drink coffee, the probability of ringing alarm is 38%. For people who drink coffee, the probability of ringing alarm is 60%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.70
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.60
0.70*0.60 - 0.30*0.38 = 0.53
0.53 > 0",mediation,alarm,1,marginal,P(Y)
290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 70%. The probability of not drinking coffee and ringing alarm is 11%. The probability of drinking coffee and ringing alarm is 42%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.70
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.42
0.42/0.70 - 0.11/0.30 = 0.22
0.22 > 0",mediation,alarm,1,correlation,P(Y | X)
291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 70%. The probability of not drinking coffee and ringing alarm is 11%. The probability of drinking coffee and ringing alarm is 42%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.70
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.42
0.42/0.70 - 0.11/0.30 = 0.22
0.22 > 0",mediation,alarm,1,correlation,P(Y | X)
293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how drinking coffee correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 40%. For people who drink coffee, the probability of ringing alarm is 80%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.80
0.80 - 0.40 = 0.40
0.40 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 40%. For people who drink coffee, the probability of ringing alarm is 80%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.80
0.80 - 0.40 = 0.40
0.40 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 1%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 44%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 90%. For people who do not drink coffee, the probability of alarm set by wife is 82%. For people who drink coffee, the probability of alarm set by wife is 78%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.01
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.44
P(Y=1 | X=1, V2=1) = 0.90
P(V2=1 | X=0) = 0.82
P(V2=1 | X=1) = 0.78
0.78 * (0.49 - 0.01)+ 0.82 * (0.90 - 0.44)= -0.02
-0.02 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
303,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. For people who do not drink coffee, the probability of ringing alarm is 40%. For people who drink coffee, the probability of ringing alarm is 80%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.80
0.77*0.80 - 0.23*0.40 = 0.71
0.71 > 0",mediation,alarm,1,marginal,P(Y)
304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 9%. The probability of drinking coffee and ringing alarm is 62%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.62
0.62/0.77 - 0.09/0.23 = 0.40
0.40 > 0",mediation,alarm,1,correlation,P(Y | X)
305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 9%. The probability of drinking coffee and ringing alarm is 62%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.62
0.62/0.77 - 0.09/0.23 = 0.40
0.40 > 0",mediation,alarm,1,correlation,P(Y | X)
308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 44%. For people who drink coffee, the probability of ringing alarm is 52%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.52
0.52 - 0.44 = 0.09
0.09 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
315,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 8%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 39%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 86%. For people who do not drink coffee, the probability of alarm set by wife is 85%. For people who drink coffee, the probability of alarm set by wife is 29%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.08
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.85
P(V2=1 | X=1) = 0.29
0.85 * (0.86 - 0.39) + 0.29 * (0.50 - 0.08) = 0.35
0.35 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
317,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 61%. For people who do not drink coffee, the probability of ringing alarm is 44%. For people who drink coffee, the probability of ringing alarm is 52%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.52
0.61*0.52 - 0.39*0.44 = 0.50
0.50 > 0",mediation,alarm,1,marginal,P(Y)
319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 61%. The probability of not drinking coffee and ringing alarm is 17%. The probability of drinking coffee and ringing alarm is 32%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.61
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.32
0.32/0.61 - 0.17/0.39 = 0.09
0.09 > 0",mediation,alarm,1,correlation,P(Y | X)
320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
324,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 22%. For people who drink coffee, the probability of ringing alarm is 80%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.80
0.80 - 0.22 = 0.58
0.58 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 1%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 43%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 47%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 92%. For people who do not drink coffee, the probability of alarm set by wife is 50%. For people who drink coffee, the probability of alarm set by wife is 74%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.01
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.92
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.74
0.74 * (0.43 - 0.01)+ 0.50 * (0.92 - 0.47)= 0.10
0.10 > 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 1%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 43%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 47%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 92%. For people who do not drink coffee, the probability of alarm set by wife is 50%. For people who drink coffee, the probability of alarm set by wife is 74%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.01
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.92
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.74
0.50 * (0.92 - 0.47) + 0.74 * (0.43 - 0.01) = 0.47
0.47 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 24%. For people who drink coffee, the probability of ringing alarm is 44%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.44
0.44 - 0.24 = 0.20
0.20 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 24%. For people who drink coffee, the probability of ringing alarm is 44%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.44
0.44 - 0.24 = 0.20
0.20 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 24%. For people who drink coffee, the probability of ringing alarm is 44%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.44
0.44 - 0.24 = 0.20
0.20 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
340,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 9%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 59%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 43%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 96%. For people who do not drink coffee, the probability of alarm set by wife is 30%. For people who drink coffee, the probability of alarm set by wife is 3%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.96
P(V2=1 | X=0) = 0.30
P(V2=1 | X=1) = 0.03
0.03 * (0.59 - 0.09)+ 0.30 * (0.96 - 0.43)= -0.13
-0.13 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 9%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 59%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 43%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 96%. For people who do not drink coffee, the probability of alarm set by wife is 30%. For people who drink coffee, the probability of alarm set by wife is 3%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.96
P(V2=1 | X=0) = 0.30
P(V2=1 | X=1) = 0.03
0.30 * (0.96 - 0.43) + 0.03 * (0.59 - 0.09) = 0.35
0.35 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 6%. The probability of drinking coffee and ringing alarm is 34%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.34
0.34/0.77 - 0.06/0.23 = 0.20
0.20 > 0",mediation,alarm,1,correlation,P(Y | X)
347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 6%. The probability of drinking coffee and ringing alarm is 34%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.34
0.34/0.77 - 0.06/0.23 = 0.20
0.20 > 0",mediation,alarm,1,correlation,P(Y | X)
348,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 53%. For people who drink coffee, the probability of ringing alarm is 82%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.82
0.82 - 0.53 = 0.29
0.29 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 9%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 52%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 95%. For people who do not drink coffee, the probability of alarm set by wife is 98%. For people who drink coffee, the probability of alarm set by wife is 70%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.98
P(V2=1 | X=1) = 0.70
0.70 * (0.54 - 0.09)+ 0.98 * (0.95 - 0.52)= -0.13
-0.13 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 9%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 54%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 52%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 95%. For people who do not drink coffee, the probability of alarm set by wife is 98%. For people who drink coffee, the probability of alarm set by wife is 70%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.98
P(V2=1 | X=1) = 0.70
0.98 * (0.95 - 0.52) + 0.70 * (0.54 - 0.09) = 0.41
0.41 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
364,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 36%. For people who drink coffee, the probability of ringing alarm is 55%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.55
0.55 - 0.36 = 0.18
0.18 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
365,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 36%. For people who drink coffee, the probability of ringing alarm is 55%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.55
0.55 - 0.36 = 0.18
0.18 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 36%. For people who drink coffee, the probability of ringing alarm is 55%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.55
0.55 - 0.36 = 0.18
0.18 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
369,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 3%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 53%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 39%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 84%. For people who do not drink coffee, the probability of alarm set by wife is 67%. For people who drink coffee, the probability of alarm set by wife is 36%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.03
P(Y=1 | X=0, V2=1) = 0.53
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.84
P(V2=1 | X=0) = 0.67
P(V2=1 | X=1) = 0.36
0.36 * (0.53 - 0.03)+ 0.67 * (0.84 - 0.39)= -0.15
-0.15 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 73%. The probability of not drinking coffee and ringing alarm is 10%. The probability of drinking coffee and ringing alarm is 40%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.40
0.40/0.73 - 0.10/0.27 = 0.18
0.18 > 0",mediation,alarm,1,correlation,P(Y | X)
375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 73%. The probability of not drinking coffee and ringing alarm is 10%. The probability of drinking coffee and ringing alarm is 40%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.40
0.40/0.73 - 0.10/0.27 = 0.18
0.18 > 0",mediation,alarm,1,correlation,P(Y | X)
376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how drinking coffee correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 41%. For people who drink coffee, the probability of ringing alarm is 75%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.75
0.75 - 0.41 = 0.34
0.34 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 6%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 49%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 92%. For people who do not drink coffee, the probability of alarm set by wife is 82%. For people who drink coffee, the probability of alarm set by wife is 61%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.92
P(V2=1 | X=0) = 0.82
P(V2=1 | X=1) = 0.61
0.61 * (0.49 - 0.06)+ 0.82 * (0.92 - 0.49)= -0.09
-0.09 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
392,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 32%. For people who drink coffee, the probability of ringing alarm is 45%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.45
0.45 - 0.32 = 0.14
0.14 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 32%. For people who drink coffee, the probability of ringing alarm is 45%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.45
0.45 - 0.32 = 0.14
0.14 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 32%. For people who drink coffee, the probability of ringing alarm is 45%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.45
0.45 - 0.32 = 0.14
0.14 > 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 4%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 39%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 88%. For people who do not drink coffee, the probability of alarm set by wife is 60%. For people who drink coffee, the probability of alarm set by wife is 13%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.04
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.88
P(V2=1 | X=0) = 0.60
P(V2=1 | X=1) = 0.13
0.13 * (0.50 - 0.04)+ 0.60 * (0.88 - 0.39)= -0.22
-0.22 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 4%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 39%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 88%. For people who do not drink coffee, the probability of alarm set by wife is 60%. For people who drink coffee, the probability of alarm set by wife is 13%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.04
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.88
P(V2=1 | X=0) = 0.60
P(V2=1 | X=1) = 0.13
0.60 * (0.88 - 0.39) + 0.13 * (0.50 - 0.04) = 0.37
0.37 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 4%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 39%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 88%. For people who do not drink coffee, the probability of alarm set by wife is 60%. For people who drink coffee, the probability of alarm set by wife is 13%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.04
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.88
P(V2=1 | X=0) = 0.60
P(V2=1 | X=1) = 0.13
0.60 * (0.88 - 0.39) + 0.13 * (0.50 - 0.04) = 0.37
0.37 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
400,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. For people who do not drink coffee, the probability of ringing alarm is 32%. For people who drink coffee, the probability of ringing alarm is 45%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.45
0.77*0.45 - 0.23*0.32 = 0.42
0.42 > 0",mediation,alarm,1,marginal,P(Y)
402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 7%. The probability of drinking coffee and ringing alarm is 35%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.35
0.35/0.77 - 0.07/0.23 = 0.14
0.14 > 0",mediation,alarm,1,correlation,P(Y | X)
403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 77%. The probability of not drinking coffee and ringing alarm is 7%. The probability of drinking coffee and ringing alarm is 35%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.35
0.35/0.77 - 0.07/0.23 = 0.14
0.14 > 0",mediation,alarm,1,correlation,P(Y | X)
407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee, the probability of ringing alarm is 33%. For people who drink coffee, the probability of ringing alarm is 90%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.90
0.90 - 0.33 = 0.57
0.57 > 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 3%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 97%. For people who do not drink coffee, the probability of alarm set by wife is 63%. For people who drink coffee, the probability of alarm set by wife is 84%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.03
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.97
P(V2=1 | X=0) = 0.63
P(V2=1 | X=1) = 0.84
0.84 * (0.50 - 0.03)+ 0.63 * (0.97 - 0.50)= 0.10
0.10 > 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
411,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 3%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 97%. For people who do not drink coffee, the probability of alarm set by wife is 63%. For people who drink coffee, the probability of alarm set by wife is 84%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.03
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.97
P(V2=1 | X=0) = 0.63
P(V2=1 | X=1) = 0.84
0.84 * (0.50 - 0.03)+ 0.63 * (0.97 - 0.50)= 0.10
0.10 > 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not drink coffee and wives that don't set the alarm, the probability of ringing alarm is 3%. For people who do not drink coffee and wives that set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that don't set the alarm, the probability of ringing alarm is 50%. For people who drink coffee and wives that set the alarm, the probability of ringing alarm is 97%. For people who do not drink coffee, the probability of alarm set by wife is 63%. For people who drink coffee, the probability of alarm set by wife is 84%.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.03
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.97
P(V2=1 | X=0) = 0.63
P(V2=1 | X=1) = 0.84
0.63 * (0.97 - 0.50) + 0.84 * (0.50 - 0.03) = 0.47
0.47 > 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of drinking coffee is 75%. For people who do not drink coffee, the probability of ringing alarm is 33%. For people who drink coffee, the probability of ringing alarm is 90%.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.75
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.90
0.75*0.90 - 0.25*0.33 = 0.76
0.76 > 0",mediation,alarm,1,marginal,P(Y)
418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how drinking coffee correlates with alarm clock case by case according to wife. Method 2: We look directly at how drinking coffee correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 37%. For people who like spicy food, the probability of dark room is 75%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.75
0.75 - 0.37 = 0.38
0.38 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
424,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 68%. For people who do not like spicy food, the probability of dark room is 37%. For people who like spicy food, the probability of dark room is 75%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.68
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.75
0.68*0.75 - 0.32*0.37 = 0.62
0.62 > 0",fork,candle,1,marginal,P(Y)
427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 68%. The probability of not liking spicy food and dark room is 12%. The probability of liking spicy food and dark room is 51%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.68
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.51
0.51/0.68 - 0.12/0.32 = 0.38
0.38 > 0",fork,candle,1,correlation,P(Y | X)
430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 74%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.74
0.74 - 0.38 = 0.36
0.36 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 74%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.74
0.74 - 0.38 = 0.36
0.36 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
432,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 74%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.74
0.74 - 0.38 = 0.36
0.36 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 74%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.74
0.74 - 0.38 = 0.36
0.36 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 44%. For people who like spicy food, the probability of dark room is 75%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.75
0.75 - 0.44 = 0.31
0.31 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 44%. For people who like spicy food, the probability of dark room is 75%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.75
0.75 - 0.44 = 0.31
0.31 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 44%. For people who like spicy food, the probability of dark room is 75%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.75
0.75 - 0.44 = 0.31
0.31 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 46%. The probability of not liking spicy food and dark room is 24%. The probability of liking spicy food and dark room is 34%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.34
0.34/0.46 - 0.24/0.54 = 0.31
0.31 > 0",fork,candle,1,correlation,P(Y | X)
448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 55%. For people who like spicy food, the probability of dark room is 89%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.89
0.89 - 0.55 = 0.35
0.35 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 55%. For people who like spicy food, the probability of dark room is 89%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.89
0.89 - 0.55 = 0.35
0.35 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 56%. For people who do not like spicy food, the probability of dark room is 55%. For people who like spicy food, the probability of dark room is 89%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.89
0.56*0.89 - 0.44*0.55 = 0.74
0.74 > 0",fork,candle,1,marginal,P(Y)
455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 56%. For people who do not like spicy food, the probability of dark room is 55%. For people who like spicy food, the probability of dark room is 89%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.89
0.56*0.89 - 0.44*0.55 = 0.74
0.74 > 0",fork,candle,1,marginal,P(Y)
458,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 39%. For people who like spicy food, the probability of dark room is 72%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.72
0.72 - 0.39 = 0.33
0.33 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
466,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 43%. The probability of not liking spicy food and dark room is 22%. The probability of liking spicy food and dark room is 31%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.31
0.31/0.43 - 0.22/0.57 = 0.33
0.33 > 0",fork,candle,1,correlation,P(Y | X)
467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 43%. The probability of not liking spicy food and dark room is 22%. The probability of liking spicy food and dark room is 31%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.31
0.31/0.43 - 0.22/0.57 = 0.33
0.33 > 0",fork,candle,1,correlation,P(Y | X)
468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 31%. For people who like spicy food, the probability of dark room is 66%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.66
0.66 - 0.31 = 0.34
0.34 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
473,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 31%. For people who like spicy food, the probability of dark room is 66%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.66
0.66 - 0.31 = 0.34
0.34 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 45%. For people who do not like spicy food, the probability of dark room is 31%. For people who like spicy food, the probability of dark room is 66%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.66
0.45*0.66 - 0.55*0.31 = 0.47
0.47 > 0",fork,candle,1,marginal,P(Y)
478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 29%. For people who like spicy food, the probability of dark room is 64%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.64
0.64 - 0.29 = 0.35
0.35 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 29%. For people who like spicy food, the probability of dark room is 64%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.64
0.64 - 0.29 = 0.35
0.35 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 29%. For people who like spicy food, the probability of dark room is 64%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.64
0.64 - 0.29 = 0.35
0.35 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 25%. For people who do not like spicy food, the probability of dark room is 29%. For people who like spicy food, the probability of dark room is 64%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.25
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.64
0.25*0.64 - 0.75*0.29 = 0.38
0.38 > 0",fork,candle,1,marginal,P(Y)
486,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 25%. The probability of not liking spicy food and dark room is 22%. The probability of liking spicy food and dark room is 16%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.16
0.16/0.25 - 0.22/0.75 = 0.35
0.35 > 0",fork,candle,1,correlation,P(Y | X)
488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 30%. For people who like spicy food, the probability of dark room is 61%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.61
0.61 - 0.30 = 0.31
0.31 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
492,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 30%. For people who like spicy food, the probability of dark room is 61%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.61
0.61 - 0.30 = 0.31
0.31 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
496,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 31%. The probability of not liking spicy food and dark room is 21%. The probability of liking spicy food and dark room is 19%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.19
0.19/0.31 - 0.21/0.69 = 0.31
0.31 > 0",fork,candle,1,correlation,P(Y | X)
497,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 31%. The probability of not liking spicy food and dark room is 21%. The probability of liking spicy food and dark room is 19%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.19
0.19/0.31 - 0.21/0.69 = 0.31
0.31 > 0",fork,candle,1,correlation,P(Y | X)
501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 72%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.72
0.72 - 0.38 = 0.34
0.34 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 72%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.72
0.72 - 0.38 = 0.34
0.34 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
505,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 29%. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 72%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.72
0.29*0.72 - 0.71*0.38 = 0.47
0.47 > 0",fork,candle,1,marginal,P(Y)
507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 29%. The probability of not liking spicy food and dark room is 27%. The probability of liking spicy food and dark room is 21%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.29
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.21
0.21/0.29 - 0.27/0.71 = 0.34
0.34 > 0",fork,candle,1,correlation,P(Y | X)
510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 48%. For people who like spicy food, the probability of dark room is 79%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.79
0.79 - 0.48 = 0.32
0.32 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 48%. For people who like spicy food, the probability of dark room is 79%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.79
0.79 - 0.48 = 0.32
0.32 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
512,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 48%. For people who like spicy food, the probability of dark room is 79%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.79
0.79 - 0.48 = 0.32
0.32 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 50%. The probability of not liking spicy food and dark room is 24%. The probability of liking spicy food and dark room is 40%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.40
0.40/0.50 - 0.24/0.50 = 0.32
0.32 > 0",fork,candle,1,correlation,P(Y | X)
519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 51%. For people who like spicy food, the probability of dark room is 93%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.93
0.93 - 0.51 = 0.42
0.42 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 51%. For people who like spicy food, the probability of dark room is 93%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.93
0.93 - 0.51 = 0.42
0.42 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 51%. For people who like spicy food, the probability of dark room is 93%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.93
0.93 - 0.51 = 0.42
0.42 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 43%. For people who do not like spicy food, the probability of dark room is 51%. For people who like spicy food, the probability of dark room is 93%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.93
0.43*0.93 - 0.57*0.51 = 0.69
0.69 > 0",fork,candle,1,marginal,P(Y)
525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 43%. For people who do not like spicy food, the probability of dark room is 51%. For people who like spicy food, the probability of dark room is 93%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.93
0.43*0.93 - 0.57*0.51 = 0.69
0.69 > 0",fork,candle,1,marginal,P(Y)
532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 48%. For people who like spicy food, the probability of dark room is 78%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.78
0.78 - 0.48 = 0.31
0.31 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
533,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 48%. For people who like spicy food, the probability of dark room is 78%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.78
0.78 - 0.48 = 0.31
0.31 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 22%. For people who do not like spicy food, the probability of dark room is 48%. For people who like spicy food, the probability of dark room is 78%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.78
0.22*0.78 - 0.78*0.48 = 0.54
0.54 > 0",fork,candle,1,marginal,P(Y)
540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 73%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.73
0.73 - 0.38 = 0.35
0.35 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 69%. For people who do not like spicy food, the probability of dark room is 38%. For people who like spicy food, the probability of dark room is 73%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.69
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.73
0.69*0.73 - 0.31*0.38 = 0.62
0.62 > 0",fork,candle,1,marginal,P(Y)
548,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 30%. For people who like spicy food, the probability of dark room is 63%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.63
0.63 - 0.30 = 0.33
0.33 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 65%. The probability of not liking spicy food and dark room is 10%. The probability of liking spicy food and dark room is 41%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.41
0.41/0.65 - 0.10/0.35 = 0.33
0.33 > 0",fork,candle,1,correlation,P(Y | X)
557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 65%. The probability of not liking spicy food and dark room is 10%. The probability of liking spicy food and dark room is 41%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.41
0.41/0.65 - 0.10/0.35 = 0.33
0.33 > 0",fork,candle,1,correlation,P(Y | X)
563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 34%. For people who like spicy food, the probability of dark room is 67%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.67
0.67 - 0.34 = 0.34
0.34 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 54%. For people who do not like spicy food, the probability of dark room is 34%. For people who like spicy food, the probability of dark room is 67%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.67
0.54*0.67 - 0.46*0.34 = 0.52
0.52 > 0",fork,candle,1,marginal,P(Y)
567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 54%. The probability of not liking spicy food and dark room is 16%. The probability of liking spicy food and dark room is 36%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.36
0.36/0.54 - 0.16/0.46 = 0.34
0.34 > 0",fork,candle,1,correlation,P(Y | X)
569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 23%. For people who like spicy food, the probability of dark room is 58%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.58
0.58 - 0.23 = 0.35
0.35 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 23%. For people who do not like spicy food, the probability of dark room is 23%. For people who like spicy food, the probability of dark room is 58%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.58
0.23*0.58 - 0.77*0.23 = 0.31
0.31 > 0",fork,candle,1,marginal,P(Y)
575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 23%. For people who do not like spicy food, the probability of dark room is 23%. For people who like spicy food, the probability of dark room is 58%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.58
0.23*0.58 - 0.77*0.23 = 0.31
0.31 > 0",fork,candle,1,marginal,P(Y)
578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 37%. For people who like spicy food, the probability of dark room is 70%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.70
0.70 - 0.37 = 0.33
0.33 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 43%. For people who like spicy food, the probability of dark room is 74%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.74
0.74 - 0.43 = 0.31
0.31 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 53%. For people who do not like spicy food, the probability of dark room is 43%. For people who like spicy food, the probability of dark room is 74%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.74
0.53*0.74 - 0.47*0.43 = 0.59
0.59 > 0",fork,candle,1,marginal,P(Y)
595,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 53%. For people who do not like spicy food, the probability of dark room is 43%. For people who like spicy food, the probability of dark room is 74%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.74
0.53*0.74 - 0.47*0.43 = 0.59
0.59 > 0",fork,candle,1,marginal,P(Y)
598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 35%. The probability of not liking spicy food and dark room is 23%. The probability of liking spicy food and dark room is 24%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.24
0.24/0.35 - 0.23/0.65 = 0.34
0.34 > 0",fork,candle,1,correlation,P(Y | X)
607,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 35%. The probability of not liking spicy food and dark room is 23%. The probability of liking spicy food and dark room is 24%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.24
0.24/0.35 - 0.23/0.65 = 0.34
0.34 > 0",fork,candle,1,correlation,P(Y | X)
609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 41%. For people who like spicy food, the probability of dark room is 74%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.74
0.74 - 0.41 = 0.32
0.32 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 41%. For people who like spicy food, the probability of dark room is 74%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.74
0.74 - 0.41 = 0.32
0.32 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 44%. The probability of not liking spicy food and dark room is 23%. The probability of liking spicy food and dark room is 33%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.33
0.33/0.44 - 0.23/0.56 = 0.32
0.32 > 0",fork,candle,1,correlation,P(Y | X)
623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 48%. For people who like spicy food, the probability of dark room is 80%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.80
0.80 - 0.48 = 0.32
0.32 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 43%. For people who do not like spicy food, the probability of dark room is 48%. For people who like spicy food, the probability of dark room is 80%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.80
0.43*0.80 - 0.57*0.48 = 0.61
0.61 > 0",fork,candle,1,marginal,P(Y)
630,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 41%. For people who like spicy food, the probability of dark room is 74%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.74
0.74 - 0.41 = 0.33
0.33 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 41%. For people who like spicy food, the probability of dark room is 74%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.74
0.74 - 0.41 = 0.33
0.33 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 38%. For people who do not like spicy food, the probability of dark room is 41%. For people who like spicy food, the probability of dark room is 74%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.38
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.74
0.38*0.74 - 0.62*0.41 = 0.53
0.53 > 0",fork,candle,1,marginal,P(Y)
636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 38%. The probability of not liking spicy food and dark room is 25%. The probability of liking spicy food and dark room is 28%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.28
0.28/0.38 - 0.25/0.62 = 0.33
0.33 > 0",fork,candle,1,correlation,P(Y | X)
642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 47%. For people who like spicy food, the probability of dark room is 82%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.82
0.82 - 0.47 = 0.35
0.35 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 63%. For people who do not like spicy food, the probability of dark room is 47%. For people who like spicy food, the probability of dark room is 82%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.82
0.63*0.82 - 0.37*0.47 = 0.69
0.69 > 0",fork,candle,1,marginal,P(Y)
648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 56%. For people who like spicy food, the probability of dark room is 90%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.90
0.90 - 0.56 = 0.34
0.34 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 56%. For people who like spicy food, the probability of dark room is 90%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.90
0.90 - 0.56 = 0.34
0.34 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 31%. The probability of not liking spicy food and dark room is 39%. The probability of liking spicy food and dark room is 28%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.28
0.28/0.31 - 0.39/0.69 = 0.34
0.34 > 0",fork,candle,1,correlation,P(Y | X)
658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
661,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 46%. For people who like spicy food, the probability of dark room is 80%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.80
0.80 - 0.46 = 0.33
0.33 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 41%. For people who like spicy food, the probability of dark room is 73%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.73
0.73 - 0.41 = 0.32
0.32 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 35%. For people who like spicy food, the probability of dark room is 69%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.69
0.69 - 0.35 = 0.34
0.34 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
681,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 35%. For people who like spicy food, the probability of dark room is 69%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.69
0.69 - 0.35 = 0.34
0.34 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 64%. The probability of not liking spicy food and dark room is 13%. The probability of liking spicy food and dark room is 44%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.44
0.44/0.64 - 0.13/0.36 = 0.34
0.34 > 0",fork,candle,1,correlation,P(Y | X)
688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
693,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 39%. For people who like spicy food, the probability of dark room is 81%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.81
0.81 - 0.39 = 0.42
0.42 > 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 25%. For people who do not like spicy food, the probability of dark room is 39%. For people who like spicy food, the probability of dark room is 81%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.25
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.81
0.25*0.81 - 0.75*0.39 = 0.50
0.50 > 0",fork,candle,1,marginal,P(Y)
696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 25%. The probability of not liking spicy food and dark room is 29%. The probability of liking spicy food and dark room is 20%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.20
0.20/0.25 - 0.29/0.75 = 0.42
0.42 > 0",fork,candle,1,correlation,P(Y | X)
700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 55%. For people who like spicy food, the probability of dark room is 86%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.86
0.86 - 0.55 = 0.31
0.31 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 26%. The probability of not liking spicy food and dark room is 41%. The probability of liking spicy food and dark room is 22%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.22
0.22/0.26 - 0.41/0.74 = 0.31
0.31 > 0",fork,candle,1,correlation,P(Y | X)
707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 26%. The probability of not liking spicy food and dark room is 41%. The probability of liking spicy food and dark room is 22%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.22
0.22/0.26 - 0.41/0.74 = 0.31
0.31 > 0",fork,candle,1,correlation,P(Y | X)
708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how liking spicy food correlates with room case by case according to the candle. Method 2: We look directly at how liking spicy food correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. For people who do not like spicy food, the probability of dark room is 33%. For people who like spicy food, the probability of dark room is 68%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.68
0.68 - 0.33 = 0.35
0.35 > 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 53%. For people who do not like spicy food, the probability of dark room is 33%. For people who like spicy food, the probability of dark room is 68%.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.68
0.53*0.68 - 0.47*0.33 = 0.52
0.52 > 0",fork,candle,1,marginal,P(Y)
715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 53%. For people who do not like spicy food, the probability of dark room is 33%. For people who like spicy food, the probability of dark room is 68%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.68
0.53*0.68 - 0.47*0.33 = 0.52
0.52 > 0",fork,candle,1,marginal,P(Y)
717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. The overall probability of liking spicy food is 53%. The probability of not liking spicy food and dark room is 15%. The probability of liking spicy food and dark room is 36%.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.36
0.36/0.53 - 0.15/0.47 = 0.35
0.35 > 0",fork,candle,1,correlation,P(Y | X)
719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how liking spicy food correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 20%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 51%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 55%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 88%. For people who have not visited England, the probability of director signing the termination letter is 37%. For people who have visited England, the probability of director signing the termination letter is 46%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.20
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0) = 0.37
P(V3=1 | X=1) = 0.46
0.46 * (0.88 - 0.55) + 0.37 * (0.51 - 0.20) = 0.36
0.36 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
724,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 86%. For people who have not visited England, the probability of employee being fired is 31%. For people who have visited England, the probability of employee being fired is 70%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.70
0.86*0.70 - 0.14*0.31 = 0.65
0.65 > 0",diamondcut,firing_employee,1,marginal,P(Y)
726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 86%. The probability of not having visited England and employee being fired is 4%. The probability of having visited England and employee being fired is 60%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.86
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.60
0.60/0.86 - 0.04/0.14 = 0.39
0.39 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 16%. For CEOs who fire employees and have visited England, the probability of employee being fired is 53%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 35%. For CEOs who fire employees and have visited England, the probability of employee being fired is 71%. The overall probability of CEO's decision to fire the employee is 11%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.16
P(Y=1 | V1=0, X=1) = 0.53
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.71
P(V1=1) = 0.11
0.89 * (0.53 - 0.16) 0.11 * (0.71 - 0.35) = 0.37
0.37 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
733,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 9%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 54%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 46%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 90%. For people who have not visited England, the probability of director signing the termination letter is 17%. For people who have visited England, the probability of director signing the termination letter is 27%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.46
P(Y=1 | X=1, V3=1) = 0.90
P(V3=1 | X=0) = 0.17
P(V3=1 | X=1) = 0.27
0.27 * (0.90 - 0.46) + 0.17 * (0.54 - 0.09) = 0.37
0.37 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
735,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 40%. For people who have not visited England, the probability of employee being fired is 16%. For people who have visited England, the probability of employee being fired is 58%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.58
0.40*0.58 - 0.60*0.16 = 0.33
0.33 > 0",diamondcut,firing_employee,1,marginal,P(Y)
736,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 40%. The probability of not having visited England and employee being fired is 10%. The probability of having visited England and employee being fired is 23%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.23
0.23/0.40 - 0.10/0.60 = 0.42
0.42 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 40%. The probability of not having visited England and employee being fired is 10%. The probability of having visited England and employee being fired is 23%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.23
0.23/0.40 - 0.10/0.60 = 0.42
0.42 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
742,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 13%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 51%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 46%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 83%. For people who have not visited England, the probability of director signing the termination letter is 53%. For people who have visited England, the probability of director signing the termination letter is 60%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.13
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.46
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0) = 0.53
P(V3=1 | X=1) = 0.60
0.60 * (0.83 - 0.46) + 0.53 * (0.51 - 0.13) = 0.33
0.33 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 23%. For CEOs who fire employees and have visited England, the probability of employee being fired is 57%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 43%. For CEOs who fire employees and have visited England, the probability of employee being fired is 79%. The overall probability of CEO's decision to fire the employee is 17%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.23
P(Y=1 | V1=0, X=1) = 0.57
P(Y=1 | V1=1, X=0) = 0.43
P(Y=1 | V1=1, X=1) = 0.79
P(V1=1) = 0.17
0.83 * (0.57 - 0.23) 0.17 * (0.79 - 0.43) = 0.35
0.35 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 23%. For CEOs who fire employees and have visited England, the probability of employee being fired is 57%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 43%. For CEOs who fire employees and have visited England, the probability of employee being fired is 79%. The overall probability of CEO's decision to fire the employee is 17%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.23
P(Y=1 | V1=0, X=1) = 0.57
P(Y=1 | V1=1, X=0) = 0.43
P(Y=1 | V1=1, X=1) = 0.79
P(V1=1) = 0.17
0.83 * (0.57 - 0.23) 0.17 * (0.79 - 0.43) = 0.35
0.35 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 32%. For people who have not visited England, the probability of employee being fired is 24%. For people who have visited England, the probability of employee being fired is 66%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.66
0.32*0.66 - 0.68*0.24 = 0.37
0.37 > 0",diamondcut,firing_employee,1,marginal,P(Y)
757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 32%. The probability of not having visited England and employee being fired is 16%. The probability of having visited England and employee being fired is 21%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.32
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.21
0.21/0.32 - 0.16/0.68 = 0.42
0.42 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 49%. The probability of not having visited England and employee being fired is 14%. The probability of having visited England and employee being fired is 37%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.37
0.37/0.49 - 0.14/0.51 = 0.48
0.48 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
770,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 16%. For CEOs who fire employees and have visited England, the probability of employee being fired is 52%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 37%. For CEOs who fire employees and have visited England, the probability of employee being fired is 71%. The overall probability of CEO's decision to fire the employee is 13%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.16
P(Y=1 | V1=0, X=1) = 0.52
P(Y=1 | V1=1, X=0) = 0.37
P(Y=1 | V1=1, X=1) = 0.71
P(V1=1) = 0.13
0.87 * (0.52 - 0.16) 0.13 * (0.71 - 0.37) = 0.36
0.36 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 10%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 52%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 47%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 84%. For people who have not visited England, the probability of director signing the termination letter is 19%. For people who have visited England, the probability of director signing the termination letter is 26%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.10
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.26
0.26 * (0.84 - 0.47) + 0.19 * (0.52 - 0.10) = 0.36
0.36 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 30%. For people who have not visited England, the probability of employee being fired is 18%. For people who have visited England, the probability of employee being fired is 57%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.30
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.57
0.30*0.57 - 0.70*0.18 = 0.30
0.30 > 0",diamondcut,firing_employee,1,marginal,P(Y)
775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 30%. For people who have not visited England, the probability of employee being fired is 18%. For people who have visited England, the probability of employee being fired is 57%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.30
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.57
0.30*0.57 - 0.70*0.18 = 0.30
0.30 > 0",diamondcut,firing_employee,1,marginal,P(Y)
777,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 30%. The probability of not having visited England and employee being fired is 13%. The probability of having visited England and employee being fired is 17%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.17
0.17/0.30 - 0.13/0.70 = 0.39
0.39 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
782,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 6%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 44%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 48%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 89%. For people who have not visited England, the probability of director signing the termination letter is 33%. For people who have visited England, the probability of director signing the termination letter is 44%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.89
P(V3=1 | X=0) = 0.33
P(V3=1 | X=1) = 0.44
0.44 * (0.89 - 0.48) + 0.33 * (0.44 - 0.06) = 0.44
0.44 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 43%. For people who have not visited England, the probability of employee being fired is 18%. For people who have visited England, the probability of employee being fired is 66%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.66
0.43*0.66 - 0.57*0.18 = 0.39
0.39 > 0",diamondcut,firing_employee,1,marginal,P(Y)
786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 43%. The probability of not having visited England and employee being fired is 11%. The probability of having visited England and employee being fired is 28%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.28
0.28/0.43 - 0.11/0.57 = 0.47
0.47 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 12%. For CEOs who fire employees and have visited England, the probability of employee being fired is 45%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 47%. For CEOs who fire employees and have visited England, the probability of employee being fired is 88%. The overall probability of CEO's decision to fire the employee is 30%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.12
P(Y=1 | V1=0, X=1) = 0.45
P(Y=1 | V1=1, X=0) = 0.47
P(Y=1 | V1=1, X=1) = 0.88
P(V1=1) = 0.30
0.70 * (0.45 - 0.12) 0.30 * (0.88 - 0.47) = 0.36
0.36 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 9%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 49%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 42%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 90%. For people who have not visited England, the probability of director signing the termination letter is 11%. For people who have visited England, the probability of director signing the termination letter is 91%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.90
P(V3=1 | X=0) = 0.11
P(V3=1 | X=1) = 0.91
0.91 * (0.90 - 0.42) + 0.11 * (0.49 - 0.09) = 0.41
0.41 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 31%. For people who have not visited England, the probability of employee being fired is 31%. For people who have visited England, the probability of employee being fired is 78%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.78
0.31*0.78 - 0.69*0.31 = 0.45
0.45 > 0",diamondcut,firing_employee,1,marginal,P(Y)
806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 31%. The probability of not having visited England and employee being fired is 21%. The probability of having visited England and employee being fired is 24%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.24
0.24/0.31 - 0.21/0.69 = 0.47
0.47 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 31%. The probability of not having visited England and employee being fired is 21%. The probability of having visited England and employee being fired is 24%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.24
0.24/0.31 - 0.21/0.69 = 0.47
0.47 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 22%. For CEOs who fire employees and have visited England, the probability of employee being fired is 61%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 44%. For CEOs who fire employees and have visited England, the probability of employee being fired is 82%. The overall probability of CEO's decision to fire the employee is 22%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.22
P(Y=1 | V1=0, X=1) = 0.61
P(Y=1 | V1=1, X=0) = 0.44
P(Y=1 | V1=1, X=1) = 0.82
P(V1=1) = 0.22
0.78 * (0.61 - 0.22) 0.22 * (0.82 - 0.44) = 0.39
0.39 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 17%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 52%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 56%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 90%. For people who have not visited England, the probability of director signing the termination letter is 23%. For people who have visited England, the probability of director signing the termination letter is 38%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.17
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.90
P(V3=1 | X=0) = 0.23
P(V3=1 | X=1) = 0.38
0.38 * (0.90 - 0.56) + 0.23 * (0.52 - 0.17) = 0.39
0.39 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 40%. For people who have not visited England, the probability of employee being fired is 25%. For people who have visited England, the probability of employee being fired is 69%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.69
0.40*0.69 - 0.60*0.25 = 0.42
0.42 > 0",diamondcut,firing_employee,1,marginal,P(Y)
818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 43%. For CEOs who fire employees and have visited England, the probability of employee being fired is 81%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 63%. For CEOs who fire employees and have visited England, the probability of employee being fired is 98%. The overall probability of CEO's decision to fire the employee is 26%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.43
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.26
0.74 * (0.81 - 0.43) 0.26 * (0.98 - 0.63) = 0.38
0.38 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 43%. For CEOs who fire employees and have visited England, the probability of employee being fired is 81%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 63%. For CEOs who fire employees and have visited England, the probability of employee being fired is 98%. The overall probability of CEO's decision to fire the employee is 26%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.43
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.26
0.74 * (0.81 - 0.43) 0.26 * (0.98 - 0.63) = 0.38
0.38 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 21%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 64%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 63%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 99%. For people who have not visited England, the probability of director signing the termination letter is 60%. For people who have visited England, the probability of director signing the termination letter is 64%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.21
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.99
P(V3=1 | X=0) = 0.60
P(V3=1 | X=1) = 0.64
0.64 * (0.99 - 0.63) + 0.60 * (0.64 - 0.21) = 0.38
0.38 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 61%. For people who have not visited England, the probability of employee being fired is 47%. For people who have visited England, the probability of employee being fired is 86%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.86
0.61*0.86 - 0.39*0.47 = 0.71
0.71 > 0",diamondcut,firing_employee,1,marginal,P(Y)
829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
833,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 15%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 55%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 52%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 87%. For people who have not visited England, the probability of director signing the termination letter is 41%. For people who have visited England, the probability of director signing the termination letter is 43%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.15
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.87
P(V3=1 | X=0) = 0.41
P(V3=1 | X=1) = 0.43
0.43 * (0.87 - 0.52) + 0.41 * (0.55 - 0.15) = 0.35
0.35 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
834,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 61%. For people who have not visited England, the probability of employee being fired is 31%. For people who have visited England, the probability of employee being fired is 67%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.67
0.61*0.67 - 0.39*0.31 = 0.53
0.53 > 0",diamondcut,firing_employee,1,marginal,P(Y)
835,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 61%. For people who have not visited England, the probability of employee being fired is 31%. For people who have visited England, the probability of employee being fired is 67%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.67
0.61*0.67 - 0.39*0.31 = 0.53
0.53 > 0",diamondcut,firing_employee,1,marginal,P(Y)
837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 61%. The probability of not having visited England and employee being fired is 12%. The probability of having visited England and employee being fired is 41%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.61
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.41
0.41/0.61 - 0.12/0.39 = 0.36
0.36 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 22%. For CEOs who fire employees and have visited England, the probability of employee being fired is 59%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 49%. For CEOs who fire employees and have visited England, the probability of employee being fired is 84%. The overall probability of CEO's decision to fire the employee is 13%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.22
P(Y=1 | V1=0, X=1) = 0.59
P(Y=1 | V1=1, X=0) = 0.49
P(Y=1 | V1=1, X=1) = 0.84
P(V1=1) = 0.13
0.87 * (0.59 - 0.22) 0.13 * (0.84 - 0.49) = 0.37
0.37 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
844,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 37%. For people who have not visited England, the probability of employee being fired is 23%. For people who have visited England, the probability of employee being fired is 66%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.66
0.37*0.66 - 0.63*0.23 = 0.39
0.39 > 0",diamondcut,firing_employee,1,marginal,P(Y)
845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 37%. For people who have not visited England, the probability of employee being fired is 23%. For people who have visited England, the probability of employee being fired is 66%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.66
0.37*0.66 - 0.63*0.23 = 0.39
0.39 > 0",diamondcut,firing_employee,1,marginal,P(Y)
848,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 11%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 51%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 45%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 88%. For people who have not visited England, the probability of director signing the termination letter is 35%. For people who have visited England, the probability of director signing the termination letter is 48%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.11
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0) = 0.35
P(V3=1 | X=1) = 0.48
0.48 * (0.88 - 0.45) + 0.35 * (0.51 - 0.11) = 0.36
0.36 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
853,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 11%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 51%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 45%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 88%. For people who have not visited England, the probability of director signing the termination letter is 35%. For people who have visited England, the probability of director signing the termination letter is 48%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.11
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0) = 0.35
P(V3=1 | X=1) = 0.48
0.48 * (0.88 - 0.45) + 0.35 * (0.51 - 0.11) = 0.36
0.36 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 17%. For CEOs who fire employees and have visited England, the probability of employee being fired is 53%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 44%. For CEOs who fire employees and have visited England, the probability of employee being fired is 79%. The overall probability of CEO's decision to fire the employee is 18%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.17
P(Y=1 | V1=0, X=1) = 0.53
P(Y=1 | V1=1, X=0) = 0.44
P(Y=1 | V1=1, X=1) = 0.79
P(V1=1) = 0.18
0.82 * (0.53 - 0.17) 0.18 * (0.79 - 0.44) = 0.35
0.35 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 17%. For CEOs who fire employees and have visited England, the probability of employee being fired is 53%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 44%. For CEOs who fire employees and have visited England, the probability of employee being fired is 79%. The overall probability of CEO's decision to fire the employee is 18%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.17
P(Y=1 | V1=0, X=1) = 0.53
P(Y=1 | V1=1, X=0) = 0.44
P(Y=1 | V1=1, X=1) = 0.79
P(V1=1) = 0.18
0.82 * (0.53 - 0.17) 0.18 * (0.79 - 0.44) = 0.35
0.35 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
862,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 8%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 58%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 44%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 93%. For people who have not visited England, the probability of director signing the termination letter is 19%. For people who have visited England, the probability of director signing the termination letter is 36%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.93
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.36
0.36 * (0.93 - 0.44) + 0.19 * (0.58 - 0.08) = 0.35
0.35 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
864,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 55%. For people who have not visited England, the probability of employee being fired is 18%. For people who have visited England, the probability of employee being fired is 61%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.61
0.55*0.61 - 0.45*0.18 = 0.42
0.42 > 0",diamondcut,firing_employee,1,marginal,P(Y)
866,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 55%. The probability of not having visited England and employee being fired is 8%. The probability of having visited England and employee being fired is 34%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.34
0.34/0.55 - 0.08/0.45 = 0.44
0.44 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 24%. For CEOs who fire employees and have visited England, the probability of employee being fired is 60%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 39%. For CEOs who fire employees and have visited England, the probability of employee being fired is 74%. The overall probability of CEO's decision to fire the employee is 18%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.24
P(Y=1 | V1=0, X=1) = 0.60
P(Y=1 | V1=1, X=0) = 0.39
P(Y=1 | V1=1, X=1) = 0.74
P(V1=1) = 0.18
0.82 * (0.60 - 0.24) 0.18 * (0.74 - 0.39) = 0.36
0.36 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 9%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 54%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 46%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 87%. For people who have not visited England, the probability of director signing the termination letter is 38%. For people who have visited England, the probability of director signing the termination letter is 50%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.46
P(Y=1 | X=1, V3=1) = 0.87
P(V3=1 | X=0) = 0.38
P(V3=1 | X=1) = 0.50
0.50 * (0.87 - 0.46) + 0.38 * (0.54 - 0.09) = 0.36
0.36 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 19%. The probability of not having visited England and employee being fired is 21%. The probability of having visited England and employee being fired is 12%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.12
0.12/0.19 - 0.21/0.81 = 0.41
0.41 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
877,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 19%. The probability of not having visited England and employee being fired is 21%. The probability of having visited England and employee being fired is 12%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.12
0.12/0.19 - 0.21/0.81 = 0.41
0.41 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
878,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 27%. For CEOs who fire employees and have visited England, the probability of employee being fired is 59%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 42%. For CEOs who fire employees and have visited England, the probability of employee being fired is 74%. The overall probability of CEO's decision to fire the employee is 12%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.27
P(Y=1 | V1=0, X=1) = 0.59
P(Y=1 | V1=1, X=0) = 0.42
P(Y=1 | V1=1, X=1) = 0.74
P(V1=1) = 0.12
0.88 * (0.59 - 0.27) 0.12 * (0.74 - 0.42) = 0.32
0.32 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 27%. For CEOs who fire employees and have visited England, the probability of employee being fired is 59%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 42%. For CEOs who fire employees and have visited England, the probability of employee being fired is 74%. The overall probability of CEO's decision to fire the employee is 12%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.27
P(Y=1 | V1=0, X=1) = 0.59
P(Y=1 | V1=1, X=0) = 0.42
P(Y=1 | V1=1, X=1) = 0.74
P(V1=1) = 0.12
0.88 * (0.59 - 0.27) 0.12 * (0.74 - 0.42) = 0.32
0.32 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
883,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 17%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 51%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 49%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 84%. For people who have not visited England, the probability of director signing the termination letter is 30%. For people who have visited England, the probability of director signing the termination letter is 38%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.17
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0) = 0.30
P(V3=1 | X=1) = 0.38
0.38 * (0.84 - 0.49) + 0.30 * (0.51 - 0.17) = 0.32
0.32 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 45%. For people who have not visited England, the probability of employee being fired is 27%. For people who have visited England, the probability of employee being fired is 62%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.62
0.45*0.62 - 0.55*0.27 = 0.43
0.43 > 0",diamondcut,firing_employee,1,marginal,P(Y)
886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 45%. The probability of not having visited England and employee being fired is 15%. The probability of having visited England and employee being fired is 28%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.28
0.28/0.45 - 0.15/0.55 = 0.35
0.35 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 13%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 52%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 49%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 88%. For people who have not visited England, the probability of director signing the termination letter is 50%. For people who have visited England, the probability of director signing the termination letter is 56%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.13
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0) = 0.50
P(V3=1 | X=1) = 0.56
0.56 * (0.88 - 0.49) + 0.50 * (0.52 - 0.13) = 0.36
0.36 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 56%. The probability of not having visited England and employee being fired is 14%. The probability of having visited England and employee being fired is 40%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.40
0.40/0.56 - 0.14/0.44 = 0.39
0.39 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
897,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 56%. The probability of not having visited England and employee being fired is 14%. The probability of having visited England and employee being fired is 40%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.40
0.40/0.56 - 0.14/0.44 = 0.39
0.39 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
900,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 34%. For CEOs who fire employees and have visited England, the probability of employee being fired is 73%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 44%. For CEOs who fire employees and have visited England, the probability of employee being fired is 83%. The overall probability of CEO's decision to fire the employee is 11%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.34
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.44
P(Y=1 | V1=1, X=1) = 0.83
P(V1=1) = 0.11
0.89 * (0.73 - 0.34) 0.11 * (0.83 - 0.44) = 0.39
0.39 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 9%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 47%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 50%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 85%. For people who have not visited England, the probability of director signing the termination letter is 66%. For people who have visited England, the probability of director signing the termination letter is 73%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.85
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.73
0.73 * (0.85 - 0.50) + 0.66 * (0.47 - 0.09) = 0.39
0.39 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 9%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 47%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 50%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 85%. For people who have not visited England, the probability of director signing the termination letter is 66%. For people who have visited England, the probability of director signing the termination letter is 73%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.85
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.73
0.73 * (0.85 - 0.50) + 0.66 * (0.47 - 0.09) = 0.39
0.39 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 24%. The probability of not having visited England and employee being fired is 26%. The probability of having visited England and employee being fired is 18%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.18
0.18/0.24 - 0.26/0.76 = 0.41
0.41 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 21%. For CEOs who fire employees and have visited England, the probability of employee being fired is 51%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 35%. For CEOs who fire employees and have visited England, the probability of employee being fired is 66%. The overall probability of CEO's decision to fire the employee is 28%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.21
P(Y=1 | V1=0, X=1) = 0.51
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.66
P(V1=1) = 0.28
0.72 * (0.51 - 0.21) 0.28 * (0.66 - 0.35) = 0.31
0.31 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 17%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 48%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 47%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 80%. For people who have not visited England, the probability of director signing the termination letter is 15%. For people who have visited England, the probability of director signing the termination letter is 39%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.17
P(Y=1 | X=0, V3=1) = 0.48
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.80
P(V3=1 | X=0) = 0.15
P(V3=1 | X=1) = 0.39
0.39 * (0.80 - 0.47) + 0.15 * (0.48 - 0.17) = 0.31
0.31 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 39%. For people who have not visited England, the probability of employee being fired is 22%. For people who have visited England, the probability of employee being fired is 60%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.60
0.39*0.60 - 0.61*0.22 = 0.37
0.37 > 0",diamondcut,firing_employee,1,marginal,P(Y)
915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 39%. For people who have not visited England, the probability of employee being fired is 22%. For people who have visited England, the probability of employee being fired is 60%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.60
0.39*0.60 - 0.61*0.22 = 0.37
0.37 > 0",diamondcut,firing_employee,1,marginal,P(Y)
919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 31%. For people who have not visited England, the probability of employee being fired is 50%. For people who have visited England, the probability of employee being fired is 87%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.87
0.31*0.87 - 0.69*0.50 = 0.62
0.62 > 0",diamondcut,firing_employee,1,marginal,P(Y)
932,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 3%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 52%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 43%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 85%. For people who have not visited England, the probability of director signing the termination letter is 22%. For people who have visited England, the probability of director signing the termination letter is 78%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.85
P(V3=1 | X=0) = 0.22
P(V3=1 | X=1) = 0.78
0.78 * (0.85 - 0.43) + 0.22 * (0.52 - 0.03) = 0.34
0.34 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 22%. For people who have not visited England, the probability of employee being fired is 14%. For people who have visited England, the probability of employee being fired is 76%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.76
0.22*0.76 - 0.78*0.14 = 0.29
0.29 > 0",diamondcut,firing_employee,1,marginal,P(Y)
938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 17%. For CEOs who fire employees and have visited England, the probability of employee being fired is 56%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 37%. For CEOs who fire employees and have visited England, the probability of employee being fired is 76%. The overall probability of CEO's decision to fire the employee is 22%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.17
P(Y=1 | V1=0, X=1) = 0.56
P(Y=1 | V1=1, X=0) = 0.37
P(Y=1 | V1=1, X=1) = 0.76
P(V1=1) = 0.22
0.78 * (0.56 - 0.17) 0.22 * (0.76 - 0.37) = 0.39
0.39 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 10%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 44%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 49%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 82%. For people who have not visited England, the probability of director signing the termination letter is 27%. For people who have visited England, the probability of director signing the termination letter is 36%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.10
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.82
P(V3=1 | X=0) = 0.27
P(V3=1 | X=1) = 0.36
0.36 * (0.82 - 0.49) + 0.27 * (0.44 - 0.10) = 0.39
0.39 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 66%. For people who have not visited England, the probability of employee being fired is 19%. For people who have visited England, the probability of employee being fired is 61%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.61
0.66*0.61 - 0.34*0.19 = 0.47
0.47 > 0",diamondcut,firing_employee,1,marginal,P(Y)
946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 66%. The probability of not having visited England and employee being fired is 7%. The probability of having visited England and employee being fired is 40%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.40
0.40/0.66 - 0.07/0.34 = 0.42
0.42 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 14%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 48%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 46%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 84%. For people who have not visited England, the probability of director signing the termination letter is 42%. For people who have visited England, the probability of director signing the termination letter is 47%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.14
P(Y=1 | X=0, V3=1) = 0.48
P(Y=1 | X=1, V3=0) = 0.46
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0) = 0.42
P(V3=1 | X=1) = 0.47
0.47 * (0.84 - 0.46) + 0.42 * (0.48 - 0.14) = 0.34
0.34 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 34%. For people who have not visited England, the probability of employee being fired is 28%. For people who have visited England, the probability of employee being fired is 64%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.34
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.64
0.34*0.64 - 0.66*0.28 = 0.40
0.40 > 0",diamondcut,firing_employee,1,marginal,P(Y)
957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 34%. The probability of not having visited England and employee being fired is 19%. The probability of having visited England and employee being fired is 22%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.34
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.22
0.22/0.34 - 0.19/0.66 = 0.36
0.36 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 19%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 59%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 60%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 99%. For people who have not visited England, the probability of director signing the termination letter is 26%. For people who have visited England, the probability of director signing the termination letter is 37%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.19
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.99
P(V3=1 | X=0) = 0.26
P(V3=1 | X=1) = 0.37
0.37 * (0.99 - 0.60) + 0.26 * (0.59 - 0.19) = 0.40
0.40 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 15%. The probability of not having visited England and employee being fired is 25%. The probability of having visited England and employee being fired is 11%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.11
0.11/0.15 - 0.25/0.85 = 0.45
0.45 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 17%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 56%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 52%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 88%. For people who have not visited England, the probability of director signing the termination letter is 31%. For people who have visited England, the probability of director signing the termination letter is 36%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.17
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0) = 0.31
P(V3=1 | X=1) = 0.36
0.36 * (0.88 - 0.52) + 0.31 * (0.56 - 0.17) = 0.34
0.34 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
974,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 43%. For people who have not visited England, the probability of employee being fired is 29%. For people who have visited England, the probability of employee being fired is 65%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.65
0.43*0.65 - 0.57*0.29 = 0.44
0.44 > 0",diamondcut,firing_employee,1,marginal,P(Y)
976,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 43%. The probability of not having visited England and employee being fired is 16%. The probability of having visited England and employee being fired is 28%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.28
0.28/0.43 - 0.16/0.57 = 0.36
0.36 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 43%. The probability of not having visited England and employee being fired is 16%. The probability of having visited England and employee being fired is 28%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.28
0.28/0.43 - 0.16/0.57 = 0.36
0.36 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look at how having visited England correlates with employee case by case according to director. Method 2: We look directly at how having visited England correlates with employee in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 22%. For CEOs who fire employees and have visited England, the probability of employee being fired is 60%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 39%. For CEOs who fire employees and have visited England, the probability of employee being fired is 76%. The overall probability of CEO's decision to fire the employee is 23%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.22
P(Y=1 | V1=0, X=1) = 0.60
P(Y=1 | V1=1, X=0) = 0.39
P(Y=1 | V1=1, X=1) = 0.76
P(V1=1) = 0.23
0.77 * (0.60 - 0.22) 0.23 * (0.76 - 0.39) = 0.38
0.38 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 7%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 57%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 45%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 93%. For people who have not visited England, the probability of director signing the termination letter is 37%. For people who have visited England, the probability of director signing the termination letter is 48%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.07
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.93
P(V3=1 | X=0) = 0.37
P(V3=1 | X=1) = 0.48
0.48 * (0.93 - 0.45) + 0.37 * (0.57 - 0.07) = 0.37
0.37 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
983,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 7%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 57%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 45%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 93%. For people who have not visited England, the probability of director signing the termination letter is 37%. For people who have visited England, the probability of director signing the termination letter is 48%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.07
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.93
P(V3=1 | X=0) = 0.37
P(V3=1 | X=1) = 0.48
0.48 * (0.93 - 0.45) + 0.37 * (0.57 - 0.07) = 0.37
0.37 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
992,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 5%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 39%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 40%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 79%. For people who have not visited England, the probability of director signing the termination letter is 42%. For people who have visited England, the probability of director signing the termination letter is 63%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.79
P(V3=1 | X=0) = 0.42
P(V3=1 | X=1) = 0.63
0.63 * (0.79 - 0.40) + 0.42 * (0.39 - 0.05) = 0.38
0.38 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For people who have not visited England and directors who don't sign termination letters, the probability of employee being fired is 5%. For people who have not visited England and directors who sign termination letters, the probability of employee being fired is 39%. For people who have visited England and directors who don't sign termination letters, the probability of employee being fired is 40%. For people who have visited England and directors who sign termination letters, the probability of employee being fired is 79%. For people who have not visited England, the probability of director signing the termination letter is 42%. For people who have visited England, the probability of director signing the termination letter is 63%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.79
P(V3=1 | X=0) = 0.42
P(V3=1 | X=1) = 0.63
0.63 * (0.79 - 0.40) + 0.42 * (0.39 - 0.05) = 0.38
0.38 > 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 14%. For people who have not visited England, the probability of employee being fired is 19%. For people who have visited England, the probability of employee being fired is 64%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.64
0.14*0.64 - 0.86*0.19 = 0.25
0.25 > 0",diamondcut,firing_employee,1,marginal,P(Y)
997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 14%. The probability of not having visited England and employee being fired is 17%. The probability of having visited England and employee being fired is 9%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.09
0.09/0.14 - 0.17/0.86 = 0.45
0.45 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
1000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 24%. For CEOs who fire employees and have visited England, the probability of employee being fired is 58%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 45%. For CEOs who fire employees and have visited England, the probability of employee being fired is 78%. The overall probability of CEO's decision to fire the employee is 15%.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.24
P(Y=1 | V1=0, X=1) = 0.58
P(Y=1 | V1=1, X=0) = 0.45
P(Y=1 | V1=1, X=1) = 0.78
P(V1=1) = 0.15
0.85 * (0.58 - 0.24) 0.15 * (0.78 - 0.45) = 0.34
0.34 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 42%. For people who have not visited England, the probability of employee being fired is 25%. For people who have visited England, the probability of employee being fired is 63%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.63
0.42*0.63 - 0.58*0.25 = 0.41
0.41 > 0",diamondcut,firing_employee,1,marginal,P(Y)
1007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. The overall probability of having visited England is 42%. The probability of not having visited England and employee being fired is 15%. The probability of having visited England and employee being fired is 27%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.27
0.27/0.42 - 0.15/0.58 = 0.38
0.38 > 0",diamondcut,firing_employee,1,correlation,P(Y | X)
1011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. For CEOs who fire employees and have not visited England, the probability of employee being fired is 18%. For CEOs who fire employees and have visited England, the probability of employee being fired is 55%. For CEOs who fire employees and have not visited England, the probability of employee being fired is 35%. For CEOs who fire employees and have visited England, the probability of employee being fired is 71%. The overall probability of CEO's decision to fire the employee is 29%.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.18
P(Y=1 | V1=0, X=1) = 0.55
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.71
P(V1=1) = 0.29
0.71 * (0.55 - 0.18) 0.29 * (0.71 - 0.35) = 0.37
0.37 > 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. Method 1: We look directly at how having visited England correlates with employee in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
1020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 53%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.53
0.53 - 0.20 = 0.33
0.33 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 53%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.53
0.53 - 0.20 = 0.33
0.33 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 55%. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 53%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.53
0.55*0.53 - 0.45*0.20 = 0.38
0.38 > 0",diamond,firing_squad,1,marginal,P(Y)
1027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 55%. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 53%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.53
0.55*0.53 - 0.45*0.20 = 0.38
0.38 > 0",diamond,firing_squad,1,marginal,P(Y)
1028,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 55%. The probability of not having a sister and the prisoner's death is 9%. The probability of having a sister and the prisoner's death is 29%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.29
0.29/0.55 - 0.09/0.45 = 0.33
0.33 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 55%. The probability of not having a sister and the prisoner's death is 9%. The probability of having a sister and the prisoner's death is 29%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.29
0.29/0.55 - 0.09/0.45 = 0.33
0.33 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 69%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.69
0.69 - 0.50 = 0.19
0.19 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1033,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 69%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.69
0.69 - 0.50 = 0.19
0.19 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 69%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.69
0.69 - 0.50 = 0.19
0.19 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 69%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.69
0.69 - 0.50 = 0.19
0.19 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 54%. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 69%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.69
0.54*0.69 - 0.46*0.50 = 0.60
0.60 > 0",diamond,firing_squad,1,marginal,P(Y)
1039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 54%. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 69%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.69
0.54*0.69 - 0.46*0.50 = 0.60
0.60 > 0",diamond,firing_squad,1,marginal,P(Y)
1041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 54%. The probability of not having a sister and the prisoner's death is 23%. The probability of having a sister and the prisoner's death is 38%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.38
0.38/0.54 - 0.23/0.46 = 0.19
0.19 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 40%. For people who have a sister, the probability of the prisoner's death is 83%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.83
0.83 - 0.40 = 0.42
0.42 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 40%. For people who have a sister, the probability of the prisoner's death is 83%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.83
0.83 - 0.40 = 0.42
0.42 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 40%. For people who have a sister, the probability of the prisoner's death is 83%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.83
0.83 - 0.40 = 0.42
0.42 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1052,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 68%. The probability of not having a sister and the prisoner's death is 13%. The probability of having a sister and the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.68
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.56
0.56/0.68 - 0.13/0.32 = 0.42
0.42 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1055,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 51%. For people who do not have a sister, the probability of the prisoner's death is 28%. For people who have a sister, the probability of the prisoner's death is 53%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.53
0.51*0.53 - 0.49*0.28 = 0.41
0.41 > 0",diamond,firing_squad,1,marginal,P(Y)
1064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 51%. The probability of not having a sister and the prisoner's death is 14%. The probability of having a sister and the prisoner's death is 27%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.27
0.27/0.51 - 0.14/0.49 = 0.26
0.26 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 51%. The probability of not having a sister and the prisoner's death is 14%. The probability of having a sister and the prisoner's death is 27%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.27
0.27/0.51 - 0.14/0.49 = 0.26
0.26 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 80%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.80
0.80 - 0.34 = 0.45
0.45 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 80%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.80
0.80 - 0.34 = 0.45
0.45 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1070,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 80%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.80
0.80 - 0.34 = 0.45
0.45 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 80%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.80
0.80 - 0.34 = 0.45
0.45 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 80%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.80
0.80 - 0.34 = 0.45
0.45 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 55%. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 80%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.80
0.55*0.80 - 0.45*0.34 = 0.59
0.59 > 0",diamond,firing_squad,1,marginal,P(Y)
1080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 16%. For people who have a sister, the probability of the prisoner's death is 37%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.37
0.37 - 0.16 = 0.21
0.21 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1083,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 16%. For people who have a sister, the probability of the prisoner's death is 37%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.37
0.37 - 0.16 = 0.21
0.21 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 52%. For people who do not have a sister, the probability of the prisoner's death is 16%. For people who have a sister, the probability of the prisoner's death is 37%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.37
0.52*0.37 - 0.48*0.16 = 0.27
0.27 > 0",diamond,firing_squad,1,marginal,P(Y)
1089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 52%. The probability of not having a sister and the prisoner's death is 8%. The probability of having a sister and the prisoner's death is 19%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.19
0.19/0.52 - 0.08/0.48 = 0.21
0.21 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1094,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 21%. For people who have a sister, the probability of the prisoner's death is 65%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.65
0.65 - 0.21 = 0.44
0.44 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 21%. For people who have a sister, the probability of the prisoner's death is 65%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.65
0.65 - 0.21 = 0.44
0.44 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 68%. For people who do not have a sister, the probability of the prisoner's death is 21%. For people who have a sister, the probability of the prisoner's death is 65%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.68
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.65
0.68*0.65 - 0.32*0.21 = 0.50
0.50 > 0",diamond,firing_squad,1,marginal,P(Y)
1099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 68%. For people who do not have a sister, the probability of the prisoner's death is 21%. For people who have a sister, the probability of the prisoner's death is 65%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.68
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.65
0.68*0.65 - 0.32*0.21 = 0.50
0.50 > 0",diamond,firing_squad,1,marginal,P(Y)
1100,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 68%. The probability of not having a sister and the prisoner's death is 7%. The probability of having a sister and the prisoner's death is 44%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.68
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.44
0.44/0.68 - 0.07/0.32 = 0.44
0.44 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1104,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 35%. For people who have a sister, the probability of the prisoner's death is 57%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.57
0.57 - 0.35 = 0.22
0.22 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 35%. For people who have a sister, the probability of the prisoner's death is 57%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.57
0.57 - 0.35 = 0.22
0.22 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 35%. For people who have a sister, the probability of the prisoner's death is 57%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.57
0.57 - 0.35 = 0.22
0.22 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 43%. The probability of not having a sister and the prisoner's death is 20%. The probability of having a sister and the prisoner's death is 25%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.25
0.25/0.43 - 0.20/0.57 = 0.22
0.22 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 70%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.70
0.70 - 0.36 = 0.34
0.34 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 55%. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 70%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.70
0.55*0.70 - 0.45*0.36 = 0.55
0.55 > 0",diamond,firing_squad,1,marginal,P(Y)
1125,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 55%. The probability of not having a sister and the prisoner's death is 16%. The probability of having a sister and the prisoner's death is 39%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.39
0.39/0.55 - 0.16/0.45 = 0.34
0.34 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 40%. For people who have a sister, the probability of the prisoner's death is 74%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.74
0.74 - 0.40 = 0.33
0.33 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 66%. The probability of not having a sister and the prisoner's death is 14%. The probability of having a sister and the prisoner's death is 48%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.48
0.48/0.66 - 0.14/0.34 = 0.33
0.33 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 66%. The probability of not having a sister and the prisoner's death is 14%. The probability of having a sister and the prisoner's death is 48%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.48
0.48/0.66 - 0.14/0.34 = 0.33
0.33 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1150,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 33%. For people who have a sister, the probability of the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.56
0.56 - 0.33 = 0.22
0.22 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 33%. For people who have a sister, the probability of the prisoner's death is 56%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.56
0.56 - 0.33 = 0.22
0.22 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 33%. For people who have a sister, the probability of the prisoner's death is 56%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.56
0.56 - 0.33 = 0.22
0.22 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 33%. For people who have a sister, the probability of the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.56
0.56 - 0.33 = 0.22
0.22 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1157,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 33%. For people who have a sister, the probability of the prisoner's death is 56%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.56
0.56 - 0.33 = 0.22
0.22 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 59%. For people who do not have a sister, the probability of the prisoner's death is 33%. For people who have a sister, the probability of the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.56
0.59*0.56 - 0.41*0.33 = 0.46
0.46 > 0",diamond,firing_squad,1,marginal,P(Y)
1160,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 59%. The probability of not having a sister and the prisoner's death is 14%. The probability of having a sister and the prisoner's death is 33%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.33
0.33/0.59 - 0.14/0.41 = 0.22
0.22 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 69%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.69
0.69 - 0.20 = 0.50
0.50 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 69%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.69
0.69 - 0.20 = 0.50
0.50 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 69%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.69
0.69 - 0.20 = 0.50
0.50 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 52%. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 69%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.69
0.52*0.69 - 0.48*0.20 = 0.45
0.45 > 0",diamond,firing_squad,1,marginal,P(Y)
1171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 52%. For people who do not have a sister, the probability of the prisoner's death is 20%. For people who have a sister, the probability of the prisoner's death is 69%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.69
0.52*0.69 - 0.48*0.20 = 0.45
0.45 > 0",diamond,firing_squad,1,marginal,P(Y)
1173,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 52%. The probability of not having a sister and the prisoner's death is 10%. The probability of having a sister and the prisoner's death is 36%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.36
0.36/0.52 - 0.10/0.48 = 0.50
0.50 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1177,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 29%. For people who have a sister, the probability of the prisoner's death is 50%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.50
0.50 - 0.29 = 0.21
0.21 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 29%. For people who have a sister, the probability of the prisoner's death is 50%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.50
0.50 - 0.29 = 0.21
0.21 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 29%. For people who have a sister, the probability of the prisoner's death is 50%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.50
0.50 - 0.29 = 0.21
0.21 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 41%. The probability of not having a sister and the prisoner's death is 17%. The probability of having a sister and the prisoner's death is 20%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.20
0.20/0.41 - 0.17/0.59 = 0.21
0.21 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1185,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 41%. The probability of not having a sister and the prisoner's death is 17%. The probability of having a sister and the prisoner's death is 20%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.20
0.20/0.41 - 0.17/0.59 = 0.21
0.21 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 31%. For people who have a sister, the probability of the prisoner's death is 75%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.75
0.75 - 0.31 = 0.44
0.44 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 31%. For people who have a sister, the probability of the prisoner's death is 75%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.75
0.75 - 0.31 = 0.44
0.44 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 76%. For people who do not have a sister, the probability of the prisoner's death is 31%. For people who have a sister, the probability of the prisoner's death is 75%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.76
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.75
0.76*0.75 - 0.24*0.31 = 0.65
0.65 > 0",diamond,firing_squad,1,marginal,P(Y)
1195,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 76%. For people who do not have a sister, the probability of the prisoner's death is 31%. For people who have a sister, the probability of the prisoner's death is 75%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.76
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.75
0.76*0.75 - 0.24*0.31 = 0.65
0.65 > 0",diamond,firing_squad,1,marginal,P(Y)
1196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 76%. The probability of not having a sister and the prisoner's death is 7%. The probability of having a sister and the prisoner's death is 58%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.58
0.58/0.76 - 0.07/0.24 = 0.44
0.44 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 76%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.76
0.76 - 0.50 = 0.26
0.26 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 76%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.76
0.76 - 0.50 = 0.26
0.26 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1203,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 76%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.76
0.76 - 0.50 = 0.26
0.26 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 76%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.76
0.76 - 0.50 = 0.26
0.26 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 77%. For people who do not have a sister, the probability of the prisoner's death is 50%. For people who have a sister, the probability of the prisoner's death is 76%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.76
0.77*0.76 - 0.23*0.50 = 0.70
0.70 > 0",diamond,firing_squad,1,marginal,P(Y)
1209,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 77%. The probability of not having a sister and the prisoner's death is 12%. The probability of having a sister and the prisoner's death is 59%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.59
0.59/0.77 - 0.12/0.23 = 0.26
0.26 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1211,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 71%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.71
0.71 - 0.34 = 0.37
0.37 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 71%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.71
0.71 - 0.34 = 0.37
0.37 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 79%. The probability of not having a sister and the prisoner's death is 7%. The probability of having a sister and the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.79
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.56
0.56/0.79 - 0.07/0.21 = 0.37
0.37 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 52%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.52
0.52 - 0.36 = 0.16
0.16 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 52%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.52
0.52 - 0.36 = 0.16
0.16 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 59%. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 52%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.52
0.59*0.52 - 0.41*0.36 = 0.46
0.46 > 0",diamond,firing_squad,1,marginal,P(Y)
1232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 59%. The probability of not having a sister and the prisoner's death is 15%. The probability of having a sister and the prisoner's death is 31%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.31
0.31/0.59 - 0.15/0.41 = 0.16
0.16 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 59%. The probability of not having a sister and the prisoner's death is 15%. The probability of having a sister and the prisoner's death is 31%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.31
0.31/0.59 - 0.15/0.41 = 0.16
0.16 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 29%. For people who have a sister, the probability of the prisoner's death is 72%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.72
0.72 - 0.29 = 0.43
0.43 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 29%. For people who have a sister, the probability of the prisoner's death is 72%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.72
0.72 - 0.29 = 0.43
0.43 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 29%. For people who have a sister, the probability of the prisoner's death is 72%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.72
0.72 - 0.29 = 0.43
0.43 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 29%. For people who have a sister, the probability of the prisoner's death is 72%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.72
0.72 - 0.29 = 0.43
0.43 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 39%. For people who have a sister, the probability of the prisoner's death is 47%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.47
0.47 - 0.39 = 0.08
0.08 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 39%. For people who have a sister, the probability of the prisoner's death is 47%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.47
0.47 - 0.39 = 0.08
0.08 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 39%. For people who have a sister, the probability of the prisoner's death is 47%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.47
0.47 - 0.39 = 0.08
0.08 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 52%. For people who do not have a sister, the probability of the prisoner's death is 39%. For people who have a sister, the probability of the prisoner's death is 47%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.47
0.52*0.47 - 0.48*0.39 = 0.43
0.43 > 0",diamond,firing_squad,1,marginal,P(Y)
1261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 24%. For people who have a sister, the probability of the prisoner's death is 71%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.71
0.71 - 0.24 = 0.47
0.47 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1262,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 24%. For people who have a sister, the probability of the prisoner's death is 71%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.71
0.71 - 0.24 = 0.47
0.47 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 24%. For people who have a sister, the probability of the prisoner's death is 71%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.71
0.71 - 0.24 = 0.47
0.47 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 73%. For people who do not have a sister, the probability of the prisoner's death is 24%. For people who have a sister, the probability of the prisoner's death is 71%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.73
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.71
0.73*0.71 - 0.27*0.24 = 0.58
0.58 > 0",diamond,firing_squad,1,marginal,P(Y)
1267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 73%. For people who do not have a sister, the probability of the prisoner's death is 24%. For people who have a sister, the probability of the prisoner's death is 71%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.73
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.71
0.73*0.71 - 0.27*0.24 = 0.58
0.58 > 0",diamond,firing_squad,1,marginal,P(Y)
1268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 73%. The probability of not having a sister and the prisoner's death is 7%. The probability of having a sister and the prisoner's death is 52%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.52
0.52/0.73 - 0.07/0.27 = 0.47
0.47 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 73%. The probability of not having a sister and the prisoner's death is 7%. The probability of having a sister and the prisoner's death is 52%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.52
0.52/0.73 - 0.07/0.27 = 0.47
0.47 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 83%. For people who have a sister, the probability of the prisoner's death is 93%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.93
0.93 - 0.83 = 0.09
0.09 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 83%. For people who have a sister, the probability of the prisoner's death is 93%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.93
0.93 - 0.83 = 0.09
0.09 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1278,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 63%. For people who do not have a sister, the probability of the prisoner's death is 83%. For people who have a sister, the probability of the prisoner's death is 93%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.93
0.63*0.93 - 0.37*0.83 = 0.89
0.89 > 0",diamond,firing_squad,1,marginal,P(Y)
1282,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 72%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.72
0.72 - 0.36 = 0.36
0.36 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 72%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.72
0.72 - 0.36 = 0.36
0.36 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 72%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.72
0.72 - 0.36 = 0.36
0.36 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 63%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.63
0.63 - 0.36 = 0.27
0.27 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1302,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 52%. For people who do not have a sister, the probability of the prisoner's death is 36%. For people who have a sister, the probability of the prisoner's death is 63%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.63
0.52*0.63 - 0.48*0.36 = 0.50
0.50 > 0",diamond,firing_squad,1,marginal,P(Y)
1304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 52%. The probability of not having a sister and the prisoner's death is 17%. The probability of having a sister and the prisoner's death is 33%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.33
0.33/0.52 - 0.17/0.48 = 0.27
0.27 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having a sister correlates with prisoner case by case according to the private. Method 2: We look directly at how having a sister correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 68%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.68
0.68 - 0.26 = 0.43
0.43 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 68%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.68
0.68 - 0.26 = 0.43
0.43 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 68%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.68
0.68 - 0.26 = 0.43
0.43 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 68%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.68
0.68 - 0.26 = 0.43
0.43 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 34%. For people who have a sister, the probability of the prisoner's death is 57%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.57
0.57 - 0.34 = 0.22
0.22 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 24%. For people who have a sister, the probability of the prisoner's death is 68%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.68
0.68 - 0.24 = 0.44
0.44 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1340,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 71%. The probability of not having a sister and the prisoner's death is 7%. The probability of having a sister and the prisoner's death is 48%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.71
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.48
0.48/0.71 - 0.07/0.29 = 0.44
0.44 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 71%. The probability of not having a sister and the prisoner's death is 7%. The probability of having a sister and the prisoner's death is 48%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.71
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.48
0.48/0.71 - 0.07/0.29 = 0.44
0.44 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having a sister correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
1344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 53%. For people who have a sister, the probability of the prisoner's death is 66%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.66
0.66 - 0.53 = 0.12
0.12 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 44%. For people who do not have a sister, the probability of the prisoner's death is 53%. For people who have a sister, the probability of the prisoner's death is 66%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.66
0.44*0.66 - 0.56*0.53 = 0.59
0.59 > 0",diamond,firing_squad,1,marginal,P(Y)
1352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 44%. The probability of not having a sister and the prisoner's death is 30%. The probability of having a sister and the prisoner's death is 29%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.29
0.29/0.44 - 0.30/0.56 = 0.12
0.12 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 44%. The probability of not having a sister and the prisoner's death is 30%. The probability of having a sister and the prisoner's death is 29%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.29
0.29/0.44 - 0.30/0.56 = 0.12
0.12 > 0",diamond,firing_squad,1,correlation,P(Y | X)
1356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 45%. For people who have a sister, the probability of the prisoner's death is 74%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.74
0.74 - 0.45 = 0.29
0.29 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 45%. For people who have a sister, the probability of the prisoner's death is 74%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.74
0.74 - 0.45 = 0.29
0.29 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 45%. For people who have a sister, the probability of the prisoner's death is 74%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.74
0.74 - 0.45 = 0.29
0.29 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.56
0.56 - 0.26 = 0.29
0.29 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.56
0.56 - 0.26 = 0.29
0.29 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.56
0.56 - 0.26 = 0.29
0.29 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 72%. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 56%.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.72
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.56
0.72*0.56 - 0.28*0.26 = 0.47
0.47 > 0",diamond,firing_squad,1,marginal,P(Y)
1375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having a sister is 72%. For people who do not have a sister, the probability of the prisoner's death is 26%. For people who have a sister, the probability of the prisoner's death is 56%.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.72
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.56
0.72*0.56 - 0.28*0.26 = 0.47
0.47 > 0",diamond,firing_squad,1,marginal,P(Y)
1384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 36%. For situations where there is a full moon, the probability of wet ground is 55%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.55
0.55 - 0.36 = 0.19
0.19 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 36%. For situations where there is a full moon, the probability of wet ground is 55%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.55
0.55 - 0.36 = 0.19
0.19 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 16%. For situations where there is no full moon, the probability of wet ground is 36%. For situations where there is a full moon, the probability of wet ground is 55%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.55
0.16*0.55 - 0.84*0.36 = 0.39
0.39 > 0",diamond,floor_wet,1,marginal,P(Y)
1389,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 16%. The probability of no full moon and wet ground is 30%. The probability of full moon and wet ground is 9%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.09
0.09/0.16 - 0.30/0.84 = 0.19
0.19 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 56%. For situations where there is a full moon, the probability of wet ground is 54%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.54
0.54 - 0.56 = -0.02
-0.02 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 16%. For situations where there is no full moon, the probability of wet ground is 56%. For situations where there is a full moon, the probability of wet ground is 54%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.54
0.16*0.54 - 0.84*0.56 = 0.55
0.55 > 0",diamond,floor_wet,1,marginal,P(Y)
1400,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 16%. The probability of no full moon and wet ground is 47%. The probability of full moon and wet ground is 8%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.08
0.08/0.16 - 0.47/0.84 = -0.02
-0.02 < 0",diamond,floor_wet,1,correlation,P(Y | X)
1402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1416,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 49%. For situations where there is a full moon, the probability of wet ground is 49%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.49 - 0.49 = -0.00
0.00 = 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 49%. For situations where there is a full moon, the probability of wet ground is 49%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.49 - 0.49 = -0.00
0.00 = 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1424,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 48%. The probability of no full moon and wet ground is 26%. The probability of full moon and wet ground is 23%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.23
0.23/0.48 - 0.26/0.52 = -0.00
0.00 = 0",diamond,floor_wet,1,correlation,P(Y | X)
1425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 48%. The probability of no full moon and wet ground is 26%. The probability of full moon and wet ground is 23%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.23
0.23/0.48 - 0.26/0.52 = -0.00
0.00 = 0",diamond,floor_wet,1,correlation,P(Y | X)
1426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 39%. For situations where there is a full moon, the probability of wet ground is 49%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.49
0.49 - 0.39 = 0.10
0.10 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 39%. For situations where there is a full moon, the probability of wet ground is 49%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.49
0.49 - 0.39 = 0.10
0.10 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 39%. For situations where there is a full moon, the probability of wet ground is 49%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.49
0.49 - 0.39 = 0.10
0.10 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1434,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 20%. For situations where there is no full moon, the probability of wet ground is 39%. For situations where there is a full moon, the probability of wet ground is 49%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.49
0.20*0.49 - 0.80*0.39 = 0.41
0.41 > 0",diamond,floor_wet,1,marginal,P(Y)
1436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 20%. The probability of no full moon and wet ground is 31%. The probability of full moon and wet ground is 10%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.10
0.10/0.20 - 0.31/0.80 = 0.10
0.10 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 20%. The probability of no full moon and wet ground is 31%. The probability of full moon and wet ground is 10%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.10
0.10/0.20 - 0.31/0.80 = 0.10
0.10 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 52%. For situations where there is a full moon, the probability of wet ground is 57%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.57
0.57 - 0.52 = 0.06
0.06 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 52%. For situations where there is a full moon, the probability of wet ground is 57%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.57
0.57 - 0.52 = 0.06
0.06 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 52%. For situations where there is a full moon, the probability of wet ground is 57%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.57
0.57 - 0.52 = 0.06
0.06 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 14%. For situations where there is no full moon, the probability of wet ground is 52%. For situations where there is a full moon, the probability of wet ground is 57%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.57
0.14*0.57 - 0.86*0.52 = 0.52
0.52 > 0",diamond,floor_wet,1,marginal,P(Y)
1449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 14%. The probability of no full moon and wet ground is 44%. The probability of full moon and wet ground is 8%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.08
0.08/0.14 - 0.44/0.86 = 0.06
0.06 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 43%. For situations where there is a full moon, the probability of wet ground is 54%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.54
0.54 - 0.43 = 0.11
0.11 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1459,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 20%. For situations where there is no full moon, the probability of wet ground is 43%. For situations where there is a full moon, the probability of wet ground is 54%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.54
0.20*0.54 - 0.80*0.43 = 0.45
0.45 > 0",diamond,floor_wet,1,marginal,P(Y)
1462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1464,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 42%. For situations where there is a full moon, the probability of wet ground is 47%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.47
0.47 - 0.42 = 0.05
0.05 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 42%. For situations where there is a full moon, the probability of wet ground is 47%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.47
0.47 - 0.42 = 0.05
0.05 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 42%. For situations where there is a full moon, the probability of wet ground is 47%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.47
0.47 - 0.42 = 0.05
0.05 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 47%. For situations where there is a full moon, the probability of wet ground is 61%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.61
0.61 - 0.47 = 0.14
0.14 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 47%. For situations where there is a full moon, the probability of wet ground is 61%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.61
0.61 - 0.47 = 0.14
0.14 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 35%. For situations where there is no full moon, the probability of wet ground is 47%. For situations where there is a full moon, the probability of wet ground is 61%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.61
0.35*0.61 - 0.65*0.47 = 0.52
0.52 > 0",diamond,floor_wet,1,marginal,P(Y)
1484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 35%. The probability of no full moon and wet ground is 31%. The probability of full moon and wet ground is 21%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.21
0.21/0.35 - 0.31/0.65 = 0.14
0.14 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1486,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1487,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 44%. For situations where there is a full moon, the probability of wet ground is 51%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.51
0.51 - 0.44 = 0.08
0.08 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 19%. For situations where there is no full moon, the probability of wet ground is 44%. For situations where there is a full moon, the probability of wet ground is 51%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.51
0.19*0.51 - 0.81*0.44 = 0.46
0.46 > 0",diamond,floor_wet,1,marginal,P(Y)
1496,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 19%. The probability of no full moon and wet ground is 35%. The probability of full moon and wet ground is 10%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.10
0.10/0.19 - 0.35/0.81 = 0.08
0.08 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 15%. For situations where there is no full moon, the probability of wet ground is 46%. For situations where there is a full moon, the probability of wet ground is 57%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.57
0.15*0.57 - 0.85*0.46 = 0.48
0.48 > 0",diamond,floor_wet,1,marginal,P(Y)
1508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 15%. The probability of no full moon and wet ground is 39%. The probability of full moon and wet ground is 8%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.08
0.08/0.15 - 0.39/0.85 = 0.11
0.11 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 15%. The probability of no full moon and wet ground is 39%. The probability of full moon and wet ground is 8%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.08
0.08/0.15 - 0.39/0.85 = 0.11
0.11 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 83%. For situations where there is a full moon, the probability of wet ground is 79%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.79
0.79 - 0.83 = -0.04
-0.04 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 83%. For situations where there is a full moon, the probability of wet ground is 79%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.79
0.79 - 0.83 = -0.04
-0.04 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 55%. For situations where there is a full moon, the probability of wet ground is 62%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.62
0.62 - 0.55 = 0.07
0.07 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 55%. For situations where there is a full moon, the probability of wet ground is 62%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.62
0.62 - 0.55 = 0.07
0.07 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 55%. For situations where there is a full moon, the probability of wet ground is 62%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.62
0.62 - 0.55 = 0.07
0.07 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 20%. The probability of no full moon and wet ground is 44%. The probability of full moon and wet ground is 12%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.12
0.12/0.20 - 0.44/0.80 = 0.07
0.07 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1535,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1536,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 53%. For situations where there is a full moon, the probability of wet ground is 63%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.63
0.63 - 0.53 = 0.10
0.10 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 53%. For situations where there is a full moon, the probability of wet ground is 63%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.63
0.63 - 0.53 = 0.10
0.10 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1542,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 44%. For situations where there is no full moon, the probability of wet ground is 53%. For situations where there is a full moon, the probability of wet ground is 63%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.63
0.44*0.63 - 0.56*0.53 = 0.58
0.58 > 0",diamond,floor_wet,1,marginal,P(Y)
1543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 44%. For situations where there is no full moon, the probability of wet ground is 53%. For situations where there is a full moon, the probability of wet ground is 63%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.63
0.44*0.63 - 0.56*0.53 = 0.58
0.58 > 0",diamond,floor_wet,1,marginal,P(Y)
1544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 44%. The probability of no full moon and wet ground is 30%. The probability of full moon and wet ground is 28%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.28
0.28/0.44 - 0.30/0.56 = 0.10
0.10 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 44%. The probability of no full moon and wet ground is 30%. The probability of full moon and wet ground is 28%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.28
0.28/0.44 - 0.30/0.56 = 0.10
0.10 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 37%. For situations where there is a full moon, the probability of wet ground is 42%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.42
0.42 - 0.37 = 0.05
0.05 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 37%. For situations where there is a full moon, the probability of wet ground is 42%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.42
0.42 - 0.37 = 0.05
0.05 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 37%. For situations where there is a full moon, the probability of wet ground is 42%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.42
0.42 - 0.37 = 0.05
0.05 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 37%. For situations where there is a full moon, the probability of wet ground is 42%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.42
0.42 - 0.37 = 0.05
0.05 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1554,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 24%. For situations where there is no full moon, the probability of wet ground is 37%. For situations where there is a full moon, the probability of wet ground is 42%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.42
0.24*0.42 - 0.76*0.37 = 0.39
0.39 > 0",diamond,floor_wet,1,marginal,P(Y)
1555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 24%. For situations where there is no full moon, the probability of wet ground is 37%. For situations where there is a full moon, the probability of wet ground is 42%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.42
0.24*0.42 - 0.76*0.37 = 0.39
0.39 > 0",diamond,floor_wet,1,marginal,P(Y)
1557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 24%. The probability of no full moon and wet ground is 28%. The probability of full moon and wet ground is 10%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.10
0.10/0.24 - 0.28/0.76 = 0.05
0.05 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 39%. For situations where there is a full moon, the probability of wet ground is 44%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.44
0.44 - 0.39 = 0.05
0.05 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 19%. The probability of no full moon and wet ground is 32%. The probability of full moon and wet ground is 8%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.08
0.08/0.19 - 0.32/0.81 = 0.05
0.05 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 61%. For situations where there is a full moon, the probability of wet ground is 70%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.70
0.70 - 0.61 = 0.10
0.10 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 61%. For situations where there is a full moon, the probability of wet ground is 70%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.70
0.70 - 0.61 = 0.10
0.10 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 61%. For situations where there is a full moon, the probability of wet ground is 70%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.70
0.70 - 0.61 = 0.10
0.10 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 48%. For situations where there is a full moon, the probability of wet ground is 62%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.62
0.62 - 0.48 = 0.13
0.13 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 48%. For situations where there is a full moon, the probability of wet ground is 62%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.62
0.62 - 0.48 = 0.13
0.13 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 48%. For situations where there is a full moon, the probability of wet ground is 62%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.62
0.62 - 0.48 = 0.13
0.13 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 48%. For situations where there is a full moon, the probability of wet ground is 62%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.62
0.62 - 0.48 = 0.13
0.13 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 48%. For situations where there is a full moon, the probability of wet ground is 62%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.62
0.62 - 0.48 = 0.13
0.13 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 19%. For situations where there is no full moon, the probability of wet ground is 48%. For situations where there is a full moon, the probability of wet ground is 62%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.62
0.19*0.62 - 0.81*0.48 = 0.51
0.51 > 0",diamond,floor_wet,1,marginal,P(Y)
1594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 48%. For situations where there is a full moon, the probability of wet ground is 61%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.61
0.61 - 0.48 = 0.12
0.12 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1602,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 31%. For situations where there is no full moon, the probability of wet ground is 48%. For situations where there is a full moon, the probability of wet ground is 61%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.61
0.31*0.61 - 0.69*0.48 = 0.53
0.53 > 0",diamond,floor_wet,1,marginal,P(Y)
1605,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 31%. The probability of no full moon and wet ground is 33%. The probability of full moon and wet ground is 19%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.19
0.19/0.31 - 0.33/0.69 = 0.12
0.12 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1607,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 38%. For situations where there is a full moon, the probability of wet ground is 43%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.43
0.43 - 0.38 = 0.05
0.05 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 38%. For situations where there is a full moon, the probability of wet ground is 43%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.43
0.43 - 0.38 = 0.05
0.05 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 38%. For situations where there is a full moon, the probability of wet ground is 43%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.43
0.43 - 0.38 = 0.05
0.05 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 38%. For situations where there is a full moon, the probability of wet ground is 43%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.43
0.43 - 0.38 = 0.05
0.05 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1615,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 49%. For situations where there is no full moon, the probability of wet ground is 38%. For situations where there is a full moon, the probability of wet ground is 43%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.43
0.49*0.43 - 0.51*0.38 = 0.40
0.40 > 0",diamond,floor_wet,1,marginal,P(Y)
1627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 28%. For situations where there is no full moon, the probability of wet ground is 39%. For situations where there is a full moon, the probability of wet ground is 46%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.28
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.46
0.28*0.46 - 0.72*0.39 = 0.42
0.42 > 0",diamond,floor_wet,1,marginal,P(Y)
1628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 28%. The probability of no full moon and wet ground is 28%. The probability of full moon and wet ground is 13%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.28
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.13
0.13/0.28 - 0.28/0.72 = 0.07
0.07 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 33%. For situations where there is a full moon, the probability of wet ground is 48%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.48
0.48 - 0.33 = 0.15
0.15 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 33%. For situations where there is a full moon, the probability of wet ground is 48%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.48
0.48 - 0.33 = 0.15
0.15 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1640,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 20%. The probability of no full moon and wet ground is 26%. The probability of full moon and wet ground is 9%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.09
0.09/0.20 - 0.26/0.80 = 0.15
0.15 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 35%. For situations where there is a full moon, the probability of wet ground is 49%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.49
0.49 - 0.35 = 0.14
0.14 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 35%. For situations where there is a full moon, the probability of wet ground is 49%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.49
0.49 - 0.35 = 0.14
0.14 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 35%. For situations where there is a full moon, the probability of wet ground is 49%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.49
0.49 - 0.35 = 0.14
0.14 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 34%. The probability of no full moon and wet ground is 23%. The probability of full moon and wet ground is 17%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.34
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.17
0.17/0.34 - 0.23/0.66 = 0.14
0.14 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 44%. For situations where there is a full moon, the probability of wet ground is 48%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.48
0.48 - 0.44 = 0.04
0.04 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 44%. For situations where there is a full moon, the probability of wet ground is 48%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.48
0.48 - 0.44 = 0.04
0.04 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 25%. For situations where there is no full moon, the probability of wet ground is 44%. For situations where there is a full moon, the probability of wet ground is 48%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.25
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.48
0.25*0.48 - 0.75*0.44 = 0.44
0.44 > 0",diamond,floor_wet,1,marginal,P(Y)
1673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 30%. For situations where there is a full moon, the probability of wet ground is 40%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.40
0.40 - 0.30 = 0.10
0.10 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 13%. For situations where there is no full moon, the probability of wet ground is 30%. For situations where there is a full moon, the probability of wet ground is 40%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.40
0.13*0.40 - 0.87*0.30 = 0.31
0.31 > 0",diamond,floor_wet,1,marginal,P(Y)
1676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 13%. The probability of no full moon and wet ground is 26%. The probability of full moon and wet ground is 5%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.05
0.05/0.13 - 0.26/0.87 = 0.10
0.10 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 13%. The probability of no full moon and wet ground is 26%. The probability of full moon and wet ground is 5%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.05
0.05/0.13 - 0.26/0.87 = 0.10
0.10 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 47%. For situations where there is a full moon, the probability of wet ground is 53%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.53
0.53 - 0.47 = 0.07
0.07 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 47%. For situations where there is a full moon, the probability of wet ground is 53%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.53
0.53 - 0.47 = 0.07
0.07 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1687,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 16%. For situations where there is no full moon, the probability of wet ground is 47%. For situations where there is a full moon, the probability of wet ground is 53%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.53
0.16*0.53 - 0.84*0.47 = 0.48
0.48 > 0",diamond,floor_wet,1,marginal,P(Y)
1688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 16%. The probability of no full moon and wet ground is 39%. The probability of full moon and wet ground is 9%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.09
0.09/0.16 - 0.39/0.84 = 0.07
0.07 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 16%. The probability of no full moon and wet ground is 39%. The probability of full moon and wet ground is 9%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.09
0.09/0.16 - 0.39/0.84 = 0.07
0.07 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 24%. For situations where there is a full moon, the probability of wet ground is 37%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.37
0.37 - 0.24 = 0.13
0.13 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 24%. For situations where there is a full moon, the probability of wet ground is 37%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.37
0.37 - 0.24 = 0.13
0.13 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 21%. For situations where there is no full moon, the probability of wet ground is 24%. For situations where there is a full moon, the probability of wet ground is 37%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.21
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.37
0.21*0.37 - 0.79*0.24 = 0.27
0.27 > 0",diamond,floor_wet,1,marginal,P(Y)
1701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 21%. The probability of no full moon and wet ground is 19%. The probability of full moon and wet ground is 8%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.21
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.08
0.08/0.21 - 0.19/0.79 = 0.13
0.13 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1703,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 32%. For situations where there is a full moon, the probability of wet ground is 37%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.37
0.37 - 0.32 = 0.04
0.04 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 32%. For situations where there is a full moon, the probability of wet ground is 37%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.37
0.37 - 0.32 = 0.04
0.04 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1713,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 43%. The probability of no full moon and wet ground is 18%. The probability of full moon and wet ground is 16%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.16
0.16/0.43 - 0.18/0.57 = 0.04
0.04 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 55%. For situations where there is a full moon, the probability of wet ground is 60%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.60
0.60 - 0.55 = 0.05
0.05 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 55%. For situations where there is a full moon, the probability of wet ground is 60%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.60
0.60 - 0.55 = 0.05
0.05 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1721,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 55%. For situations where there is a full moon, the probability of wet ground is 60%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.60
0.60 - 0.55 = 0.05
0.05 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
1723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 41%. For situations where there is no full moon, the probability of wet ground is 55%. For situations where there is a full moon, the probability of wet ground is 60%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.60
0.41*0.60 - 0.59*0.55 = 0.58
0.58 > 0",diamond,floor_wet,1,marginal,P(Y)
1725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 41%. The probability of no full moon and wet ground is 32%. The probability of full moon and wet ground is 25%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.25
0.25/0.41 - 0.32/0.59 = 0.05
0.05 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 31%. For situations where there is a full moon, the probability of wet ground is 46%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.46
0.46 - 0.31 = 0.15
0.15 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 31%. For situations where there is a full moon, the probability of wet ground is 46%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.46
0.46 - 0.31 = 0.15
0.15 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 31%. For situations where there is a full moon, the probability of wet ground is 46%.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.46
0.46 - 0.31 = 0.15
0.15 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. For situations where there is no full moon, the probability of wet ground is 31%. For situations where there is a full moon, the probability of wet ground is 46%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.46
0.46 - 0.31 = 0.15
0.15 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1736,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. The overall probability of full moon is 12%. The probability of no full moon and wet ground is 27%. The probability of full moon and wet ground is 6%.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.06
0.06/0.12 - 0.27/0.88 = 0.15
0.15 > 0",diamond,floor_wet,1,correlation,P(Y | X)
1738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look at how full moon correlates with ground case by case according to sprinkler. Method 2: We look directly at how full moon correlates with ground in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. Method 1: We look directly at how full moon correlates with ground in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
1740,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 21%. For people who like spicy food, the probability of the forest on fire is 92%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.92
0.92 - 0.21 = 0.71
0.71 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 21%. For people who do not like spicy food, the probability of the forest on fire is 21%. For people who like spicy food, the probability of the forest on fire is 92%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.21
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.92
0.21*0.92 - 0.79*0.21 = 0.36
0.36 > 0",fork,forest_fire,1,marginal,P(Y)
1747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 21%. The probability of not liking spicy food and the forest on fire is 16%. The probability of liking spicy food and the forest on fire is 20%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.21
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.20
0.20/0.21 - 0.16/0.79 = 0.71
0.71 > 0",fork,forest_fire,1,correlation,P(Y | X)
1748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 38%. For people who like spicy food, the probability of the forest on fire is 78%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.78
0.78 - 0.38 = 0.40
0.40 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 38%. For people who like spicy food, the probability of the forest on fire is 78%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.78
0.78 - 0.38 = 0.40
0.40 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 1%. The probability of not liking spicy food and the forest on fire is 38%. The probability of liking spicy food and the forest on fire is 1%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.01
0.01/0.01 - 0.38/0.99 = 0.40
0.40 > 0",fork,forest_fire,1,correlation,P(Y | X)
1758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 18%. For people who like spicy food, the probability of the forest on fire is 57%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.57
0.57 - 0.18 = 0.39
0.39 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1764,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 5%. For people who do not like spicy food, the probability of the forest on fire is 18%. For people who like spicy food, the probability of the forest on fire is 57%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.57
0.05*0.57 - 0.95*0.18 = 0.20
0.20 > 0",fork,forest_fire,1,marginal,P(Y)
1769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 14%. For people who do not like spicy food, the probability of the forest on fire is 35%. For people who like spicy food, the probability of the forest on fire is 67%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.67
0.14*0.67 - 0.86*0.35 = 0.39
0.39 > 0",fork,forest_fire,1,marginal,P(Y)
1777,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 14%. The probability of not liking spicy food and the forest on fire is 30%. The probability of liking spicy food and the forest on fire is 9%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.09
0.09/0.14 - 0.30/0.86 = 0.32
0.32 > 0",fork,forest_fire,1,correlation,P(Y | X)
1779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 19%. For people who like spicy food, the probability of the forest on fire is 60%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.60
0.60 - 0.19 = 0.41
0.41 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 9%. For people who do not like spicy food, the probability of the forest on fire is 19%. For people who like spicy food, the probability of the forest on fire is 60%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.60
0.09*0.60 - 0.91*0.19 = 0.23
0.23 > 0",fork,forest_fire,1,marginal,P(Y)
1786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 9%. The probability of not liking spicy food and the forest on fire is 18%. The probability of liking spicy food and the forest on fire is 5%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.05
0.05/0.09 - 0.18/0.91 = 0.41
0.41 > 0",fork,forest_fire,1,correlation,P(Y | X)
1789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 38%. For people who like spicy food, the probability of the forest on fire is 80%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.80 - 0.38 = 0.42
0.42 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 38%. For people who like spicy food, the probability of the forest on fire is 80%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.80 - 0.38 = 0.42
0.42 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 3%. For people who do not like spicy food, the probability of the forest on fire is 38%. For people who like spicy food, the probability of the forest on fire is 80%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.03*0.80 - 0.97*0.38 = 0.39
0.39 > 0",fork,forest_fire,1,marginal,P(Y)
1796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 3%. The probability of not liking spicy food and the forest on fire is 37%. The probability of liking spicy food and the forest on fire is 2%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.37/0.97 = 0.42
0.42 > 0",fork,forest_fire,1,correlation,P(Y | X)
1801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 43%. For people who like spicy food, the probability of the forest on fire is 81%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.81
0.81 - 0.43 = 0.38
0.38 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 43%. For people who like spicy food, the probability of the forest on fire is 81%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.81
0.81 - 0.43 = 0.38
0.38 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 16%. The probability of not liking spicy food and the forest on fire is 36%. The probability of liking spicy food and the forest on fire is 13%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.13
0.13/0.16 - 0.36/0.84 = 0.38
0.38 > 0",fork,forest_fire,1,correlation,P(Y | X)
1808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 29%. For people who do not like spicy food, the probability of the forest on fire is 15%. For people who like spicy food, the probability of the forest on fire is 50%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.15
P(Y=1 | X=1) = 0.50
0.29*0.50 - 0.71*0.15 = 0.25
0.25 > 0",fork,forest_fire,1,marginal,P(Y)
1818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 50%. For people who like spicy food, the probability of the forest on fire is 95%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.95
0.95 - 0.50 = 0.44
0.44 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1823,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 50%. For people who like spicy food, the probability of the forest on fire is 95%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.95
0.95 - 0.50 = 0.44
0.44 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 13%. For people who do not like spicy food, the probability of the forest on fire is 50%. For people who like spicy food, the probability of the forest on fire is 95%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.95
0.13*0.95 - 0.87*0.50 = 0.56
0.56 > 0",fork,forest_fire,1,marginal,P(Y)
1826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 13%. The probability of not liking spicy food and the forest on fire is 43%. The probability of liking spicy food and the forest on fire is 13%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.13
0.13/0.13 - 0.43/0.87 = 0.44
0.44 > 0",fork,forest_fire,1,correlation,P(Y | X)
1827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 13%. The probability of not liking spicy food and the forest on fire is 43%. The probability of liking spicy food and the forest on fire is 13%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.13
0.13/0.13 - 0.43/0.87 = 0.44
0.44 > 0",fork,forest_fire,1,correlation,P(Y | X)
1833,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 37%. For people who like spicy food, the probability of the forest on fire is 67%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.67
0.67 - 0.37 = 0.30
0.30 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1835,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 5%. For people who do not like spicy food, the probability of the forest on fire is 37%. For people who like spicy food, the probability of the forest on fire is 67%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.67
0.05*0.67 - 0.95*0.37 = 0.38
0.38 > 0",fork,forest_fire,1,marginal,P(Y)
1836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 5%. The probability of not liking spicy food and the forest on fire is 35%. The probability of liking spicy food and the forest on fire is 3%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.35/0.95 = 0.30
0.30 > 0",fork,forest_fire,1,correlation,P(Y | X)
1838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 42%. For people who like spicy food, the probability of the forest on fire is 76%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.76
0.76 - 0.42 = 0.34
0.34 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 28%. For people who like spicy food, the probability of the forest on fire is 74%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.74
0.74 - 0.28 = 0.46
0.46 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 28%. For people who like spicy food, the probability of the forest on fire is 74%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.74
0.74 - 0.28 = 0.46
0.46 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 28%. For people who do not like spicy food, the probability of the forest on fire is 28%. For people who like spicy food, the probability of the forest on fire is 74%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.28
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.74
0.28*0.74 - 0.72*0.28 = 0.41
0.41 > 0",fork,forest_fire,1,marginal,P(Y)
1855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 28%. For people who do not like spicy food, the probability of the forest on fire is 28%. For people who like spicy food, the probability of the forest on fire is 74%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.28
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.74
0.28*0.74 - 0.72*0.28 = 0.41
0.41 > 0",fork,forest_fire,1,marginal,P(Y)
1858,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 34%. For people who like spicy food, the probability of the forest on fire is 67%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.67
0.67 - 0.34 = 0.33
0.33 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 34%. For people who like spicy food, the probability of the forest on fire is 67%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.67
0.67 - 0.34 = 0.33
0.33 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1862,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 34%. For people who like spicy food, the probability of the forest on fire is 67%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.67
0.67 - 0.34 = 0.33
0.33 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 43%. For people who like spicy food, the probability of the forest on fire is 77%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.77
0.77 - 0.43 = 0.34
0.34 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1877,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 28%. The probability of not liking spicy food and the forest on fire is 31%. The probability of liking spicy food and the forest on fire is 21%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.28
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.21
0.21/0.28 - 0.31/0.72 = 0.34
0.34 > 0",fork,forest_fire,1,correlation,P(Y | X)
1888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1892,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 35%. For people who like spicy food, the probability of the forest on fire is 84%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.84
0.84 - 0.35 = 0.48
0.48 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 35%. For people who like spicy food, the probability of the forest on fire is 84%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.84
0.84 - 0.35 = 0.48
0.48 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 1%. For people who do not like spicy food, the probability of the forest on fire is 35%. For people who like spicy food, the probability of the forest on fire is 84%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.84
0.01*0.84 - 0.99*0.35 = 0.36
0.36 > 0",fork,forest_fire,1,marginal,P(Y)
1896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 1%. The probability of not liking spicy food and the forest on fire is 35%. The probability of liking spicy food and the forest on fire is 1%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.01
0.01/0.01 - 0.35/0.99 = 0.48
0.48 > 0",fork,forest_fire,1,correlation,P(Y | X)
1898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1900,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 52%. For people who like spicy food, the probability of the forest on fire is 88%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.88
0.88 - 0.52 = 0.36
0.36 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 52%. For people who like spicy food, the probability of the forest on fire is 88%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.88
0.88 - 0.52 = 0.36
0.36 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1907,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 30%. The probability of not liking spicy food and the forest on fire is 37%. The probability of liking spicy food and the forest on fire is 26%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.26
0.26/0.30 - 0.37/0.70 = 0.36
0.36 > 0",fork,forest_fire,1,correlation,P(Y | X)
1914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 24%. For people who do not like spicy food, the probability of the forest on fire is 34%. For people who like spicy food, the probability of the forest on fire is 60%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.60
0.24*0.60 - 0.76*0.34 = 0.41
0.41 > 0",fork,forest_fire,1,marginal,P(Y)
1915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 24%. For people who do not like spicy food, the probability of the forest on fire is 34%. For people who like spicy food, the probability of the forest on fire is 60%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.60
0.24*0.60 - 0.76*0.34 = 0.41
0.41 > 0",fork,forest_fire,1,marginal,P(Y)
1923,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 36%. For people who like spicy food, the probability of the forest on fire is 75%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.75
0.75 - 0.36 = 0.38
0.38 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 22%. For people who do not like spicy food, the probability of the forest on fire is 36%. For people who like spicy food, the probability of the forest on fire is 75%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.75
0.22*0.75 - 0.78*0.36 = 0.45
0.45 > 0",fork,forest_fire,1,marginal,P(Y)
1928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1930,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 47%. For people who like spicy food, the probability of the forest on fire is 75%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.75
0.75 - 0.47 = 0.27
0.27 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1932,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 47%. For people who like spicy food, the probability of the forest on fire is 75%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.75
0.75 - 0.47 = 0.27
0.27 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1936,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 30%. The probability of not liking spicy food and the forest on fire is 33%. The probability of liking spicy food and the forest on fire is 22%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.22
0.22/0.30 - 0.33/0.70 = 0.27
0.27 > 0",fork,forest_fire,1,correlation,P(Y | X)
1938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 28%. For people who like spicy food, the probability of the forest on fire is 86%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.86
0.86 - 0.28 = 0.58
0.58 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 28%. For people who like spicy food, the probability of the forest on fire is 86%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.86
0.86 - 0.28 = 0.58
0.58 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 14%. For people who do not like spicy food, the probability of the forest on fire is 28%. For people who like spicy food, the probability of the forest on fire is 86%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.86
0.14*0.86 - 0.86*0.28 = 0.36
0.36 > 0",fork,forest_fire,1,marginal,P(Y)
1948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 27%. For people who like spicy food, the probability of the forest on fire is 60%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.60
0.60 - 0.27 = 0.34
0.34 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 27%. For people who like spicy food, the probability of the forest on fire is 60%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.60
0.60 - 0.27 = 0.34
0.34 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 27%. For people who like spicy food, the probability of the forest on fire is 60%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.60
0.60 - 0.27 = 0.34
0.34 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 22%. For people who do not like spicy food, the probability of the forest on fire is 27%. For people who like spicy food, the probability of the forest on fire is 60%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.60
0.22*0.60 - 0.78*0.27 = 0.34
0.34 > 0",fork,forest_fire,1,marginal,P(Y)
1958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 36%. For people who like spicy food, the probability of the forest on fire is 65%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.65
0.65 - 0.36 = 0.29
0.29 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 22%. For people who do not like spicy food, the probability of the forest on fire is 36%. For people who like spicy food, the probability of the forest on fire is 65%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.65
0.22*0.65 - 0.78*0.36 = 0.42
0.42 > 0",fork,forest_fire,1,marginal,P(Y)
1966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 22%. The probability of not liking spicy food and the forest on fire is 28%. The probability of liking spicy food and the forest on fire is 14%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.22
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.14
0.14/0.22 - 0.28/0.78 = 0.29
0.29 > 0",fork,forest_fire,1,correlation,P(Y | X)
1973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 41%. For people who like spicy food, the probability of the forest on fire is 82%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.82
0.82 - 0.41 = 0.41
0.41 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 7%. For people who do not like spicy food, the probability of the forest on fire is 41%. For people who like spicy food, the probability of the forest on fire is 82%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.82
0.07*0.82 - 0.93*0.41 = 0.44
0.44 > 0",fork,forest_fire,1,marginal,P(Y)
1976,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 7%. The probability of not liking spicy food and the forest on fire is 38%. The probability of liking spicy food and the forest on fire is 6%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.06
0.06/0.07 - 0.38/0.93 = 0.41
0.41 > 0",fork,forest_fire,1,correlation,P(Y | X)
1977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 7%. The probability of not liking spicy food and the forest on fire is 38%. The probability of liking spicy food and the forest on fire is 6%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.06
0.06/0.07 - 0.38/0.93 = 0.41
0.41 > 0",fork,forest_fire,1,correlation,P(Y | X)
1978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
1982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 43%. For people who like spicy food, the probability of the forest on fire is 72%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.72
0.72 - 0.43 = 0.29
0.29 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1983,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 43%. For people who like spicy food, the probability of the forest on fire is 72%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.72
0.72 - 0.43 = 0.29
0.29 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 10%. The probability of not liking spicy food and the forest on fire is 39%. The probability of liking spicy food and the forest on fire is 7%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.07
0.07/0.10 - 0.39/0.90 = 0.29
0.29 > 0",fork,forest_fire,1,correlation,P(Y | X)
1991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 23%. For people who like spicy food, the probability of the forest on fire is 58%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.58
0.58 - 0.23 = 0.35
0.35 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
1993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 23%. For people who like spicy food, the probability of the forest on fire is 58%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.58
0.58 - 0.23 = 0.35
0.35 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
1996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 5%. The probability of not liking spicy food and the forest on fire is 21%. The probability of liking spicy food and the forest on fire is 3%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.21/0.95 = 0.35
0.35 > 0",fork,forest_fire,1,correlation,P(Y | X)
1998,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
2000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 26%. For people who like spicy food, the probability of the forest on fire is 69%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.69
0.69 - 0.26 = 0.43
0.43 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 26%. For people who like spicy food, the probability of the forest on fire is 69%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.69
0.69 - 0.26 = 0.43
0.43 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 3%. For people who do not like spicy food, the probability of the forest on fire is 26%. For people who like spicy food, the probability of the forest on fire is 69%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.69
0.03*0.69 - 0.97*0.26 = 0.28
0.28 > 0",fork,forest_fire,1,marginal,P(Y)
2005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 3%. For people who do not like spicy food, the probability of the forest on fire is 26%. For people who like spicy food, the probability of the forest on fire is 69%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.69
0.03*0.69 - 0.97*0.26 = 0.28
0.28 > 0",fork,forest_fire,1,marginal,P(Y)
2008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
2009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
2011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 34%. For people who like spicy food, the probability of the forest on fire is 63%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.63
0.63 - 0.34 = 0.30
0.30 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2013,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 34%. For people who like spicy food, the probability of the forest on fire is 63%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.63
0.63 - 0.34 = 0.30
0.30 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 24%. For people who do not like spicy food, the probability of the forest on fire is 34%. For people who like spicy food, the probability of the forest on fire is 63%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.63
0.24*0.63 - 0.76*0.34 = 0.41
0.41 > 0",fork,forest_fire,1,marginal,P(Y)
2017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 24%. The probability of not liking spicy food and the forest on fire is 25%. The probability of liking spicy food and the forest on fire is 15%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.15
0.15/0.24 - 0.25/0.76 = 0.30
0.30 > 0",fork,forest_fire,1,correlation,P(Y | X)
2019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
2020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 39%. For people who like spicy food, the probability of the forest on fire is 68%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.68
0.68 - 0.39 = 0.29
0.29 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2021,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 39%. For people who like spicy food, the probability of the forest on fire is 68%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.68
0.68 - 0.39 = 0.29
0.29 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 17%. For people who do not like spicy food, the probability of the forest on fire is 39%. For people who like spicy food, the probability of the forest on fire is 68%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.68
0.17*0.68 - 0.83*0.39 = 0.44
0.44 > 0",fork,forest_fire,1,marginal,P(Y)
2029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how liking spicy food correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
2030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 17%. For people who like spicy food, the probability of the forest on fire is 66%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.66
0.66 - 0.17 = 0.49
0.49 > 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not like spicy food, the probability of the forest on fire is 17%. For people who like spicy food, the probability of the forest on fire is 66%.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.66
0.66 - 0.17 = 0.49
0.49 > 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2036,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of liking spicy food is 27%. The probability of not liking spicy food and the forest on fire is 13%. The probability of liking spicy food and the forest on fire is 18%.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.27
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.18
0.18/0.27 - 0.13/0.73 = 0.49
0.49 > 0",fork,forest_fire,1,correlation,P(Y | X)
2038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how liking spicy food correlates with the forest case by case according to the smoker. Method 2: We look directly at how liking spicy food correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
2041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 77%. For situations where there is a solar eclipse, the probability of arriving to school on time is 41%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.41
0.41 - 0.77 = -0.36
-0.36 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 89%. For situations where there is no solar eclipse, the probability of arriving to school on time is 77%. For situations where there is a solar eclipse, the probability of arriving to school on time is 41%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.41
0.89*0.41 - 0.11*0.77 = 0.45
0.45 > 0",fork,getting_late,1,marginal,P(Y)
2046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 89%. The probability of no solar eclipse and arriving to school on time is 8%. The probability of solar eclipse and arriving to school on time is 37%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.37
0.37/0.89 - 0.08/0.11 = -0.36
-0.36 < 0",fork,getting_late,1,correlation,P(Y | X)
2050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 88%. For situations where there is a solar eclipse, the probability of arriving to school on time is 35%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.35
0.35 - 0.88 = -0.52
-0.52 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 88%. For situations where there is a solar eclipse, the probability of arriving to school on time is 35%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.35
0.35 - 0.88 = -0.52
-0.52 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2055,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 40%. For situations where there is no solar eclipse, the probability of arriving to school on time is 88%. For situations where there is a solar eclipse, the probability of arriving to school on time is 35%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.35
0.40*0.35 - 0.60*0.88 = 0.67
0.67 > 0",fork,getting_late,1,marginal,P(Y)
2056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 40%. The probability of no solar eclipse and arriving to school on time is 53%. The probability of solar eclipse and arriving to school on time is 14%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.14
0.14/0.40 - 0.53/0.60 = -0.52
-0.52 < 0",fork,getting_late,1,correlation,P(Y | X)
2060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 74%. For situations where there is a solar eclipse, the probability of arriving to school on time is 38%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.38
0.38 - 0.74 = -0.36
-0.36 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2062,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 74%. For situations where there is a solar eclipse, the probability of arriving to school on time is 38%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.38
0.38 - 0.74 = -0.36
-0.36 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 74%. For situations where there is a solar eclipse, the probability of arriving to school on time is 38%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.38
0.38 - 0.74 = -0.36
-0.36 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 53%. The probability of no solar eclipse and arriving to school on time is 35%. The probability of solar eclipse and arriving to school on time is 20%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.20
0.20/0.53 - 0.35/0.47 = -0.36
-0.36 < 0",fork,getting_late,1,correlation,P(Y | X)
2068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 69%. For situations where there is a solar eclipse, the probability of arriving to school on time is 36%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.36
0.36 - 0.69 = -0.33
-0.33 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 69%. For situations where there is a solar eclipse, the probability of arriving to school on time is 36%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.36
0.36 - 0.69 = -0.33
-0.33 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 33%. The probability of no solar eclipse and arriving to school on time is 46%. The probability of solar eclipse and arriving to school on time is 12%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.33
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.12
0.12/0.33 - 0.46/0.67 = -0.33
-0.33 < 0",fork,getting_late,1,correlation,P(Y | X)
2085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 65%. For situations where there is no solar eclipse, the probability of arriving to school on time is 67%. For situations where there is a solar eclipse, the probability of arriving to school on time is 37%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.65
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.37
0.65*0.37 - 0.35*0.67 = 0.48
0.48 > 0",fork,getting_late,1,marginal,P(Y)
2087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 65%. The probability of no solar eclipse and arriving to school on time is 23%. The probability of solar eclipse and arriving to school on time is 24%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.24
0.24/0.65 - 0.23/0.35 = -0.30
-0.30 < 0",fork,getting_late,1,correlation,P(Y | X)
2092,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 59%. For situations where there is a solar eclipse, the probability of arriving to school on time is 33%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.33
0.33 - 0.59 = -0.27
-0.27 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 32%. The probability of no solar eclipse and arriving to school on time is 41%. The probability of solar eclipse and arriving to school on time is 10%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.32
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.10
0.10/0.32 - 0.41/0.68 = -0.27
-0.27 < 0",fork,getting_late,1,correlation,P(Y | X)
2105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 71%. For situations where there is no solar eclipse, the probability of arriving to school on time is 66%. For situations where there is a solar eclipse, the probability of arriving to school on time is 26%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.26
0.71*0.26 - 0.29*0.66 = 0.38
0.38 > 0",fork,getting_late,1,marginal,P(Y)
2106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 71%. The probability of no solar eclipse and arriving to school on time is 19%. The probability of solar eclipse and arriving to school on time is 19%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.71
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.19
0.19/0.71 - 0.19/0.29 = -0.40
-0.40 < 0",fork,getting_late,1,correlation,P(Y | X)
2108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2111,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 62%. For situations where there is a solar eclipse, the probability of arriving to school on time is 31%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.31
0.31 - 0.62 = -0.31
-0.31 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 62%. For situations where there is a solar eclipse, the probability of arriving to school on time is 31%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.31
0.31 - 0.62 = -0.31
-0.31 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 42%. For situations where there is no solar eclipse, the probability of arriving to school on time is 62%. For situations where there is a solar eclipse, the probability of arriving to school on time is 31%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.31
0.42*0.31 - 0.58*0.62 = 0.49
0.49 > 0",fork,getting_late,1,marginal,P(Y)
2116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 42%. The probability of no solar eclipse and arriving to school on time is 36%. The probability of solar eclipse and arriving to school on time is 13%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.13
0.13/0.42 - 0.36/0.58 = -0.31
-0.31 < 0",fork,getting_late,1,correlation,P(Y | X)
2119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2122,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 76%. For situations where there is a solar eclipse, the probability of arriving to school on time is 25%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.25
0.25 - 0.76 = -0.51
-0.51 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 76%. For situations where there is a solar eclipse, the probability of arriving to school on time is 25%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.25
0.25 - 0.76 = -0.51
-0.51 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 58%. The probability of no solar eclipse and arriving to school on time is 32%. The probability of solar eclipse and arriving to school on time is 15%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.15
0.15/0.58 - 0.32/0.42 = -0.51
-0.51 < 0",fork,getting_late,1,correlation,P(Y | X)
2130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 81%. For situations where there is a solar eclipse, the probability of arriving to school on time is 48%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.48
0.48 - 0.81 = -0.32
-0.32 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 81%. For situations where there is a solar eclipse, the probability of arriving to school on time is 48%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.48
0.48 - 0.81 = -0.32
-0.32 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 38%. For situations where there is no solar eclipse, the probability of arriving to school on time is 81%. For situations where there is a solar eclipse, the probability of arriving to school on time is 48%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.38
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.48
0.38*0.48 - 0.62*0.81 = 0.68
0.68 > 0",fork,getting_late,1,marginal,P(Y)
2136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 38%. The probability of no solar eclipse and arriving to school on time is 50%. The probability of solar eclipse and arriving to school on time is 19%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.19
0.19/0.38 - 0.50/0.62 = -0.32
-0.32 < 0",fork,getting_late,1,correlation,P(Y | X)
2138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 64%. For situations where there is a solar eclipse, the probability of arriving to school on time is 33%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.33
0.33 - 0.64 = -0.31
-0.31 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 64%. For situations where there is a solar eclipse, the probability of arriving to school on time is 33%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.33
0.33 - 0.64 = -0.31
-0.31 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 56%. For situations where there is a solar eclipse, the probability of arriving to school on time is 24%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.24
0.24 - 0.56 = -0.32
-0.32 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 56%. For situations where there is a solar eclipse, the probability of arriving to school on time is 24%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.24
0.24 - 0.56 = -0.32
-0.32 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 49%. For situations where there is a solar eclipse, the probability of arriving to school on time is 14%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.14
0.14 - 0.49 = -0.36
-0.36 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2166,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 85%. The probability of no solar eclipse and arriving to school on time is 7%. The probability of solar eclipse and arriving to school on time is 12%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.12
0.12/0.85 - 0.07/0.15 = -0.36
-0.36 < 0",fork,getting_late,1,correlation,P(Y | X)
2167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 85%. The probability of no solar eclipse and arriving to school on time is 7%. The probability of solar eclipse and arriving to school on time is 12%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.12
0.12/0.85 - 0.07/0.15 = -0.36
-0.36 < 0",fork,getting_late,1,correlation,P(Y | X)
2170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 49%. For situations where there is a solar eclipse, the probability of arriving to school on time is 8%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.08
0.08 - 0.49 = -0.41
-0.41 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 49%. For situations where there is a solar eclipse, the probability of arriving to school on time is 8%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.08
0.08 - 0.49 = -0.41
-0.41 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 49%. For situations where there is a solar eclipse, the probability of arriving to school on time is 8%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.08
0.08 - 0.49 = -0.41
-0.41 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 64%. For situations where there is a solar eclipse, the probability of arriving to school on time is 25%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.25
0.25 - 0.64 = -0.40
-0.40 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2185,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 51%. For situations where there is no solar eclipse, the probability of arriving to school on time is 64%. For situations where there is a solar eclipse, the probability of arriving to school on time is 25%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.25
0.51*0.25 - 0.49*0.64 = 0.44
0.44 > 0",fork,getting_late,1,marginal,P(Y)
2187,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 51%. The probability of no solar eclipse and arriving to school on time is 31%. The probability of solar eclipse and arriving to school on time is 13%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.13
0.13/0.51 - 0.31/0.49 = -0.40
-0.40 < 0",fork,getting_late,1,correlation,P(Y | X)
2188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 95%. For situations where there is a solar eclipse, the probability of arriving to school on time is 31%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.31
0.31 - 0.95 = -0.64
-0.64 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 48%. For situations where there is no solar eclipse, the probability of arriving to school on time is 95%. For situations where there is a solar eclipse, the probability of arriving to school on time is 31%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.31
0.48*0.31 - 0.52*0.95 = 0.64
0.64 > 0",fork,getting_late,1,marginal,P(Y)
2196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 48%. The probability of no solar eclipse and arriving to school on time is 49%. The probability of solar eclipse and arriving to school on time is 15%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.15
0.15/0.48 - 0.49/0.52 = -0.64
-0.64 < 0",fork,getting_late,1,correlation,P(Y | X)
2198,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 60%. For situations where there is a solar eclipse, the probability of arriving to school on time is 33%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.33
0.33 - 0.60 = -0.27
-0.27 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 64%. For situations where there is no solar eclipse, the probability of arriving to school on time is 60%. For situations where there is a solar eclipse, the probability of arriving to school on time is 33%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.64
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.33
0.64*0.33 - 0.36*0.60 = 0.43
0.43 > 0",fork,getting_late,1,marginal,P(Y)
2206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 64%. The probability of no solar eclipse and arriving to school on time is 22%. The probability of solar eclipse and arriving to school on time is 21%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.21
0.21/0.64 - 0.22/0.36 = -0.27
-0.27 < 0",fork,getting_late,1,correlation,P(Y | X)
2207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 64%. The probability of no solar eclipse and arriving to school on time is 22%. The probability of solar eclipse and arriving to school on time is 21%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.21
0.21/0.64 - 0.22/0.36 = -0.27
-0.27 < 0",fork,getting_late,1,correlation,P(Y | X)
2213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 71%. For situations where there is a solar eclipse, the probability of arriving to school on time is 24%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.24
0.24 - 0.71 = -0.47
-0.47 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 56%. For situations where there is a solar eclipse, the probability of arriving to school on time is 24%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.24
0.24 - 0.56 = -0.32
-0.32 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 81%. For situations where there is no solar eclipse, the probability of arriving to school on time is 56%. For situations where there is a solar eclipse, the probability of arriving to school on time is 24%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.24
0.81*0.24 - 0.19*0.56 = 0.30
0.30 > 0",fork,getting_late,1,marginal,P(Y)
2225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 81%. For situations where there is no solar eclipse, the probability of arriving to school on time is 56%. For situations where there is a solar eclipse, the probability of arriving to school on time is 24%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.24
0.81*0.24 - 0.19*0.56 = 0.30
0.30 > 0",fork,getting_late,1,marginal,P(Y)
2227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 81%. The probability of no solar eclipse and arriving to school on time is 11%. The probability of solar eclipse and arriving to school on time is 19%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.19
0.19/0.81 - 0.11/0.19 = -0.32
-0.32 < 0",fork,getting_late,1,correlation,P(Y | X)
2230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 74%. For situations where there is a solar eclipse, the probability of arriving to school on time is 30%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.30
0.30 - 0.74 = -0.44
-0.44 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 74%. For situations where there is a solar eclipse, the probability of arriving to school on time is 30%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.30
0.30 - 0.74 = -0.44
-0.44 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 74%. For situations where there is a solar eclipse, the probability of arriving to school on time is 30%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.30
0.30 - 0.74 = -0.44
-0.44 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 32%. For situations where there is no solar eclipse, the probability of arriving to school on time is 74%. For situations where there is a solar eclipse, the probability of arriving to school on time is 30%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.30
0.32*0.30 - 0.68*0.74 = 0.60
0.60 > 0",fork,getting_late,1,marginal,P(Y)
2237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 32%. The probability of no solar eclipse and arriving to school on time is 51%. The probability of solar eclipse and arriving to school on time is 10%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.32
P(Y=1, X=0=1) = 0.51
P(Y=1, X=1=1) = 0.10
0.10/0.32 - 0.51/0.68 = -0.44
-0.44 < 0",fork,getting_late,1,correlation,P(Y | X)
2239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 85%. For situations where there is a solar eclipse, the probability of arriving to school on time is 49%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.49
0.49 - 0.85 = -0.37
-0.37 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 85%. For situations where there is a solar eclipse, the probability of arriving to school on time is 49%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.49
0.49 - 0.85 = -0.37
-0.37 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 63%. The probability of no solar eclipse and arriving to school on time is 32%. The probability of solar eclipse and arriving to school on time is 31%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.31
0.31/0.63 - 0.32/0.37 = -0.37
-0.37 < 0",fork,getting_late,1,correlation,P(Y | X)
2247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 63%. The probability of no solar eclipse and arriving to school on time is 32%. The probability of solar eclipse and arriving to school on time is 31%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.31
0.31/0.63 - 0.32/0.37 = -0.37
-0.37 < 0",fork,getting_late,1,correlation,P(Y | X)
2248,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 39%. For situations where there is a solar eclipse, the probability of arriving to school on time is 4%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.04
0.04 - 0.39 = -0.34
-0.34 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 49%. For situations where there is no solar eclipse, the probability of arriving to school on time is 39%. For situations where there is a solar eclipse, the probability of arriving to school on time is 4%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.04
0.49*0.04 - 0.51*0.39 = 0.22
0.22 > 0",fork,getting_late,1,marginal,P(Y)
2255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 49%. For situations where there is no solar eclipse, the probability of arriving to school on time is 39%. For situations where there is a solar eclipse, the probability of arriving to school on time is 4%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.04
0.49*0.04 - 0.51*0.39 = 0.22
0.22 > 0",fork,getting_late,1,marginal,P(Y)
2256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 49%. The probability of no solar eclipse and arriving to school on time is 20%. The probability of solar eclipse and arriving to school on time is 2%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.02
0.02/0.49 - 0.20/0.51 = -0.34
-0.34 < 0",fork,getting_late,1,correlation,P(Y | X)
2258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 56%. For situations where there is a solar eclipse, the probability of arriving to school on time is 18%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.18
0.18 - 0.56 = -0.39
-0.39 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2262,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 56%. For situations where there is a solar eclipse, the probability of arriving to school on time is 18%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.18
0.18 - 0.56 = -0.39
-0.39 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 72%. For situations where there is no solar eclipse, the probability of arriving to school on time is 56%. For situations where there is a solar eclipse, the probability of arriving to school on time is 18%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.72
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.18
0.72*0.18 - 0.28*0.56 = 0.28
0.28 > 0",fork,getting_late,1,marginal,P(Y)
2267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 72%. The probability of no solar eclipse and arriving to school on time is 16%. The probability of solar eclipse and arriving to school on time is 13%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.72
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.13
0.13/0.72 - 0.16/0.28 = -0.39
-0.39 < 0",fork,getting_late,1,correlation,P(Y | X)
2268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 88%. For situations where there is a solar eclipse, the probability of arriving to school on time is 45%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.45
0.45 - 0.88 = -0.43
-0.43 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 88%. For situations where there is a solar eclipse, the probability of arriving to school on time is 45%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.45
0.45 - 0.88 = -0.43
-0.43 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 88%. For situations where there is a solar eclipse, the probability of arriving to school on time is 45%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.45
0.45 - 0.88 = -0.43
-0.43 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 42%. For situations where there is no solar eclipse, the probability of arriving to school on time is 88%. For situations where there is a solar eclipse, the probability of arriving to school on time is 45%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.45
0.42*0.45 - 0.58*0.88 = 0.70
0.70 > 0",fork,getting_late,1,marginal,P(Y)
2285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 79%. For situations where there is no solar eclipse, the probability of arriving to school on time is 81%. For situations where there is a solar eclipse, the probability of arriving to school on time is 41%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.79
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.41
0.79*0.41 - 0.21*0.81 = 0.49
0.49 > 0",fork,getting_late,1,marginal,P(Y)
2289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 50%. For situations where there is a solar eclipse, the probability of arriving to school on time is 5%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.05
0.05 - 0.50 = -0.45
-0.45 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 50%. For situations where there is a solar eclipse, the probability of arriving to school on time is 5%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.05
0.05 - 0.50 = -0.45
-0.45 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 50%. For situations where there is a solar eclipse, the probability of arriving to school on time is 5%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.05
0.05 - 0.50 = -0.45
-0.45 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 40%. For situations where there is no solar eclipse, the probability of arriving to school on time is 50%. For situations where there is a solar eclipse, the probability of arriving to school on time is 5%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.05
0.40*0.05 - 0.60*0.50 = 0.32
0.32 > 0",fork,getting_late,1,marginal,P(Y)
2295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 40%. For situations where there is no solar eclipse, the probability of arriving to school on time is 50%. For situations where there is a solar eclipse, the probability of arriving to school on time is 5%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.05
0.40*0.05 - 0.60*0.50 = 0.32
0.32 > 0",fork,getting_late,1,marginal,P(Y)
2309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2310,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 86%. For situations where there is a solar eclipse, the probability of arriving to school on time is 47%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.47
0.47 - 0.86 = -0.39
-0.39 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 86%. For situations where there is a solar eclipse, the probability of arriving to school on time is 47%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.47
0.47 - 0.86 = -0.39
-0.39 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 86%. For situations where there is a solar eclipse, the probability of arriving to school on time is 47%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.47
0.47 - 0.86 = -0.39
-0.39 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 48%. For situations where there is no solar eclipse, the probability of arriving to school on time is 86%. For situations where there is a solar eclipse, the probability of arriving to school on time is 47%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.47
0.48*0.47 - 0.52*0.86 = 0.67
0.67 > 0",fork,getting_late,1,marginal,P(Y)
2316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 48%. The probability of no solar eclipse and arriving to school on time is 44%. The probability of solar eclipse and arriving to school on time is 23%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.23
0.23/0.48 - 0.44/0.52 = -0.39
-0.39 < 0",fork,getting_late,1,correlation,P(Y | X)
2318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 60%. For situations where there is a solar eclipse, the probability of arriving to school on time is 26%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.26
0.26 - 0.60 = -0.35
-0.35 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 60%. For situations where there is a solar eclipse, the probability of arriving to school on time is 26%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.26
0.26 - 0.60 = -0.35
-0.35 < 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 49%. The probability of no solar eclipse and arriving to school on time is 31%. The probability of solar eclipse and arriving to school on time is 13%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.13
0.13/0.49 - 0.31/0.51 = -0.35
-0.35 < 0",fork,getting_late,1,correlation,P(Y | X)
2327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 49%. The probability of no solar eclipse and arriving to school on time is 31%. The probability of solar eclipse and arriving to school on time is 13%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.13
0.13/0.49 - 0.31/0.51 = -0.35
-0.35 < 0",fork,getting_late,1,correlation,P(Y | X)
2330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. For situations where there is no solar eclipse, the probability of arriving to school on time is 60%. For situations where there is a solar eclipse, the probability of arriving to school on time is 22%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.22
0.22 - 0.60 = -0.38
-0.38 < 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 61%. For situations where there is no solar eclipse, the probability of arriving to school on time is 60%. For situations where there is a solar eclipse, the probability of arriving to school on time is 22%.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.22
0.61*0.22 - 0.39*0.60 = 0.37
0.37 > 0",fork,getting_late,1,marginal,P(Y)
2335,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. The overall probability of solar eclipse is 61%. For situations where there is no solar eclipse, the probability of arriving to school on time is 60%. For situations where there is a solar eclipse, the probability of arriving to school on time is 22%.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.22
0.61*0.22 - 0.39*0.60 = 0.37
0.37 > 0",fork,getting_late,1,marginal,P(Y)
2338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look at how solar eclipse correlates with Alice arriving to school case by case according to traffic. Method 2: We look directly at how solar eclipse correlates with Alice arriving to school in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2339,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. Method 1: We look directly at how solar eclipse correlates with Alice arriving to school in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
2340,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 27%. For people who went to tanning salons, the probability of large feet is 83%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.83
0.83 - 0.27 = 0.56
0.56 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 27%. For people who went to tanning salons, the probability of large feet is 83%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.83
0.83 - 0.27 = 0.56
0.56 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 27%. For people who went to tanning salons, the probability of large feet is 83%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.83
0.83 - 0.27 = 0.56
0.56 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 3%. For people not using tanning salon treatments, the probability of large feet is 27%. For people who went to tanning salons, the probability of large feet is 83%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.83
0.03*0.83 - 0.97*0.27 = 0.28
0.28 > 0",fork,getting_tanned,1,marginal,P(Y)
2347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 3%. The probability of no tanning salon treatment and large feet is 26%. The probability of tanning salon treatment and large feet is 2%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.26/0.97 = 0.56
0.56 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2350,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 31%. For people who went to tanning salons, the probability of large feet is 95%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.95
0.95 - 0.31 = 0.64
0.64 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 31%. For people who went to tanning salons, the probability of large feet is 95%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.95
0.95 - 0.31 = 0.64
0.64 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 8%. For people not using tanning salon treatments, the probability of large feet is 31%. For people who went to tanning salons, the probability of large feet is 95%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.95
0.08*0.95 - 0.92*0.31 = 0.36
0.36 > 0",fork,getting_tanned,1,marginal,P(Y)
2356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 8%. The probability of no tanning salon treatment and large feet is 28%. The probability of tanning salon treatment and large feet is 8%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.08
0.08/0.08 - 0.28/0.92 = 0.64
0.64 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 8%. The probability of no tanning salon treatment and large feet is 28%. The probability of tanning salon treatment and large feet is 8%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.08
0.08/0.08 - 0.28/0.92 = 0.64
0.64 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look directly at how tanning salon treatment correlates with foot size in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 17%. For people who went to tanning salons, the probability of large feet is 67%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.67
0.67 - 0.17 = 0.50
0.50 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 17%. For people who went to tanning salons, the probability of large feet is 67%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.67
0.67 - 0.17 = 0.50
0.50 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2365,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 2%. For people not using tanning salon treatments, the probability of large feet is 17%. For people who went to tanning salons, the probability of large feet is 67%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.67
0.02*0.67 - 0.98*0.17 = 0.18
0.18 > 0",fork,getting_tanned,1,marginal,P(Y)
2366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 2%. The probability of no tanning salon treatment and large feet is 17%. The probability of tanning salon treatment and large feet is 2%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.02
0.02/0.02 - 0.17/0.98 = 0.50
0.50 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 24%. For people who went to tanning salons, the probability of large feet is 68%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.68
0.68 - 0.24 = 0.45
0.45 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 24%. For people who went to tanning salons, the probability of large feet is 68%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.68
0.68 - 0.24 = 0.45
0.45 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look directly at how tanning salon treatment correlates with foot size in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 23%. For people who went to tanning salons, the probability of large feet is 71%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.71
0.71 - 0.23 = 0.48
0.48 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 0%. The probability of no tanning salon treatment and large feet is 23%. The probability of tanning salon treatment and large feet is 0%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.00
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.00
0.00/0.00 - 0.23/1.00 = 0.48
0.48 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 4%. For people not using tanning salon treatments, the probability of large feet is 39%. For people who went to tanning salons, the probability of large feet is 85%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.85
0.04*0.85 - 0.96*0.39 = 0.41
0.41 > 0",fork,getting_tanned,1,marginal,P(Y)
2398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 15%. For people who went to tanning salons, the probability of large feet is 70%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.15
P(Y=1 | X=1) = 0.70
0.70 - 0.15 = 0.54
0.54 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 15%. For people who went to tanning salons, the probability of large feet is 70%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.15
P(Y=1 | X=1) = 0.70
0.70 - 0.15 = 0.54
0.54 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 15%. For people who went to tanning salons, the probability of large feet is 70%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.15
P(Y=1 | X=1) = 0.70
0.70 - 0.15 = 0.54
0.54 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 4%. For people not using tanning salon treatments, the probability of large feet is 15%. For people who went to tanning salons, the probability of large feet is 70%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.15
P(Y=1 | X=1) = 0.70
0.04*0.70 - 0.96*0.15 = 0.18
0.18 > 0",fork,getting_tanned,1,marginal,P(Y)
2406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 4%. The probability of no tanning salon treatment and large feet is 15%. The probability of tanning salon treatment and large feet is 3%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.03
0.03/0.04 - 0.15/0.96 = 0.54
0.54 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 6%. For people not using tanning salon treatments, the probability of large feet is 31%. For people who went to tanning salons, the probability of large feet is 85%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.85
0.06*0.85 - 0.94*0.31 = 0.34
0.34 > 0",fork,getting_tanned,1,marginal,P(Y)
2415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 6%. For people not using tanning salon treatments, the probability of large feet is 31%. For people who went to tanning salons, the probability of large feet is 85%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.85
0.06*0.85 - 0.94*0.31 = 0.34
0.34 > 0",fork,getting_tanned,1,marginal,P(Y)
2424,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. For people not using tanning salon treatments, the probability of large feet is 16%. For people who went to tanning salons, the probability of large feet is 66%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.66
0.05*0.66 - 0.95*0.16 = 0.19
0.19 > 0",fork,getting_tanned,1,marginal,P(Y)
2425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. For people not using tanning salon treatments, the probability of large feet is 16%. For people who went to tanning salons, the probability of large feet is 66%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.66
0.05*0.66 - 0.95*0.16 = 0.19
0.19 > 0",fork,getting_tanned,1,marginal,P(Y)
2430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 25%. For people who went to tanning salons, the probability of large feet is 77%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.77
0.77 - 0.25 = 0.51
0.51 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2432,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 25%. For people who went to tanning salons, the probability of large feet is 77%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.77
0.77 - 0.25 = 0.51
0.51 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 25%. For people who went to tanning salons, the probability of large feet is 77%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.77
0.77 - 0.25 = 0.51
0.51 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look directly at how tanning salon treatment correlates with foot size in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 25%. For people who went to tanning salons, the probability of large feet is 73%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.73
0.73 - 0.25 = 0.49
0.49 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 25%. For people who went to tanning salons, the probability of large feet is 73%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.73
0.73 - 0.25 = 0.49
0.49 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2445,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 3%. For people not using tanning salon treatments, the probability of large feet is 25%. For people who went to tanning salons, the probability of large feet is 73%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.73
0.03*0.73 - 0.97*0.25 = 0.26
0.26 > 0",fork,getting_tanned,1,marginal,P(Y)
2446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 3%. The probability of no tanning salon treatment and large feet is 24%. The probability of tanning salon treatment and large feet is 2%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.24/0.97 = 0.49
0.49 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 3%. The probability of no tanning salon treatment and large feet is 24%. The probability of tanning salon treatment and large feet is 2%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.24/0.97 = 0.49
0.49 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 23%. For people who went to tanning salons, the probability of large feet is 76%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.76
0.76 - 0.23 = 0.53
0.53 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 23%. For people who went to tanning salons, the probability of large feet is 76%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.76
0.76 - 0.23 = 0.53
0.53 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. For people not using tanning salon treatments, the probability of large feet is 23%. For people who went to tanning salons, the probability of large feet is 76%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.76
0.05*0.76 - 0.95*0.23 = 0.25
0.25 > 0",fork,getting_tanned,1,marginal,P(Y)
2467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 7%. The probability of no tanning salon treatment and large feet is 26%. The probability of tanning salon treatment and large feet is 5%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.05
0.05/0.07 - 0.26/0.93 = 0.48
0.48 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 22%. For people who went to tanning salons, the probability of large feet is 78%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.78
0.78 - 0.22 = 0.56
0.56 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2475,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 1%. For people not using tanning salon treatments, the probability of large feet is 22%. For people who went to tanning salons, the probability of large feet is 78%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.78
0.01*0.78 - 0.99*0.22 = 0.23
0.23 > 0",fork,getting_tanned,1,marginal,P(Y)
2478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 21%. For people who went to tanning salons, the probability of large feet is 72%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.72
0.72 - 0.21 = 0.51
0.51 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 21%. For people who went to tanning salons, the probability of large feet is 72%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.72
0.72 - 0.21 = 0.51
0.51 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2485,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 1%. For people not using tanning salon treatments, the probability of large feet is 21%. For people who went to tanning salons, the probability of large feet is 72%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.72
0.01*0.72 - 0.99*0.21 = 0.21
0.21 > 0",fork,getting_tanned,1,marginal,P(Y)
2489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look directly at how tanning salon treatment correlates with foot size in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2491,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 27%. For people who went to tanning salons, the probability of large feet is 81%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.81
0.81 - 0.27 = 0.55
0.55 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 3%. For people not using tanning salon treatments, the probability of large feet is 27%. For people who went to tanning salons, the probability of large feet is 81%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.81
0.03*0.81 - 0.97*0.27 = 0.28
0.28 > 0",fork,getting_tanned,1,marginal,P(Y)
2500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 23%. For people who went to tanning salons, the probability of large feet is 82%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.82
0.82 - 0.23 = 0.59
0.59 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2514,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. For people not using tanning salon treatments, the probability of large feet is 14%. For people who went to tanning salons, the probability of large feet is 60%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.60
0.05*0.60 - 0.95*0.14 = 0.16
0.16 > 0",fork,getting_tanned,1,marginal,P(Y)
2516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. The probability of no tanning salon treatment and large feet is 13%. The probability of tanning salon treatment and large feet is 3%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.13/0.95 = 0.47
0.47 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. The probability of no tanning salon treatment and large feet is 13%. The probability of tanning salon treatment and large feet is 3%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.13/0.95 = 0.47
0.47 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 13%. For people who went to tanning salons, the probability of large feet is 70%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.70
0.70 - 0.13 = 0.57
0.57 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 13%. For people who went to tanning salons, the probability of large feet is 70%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.70
0.70 - 0.13 = 0.57
0.57 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 13%. For people who went to tanning salons, the probability of large feet is 70%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.70
0.70 - 0.13 = 0.57
0.57 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 10%. For people not using tanning salon treatments, the probability of large feet is 13%. For people who went to tanning salons, the probability of large feet is 70%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.70
0.10*0.70 - 0.90*0.13 = 0.18
0.18 > 0",fork,getting_tanned,1,marginal,P(Y)
2525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 10%. For people not using tanning salon treatments, the probability of large feet is 13%. For people who went to tanning salons, the probability of large feet is 70%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.70
0.10*0.70 - 0.90*0.13 = 0.18
0.18 > 0",fork,getting_tanned,1,marginal,P(Y)
2526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 10%. The probability of no tanning salon treatment and large feet is 11%. The probability of tanning salon treatment and large feet is 7%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.07
0.07/0.10 - 0.11/0.90 = 0.57
0.57 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 6%. For people who went to tanning salons, the probability of large feet is 57%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.57
0.57 - 0.06 = 0.51
0.51 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2537,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. The probability of no tanning salon treatment and large feet is 6%. The probability of tanning salon treatment and large feet is 3%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.06/0.95 = 0.51
0.51 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 7%. For people who went to tanning salons, the probability of large feet is 59%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.59
0.59 - 0.07 = 0.52
0.52 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 7%. For people who went to tanning salons, the probability of large feet is 59%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.59
0.59 - 0.07 = 0.52
0.52 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 6%. For people not using tanning salon treatments, the probability of large feet is 7%. For people who went to tanning salons, the probability of large feet is 59%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.59
0.06*0.59 - 0.94*0.07 = 0.10
0.10 > 0",fork,getting_tanned,1,marginal,P(Y)
2548,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2554,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 2%. For people not using tanning salon treatments, the probability of large feet is 14%. For people who went to tanning salons, the probability of large feet is 74%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.74
0.02*0.74 - 0.98*0.14 = 0.15
0.15 > 0",fork,getting_tanned,1,marginal,P(Y)
2557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 2%. The probability of no tanning salon treatment and large feet is 14%. The probability of tanning salon treatment and large feet is 1%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.14/0.98 = 0.60
0.60 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 30%. For people who went to tanning salons, the probability of large feet is 84%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.84
0.84 - 0.30 = 0.54
0.54 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 30%. For people who went to tanning salons, the probability of large feet is 84%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.84
0.84 - 0.30 = 0.54
0.54 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 30%. For people who went to tanning salons, the probability of large feet is 84%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.84
0.84 - 0.30 = 0.54
0.54 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 8%. For people not using tanning salon treatments, the probability of large feet is 30%. For people who went to tanning salons, the probability of large feet is 84%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.84
0.08*0.84 - 0.92*0.30 = 0.34
0.34 > 0",fork,getting_tanned,1,marginal,P(Y)
2565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 8%. For people not using tanning salon treatments, the probability of large feet is 30%. For people who went to tanning salons, the probability of large feet is 84%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.84
0.08*0.84 - 0.92*0.30 = 0.34
0.34 > 0",fork,getting_tanned,1,marginal,P(Y)
2568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look directly at how tanning salon treatment correlates with foot size in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 42%. For people who went to tanning salons, the probability of large feet is 90%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.90
0.90 - 0.42 = 0.48
0.48 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. For people not using tanning salon treatments, the probability of large feet is 42%. For people who went to tanning salons, the probability of large feet is 90%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.90
0.05*0.90 - 0.95*0.42 = 0.44
0.44 > 0",fork,getting_tanned,1,marginal,P(Y)
2577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 5%. The probability of no tanning salon treatment and large feet is 40%. The probability of tanning salon treatment and large feet is 4%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.04
0.04/0.05 - 0.40/0.95 = 0.48
0.48 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 7%. For people who went to tanning salons, the probability of large feet is 60%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.60
0.60 - 0.07 = 0.52
0.52 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 4%. For people not using tanning salon treatments, the probability of large feet is 7%. For people who went to tanning salons, the probability of large feet is 60%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.60
0.04*0.60 - 0.96*0.07 = 0.10
0.10 > 0",fork,getting_tanned,1,marginal,P(Y)
2586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 4%. The probability of no tanning salon treatment and large feet is 7%. The probability of tanning salon treatment and large feet is 3%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.03
0.03/0.04 - 0.07/0.96 = 0.52
0.52 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 28%. For people who went to tanning salons, the probability of large feet is 85%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.85
0.85 - 0.28 = 0.56
0.56 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 28%. For people who went to tanning salons, the probability of large feet is 85%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.85
0.85 - 0.28 = 0.56
0.56 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 0%. The probability of no tanning salon treatment and large feet is 28%. The probability of tanning salon treatment and large feet is 0%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.00
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.00
0.00/0.00 - 0.28/1.00 = 0.56
0.56 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2597,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 0%. The probability of no tanning salon treatment and large feet is 28%. The probability of tanning salon treatment and large feet is 0%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.00
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.00
0.00/0.00 - 0.28/1.00 = 0.56
0.56 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2600,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 17%. For people who went to tanning salons, the probability of large feet is 70%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.70
0.70 - 0.17 = 0.53
0.53 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 1%. The probability of no tanning salon treatment and large feet is 16%. The probability of tanning salon treatment and large feet is 1%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.01
0.01/0.01 - 0.16/0.99 = 0.53
0.53 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 26%. For people who went to tanning salons, the probability of large feet is 78%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.78
0.78 - 0.26 = 0.52
0.52 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look at how tanning salon treatment correlates with foot size case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2620,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 36%. For people who went to tanning salons, the probability of large feet is 88%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.88
0.88 - 0.36 = 0.51
0.51 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 36%. For people who went to tanning salons, the probability of large feet is 88%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.88
0.88 - 0.36 = 0.51
0.51 > 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2625,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 9%. For people not using tanning salon treatments, the probability of large feet is 36%. For people who went to tanning salons, the probability of large feet is 88%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.88
0.09*0.88 - 0.91*0.36 = 0.41
0.41 > 0",fork,getting_tanned,1,marginal,P(Y)
2627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 9%. The probability of no tanning salon treatment and large feet is 33%. The probability of tanning salon treatment and large feet is 8%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.08
0.08/0.09 - 0.33/0.91 = 0.51
0.51 > 0",fork,getting_tanned,1,correlation,P(Y | X)
2629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look directly at how tanning salon treatment correlates with foot size in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. For people not using tanning salon treatments, the probability of large feet is 25%. For people who went to tanning salons, the probability of large feet is 71%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.71
0.71 - 0.25 = 0.45
0.45 > 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. The overall probability of tanning salon treatment is 3%. For people not using tanning salon treatments, the probability of large feet is 25%. For people who went to tanning salons, the probability of large feet is 71%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.71
0.03*0.71 - 0.97*0.25 = 0.27
0.27 > 0",fork,getting_tanned,1,marginal,P(Y)
2639,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. Method 1: We look directly at how tanning salon treatment correlates with foot size in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
2643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 53%. For those who choose to take the elevator, the probability of large feet is 45%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.45
0.45 - 0.53 = -0.08
-0.08 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 64%. For those who choose to take the stairs, the probability of large feet is 53%. For those who choose to take the elevator, the probability of large feet is 45%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.64
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.45
0.64*0.45 - 0.36*0.53 = 0.48
0.48 > 0",mediation,penguin,1,marginal,P(Y)
2649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 64%. For those who choose to take the stairs, the probability of large feet is 53%. For those who choose to take the elevator, the probability of large feet is 45%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.64
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.45
0.64*0.45 - 0.36*0.53 = 0.48
0.48 > 0",mediation,penguin,1,marginal,P(Y)
2650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 64%. The probability of taking the stairs and large feet is 19%. The probability of taking the elevator and large feet is 29%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.29
0.29/0.64 - 0.19/0.36 = -0.08
-0.08 < 0",mediation,penguin,1,correlation,P(Y | X)
2651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 64%. The probability of taking the stairs and large feet is 19%. The probability of taking the elevator and large feet is 29%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.29
0.29/0.64 - 0.19/0.36 = -0.08
-0.08 < 0",mediation,penguin,1,correlation,P(Y | X)
2655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 54%. For those who choose to take the elevator, the probability of large feet is 49%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.49
0.49 - 0.54 = -0.05
-0.05 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 54%. For those who choose to take the elevator, the probability of large feet is 49%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.49
0.49 - 0.54 = -0.05
-0.05 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 15%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 58%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 30%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 73%. For those who choose to take the stairs, the probability of penguin happiness is 90%. For those who choose to take the elevator, the probability of penguin happiness is 46%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.30
P(Y=1 | X=1, V2=1) = 0.73
P(V2=1 | X=0) = 0.90
P(V2=1 | X=1) = 0.46
0.46 * (0.58 - 0.15)+ 0.90 * (0.73 - 0.30)= -0.19
-0.19 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 15%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 58%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 30%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 73%. For those who choose to take the stairs, the probability of penguin happiness is 90%. For those who choose to take the elevator, the probability of penguin happiness is 46%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.30
P(Y=1 | X=1, V2=1) = 0.73
P(V2=1 | X=0) = 0.90
P(V2=1 | X=1) = 0.46
0.46 * (0.58 - 0.15)+ 0.90 * (0.73 - 0.30)= -0.19
-0.19 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2661,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 15%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 58%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 30%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 73%. For those who choose to take the stairs, the probability of penguin happiness is 90%. For those who choose to take the elevator, the probability of penguin happiness is 46%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.30
P(Y=1 | X=1, V2=1) = 0.73
P(V2=1 | X=0) = 0.90
P(V2=1 | X=1) = 0.46
0.90 * (0.73 - 0.30) + 0.46 * (0.58 - 0.15) = 0.14
0.14 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 49%. The probability of taking the stairs and large feet is 28%. The probability of taking the elevator and large feet is 24%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.24
0.24/0.49 - 0.28/0.51 = -0.05
-0.05 < 0",mediation,penguin,1,correlation,P(Y | X)
2666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 53%. For those who choose to take the elevator, the probability of large feet is 53%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.53
0.53 - 0.53 = 0.00
0.00 = 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2674,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 29%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 63%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 36%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 72%. For those who choose to take the stairs, the probability of penguin happiness is 70%. For those who choose to take the elevator, the probability of penguin happiness is 47%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.29
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.36
P(Y=1 | X=1, V2=1) = 0.72
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.47
0.70 * (0.72 - 0.36) + 0.47 * (0.63 - 0.29) = 0.08
0.08 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 79%. The probability of taking the stairs and large feet is 11%. The probability of taking the elevator and large feet is 42%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.79
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.42
0.42/0.79 - 0.11/0.21 = 0.00
0.00 = 0",mediation,penguin,1,correlation,P(Y | X)
2680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 42%. For those who choose to take the elevator, the probability of large feet is 49%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.49
0.49 - 0.42 = 0.07
0.07 > 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 42%. For those who choose to take the elevator, the probability of large feet is 49%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.49
0.49 - 0.42 = 0.07
0.07 > 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 42%. For those who choose to take the elevator, the probability of large feet is 49%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.49
0.49 - 0.42 = 0.07
0.07 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 42%. For those who choose to take the elevator, the probability of large feet is 49%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.49
0.49 - 0.42 = 0.07
0.07 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 16%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 63%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 29%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 75%. For those who choose to take the stairs, the probability of penguin happiness is 55%. For those who choose to take the elevator, the probability of penguin happiness is 43%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.16
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.29
P(Y=1 | X=1, V2=1) = 0.75
P(V2=1 | X=0) = 0.55
P(V2=1 | X=1) = 0.43
0.43 * (0.63 - 0.16)+ 0.55 * (0.75 - 0.29)= -0.06
-0.06 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 37%. For those who choose to take the stairs, the probability of large feet is 42%. For those who choose to take the elevator, the probability of large feet is 49%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.49
0.37*0.49 - 0.63*0.42 = 0.45
0.45 > 0",mediation,penguin,1,marginal,P(Y)
2696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 65%. For those who choose to take the elevator, the probability of large feet is 55%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.55
0.55 - 0.65 = -0.10
-0.10 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 65%. For those who choose to take the elevator, the probability of large feet is 55%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.55
0.55 - 0.65 = -0.10
-0.10 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 65%. For those who choose to take the elevator, the probability of large feet is 55%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.55
0.55 - 0.65 = -0.10
-0.10 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 65%. For those who choose to take the elevator, the probability of large feet is 55%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.55
0.55 - 0.65 = -0.10
-0.10 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 29%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 67%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 40%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 76%. For those who choose to take the stairs, the probability of penguin happiness is 93%. For those who choose to take the elevator, the probability of penguin happiness is 40%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.29
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.40
P(Y=1 | X=1, V2=1) = 0.76
P(V2=1 | X=0) = 0.93
P(V2=1 | X=1) = 0.40
0.40 * (0.67 - 0.29)+ 0.93 * (0.76 - 0.40)= -0.21
-0.21 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 29%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 67%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 40%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 76%. For those who choose to take the stairs, the probability of penguin happiness is 93%. For those who choose to take the elevator, the probability of penguin happiness is 40%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.29
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.40
P(Y=1 | X=1, V2=1) = 0.76
P(V2=1 | X=0) = 0.93
P(V2=1 | X=1) = 0.40
0.40 * (0.67 - 0.29)+ 0.93 * (0.76 - 0.40)= -0.21
-0.21 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2716,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 38%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 85%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 53%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 93%. For those who choose to take the stairs, the probability of penguin happiness is 61%. For those who choose to take the elevator, the probability of penguin happiness is 42%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.85
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.93
P(V2=1 | X=0) = 0.61
P(V2=1 | X=1) = 0.42
0.61 * (0.93 - 0.53) + 0.42 * (0.85 - 0.38) = 0.11
0.11 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 66%. For those who choose to take the stairs, the probability of large feet is 66%. For those who choose to take the elevator, the probability of large feet is 70%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.70
0.66*0.70 - 0.34*0.66 = 0.68
0.68 > 0",mediation,penguin,1,marginal,P(Y)
2720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 66%. The probability of taking the stairs and large feet is 22%. The probability of taking the elevator and large feet is 46%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.46
0.46/0.66 - 0.22/0.34 = 0.03
0.03 > 0",mediation,penguin,1,correlation,P(Y | X)
2722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 29%. For those who choose to take the elevator, the probability of large feet is 27%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.27
0.27 - 0.29 = -0.03
-0.03 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 29%. For those who choose to take the elevator, the probability of large feet is 27%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.27
0.27 - 0.29 = -0.03
-0.03 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 11%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 61%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 22%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 73%. For those who choose to take the stairs, the probability of penguin happiness is 37%. For those who choose to take the elevator, the probability of penguin happiness is 10%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.11
P(Y=1 | X=0, V2=1) = 0.61
P(Y=1 | X=1, V2=0) = 0.22
P(Y=1 | X=1, V2=1) = 0.73
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.10
0.37 * (0.73 - 0.22) + 0.10 * (0.61 - 0.11) = 0.11
0.11 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2733,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 65%. For those who choose to take the stairs, the probability of large feet is 29%. For those who choose to take the elevator, the probability of large feet is 27%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.65
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.27
0.65*0.27 - 0.35*0.29 = 0.28
0.28 > 0",mediation,penguin,1,marginal,P(Y)
2734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 65%. The probability of taking the stairs and large feet is 10%. The probability of taking the elevator and large feet is 17%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.17
0.17/0.65 - 0.10/0.35 = -0.03
-0.03 < 0",mediation,penguin,1,correlation,P(Y | X)
2736,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 43%. For those who choose to take the elevator, the probability of large feet is 50%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.50
0.50 - 0.43 = 0.06
0.06 > 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2740,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 43%. For those who choose to take the elevator, the probability of large feet is 50%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.50
0.50 - 0.43 = 0.06
0.06 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2742,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 6%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 60%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 23%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 77%. For those who choose to take the stairs, the probability of penguin happiness is 68%. For those who choose to take the elevator, the probability of penguin happiness is 50%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.68
P(V2=1 | X=1) = 0.50
0.50 * (0.60 - 0.06)+ 0.68 * (0.77 - 0.23)= -0.10
-0.10 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2743,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 6%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 60%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 23%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 77%. For those who choose to take the stairs, the probability of penguin happiness is 68%. For those who choose to take the elevator, the probability of penguin happiness is 50%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.68
P(V2=1 | X=1) = 0.50
0.50 * (0.60 - 0.06)+ 0.68 * (0.77 - 0.23)= -0.10
-0.10 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2744,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 6%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 60%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 23%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 77%. For those who choose to take the stairs, the probability of penguin happiness is 68%. For those who choose to take the elevator, the probability of penguin happiness is 50%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.68
P(V2=1 | X=1) = 0.50
0.68 * (0.77 - 0.23) + 0.50 * (0.60 - 0.06) = 0.17
0.17 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 77%. For those who choose to take the stairs, the probability of large feet is 43%. For those who choose to take the elevator, the probability of large feet is 50%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.50
0.77*0.50 - 0.23*0.43 = 0.48
0.48 > 0",mediation,penguin,1,marginal,P(Y)
2748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 77%. The probability of taking the stairs and large feet is 10%. The probability of taking the elevator and large feet is 38%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.38
0.38/0.77 - 0.10/0.23 = 0.06
0.06 > 0",mediation,penguin,1,correlation,P(Y | X)
2749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 77%. The probability of taking the stairs and large feet is 10%. The probability of taking the elevator and large feet is 38%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.38
0.38/0.77 - 0.10/0.23 = 0.06
0.06 > 0",mediation,penguin,1,correlation,P(Y | X)
2750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2752,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 48%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.48
0.48 - 0.46 = 0.02
0.02 > 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2753,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 48%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.48
0.48 - 0.46 = 0.02
0.02 > 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 48%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.48
0.48 - 0.46 = 0.02
0.02 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 15%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 63%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 29%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 77%. For those who choose to take the stairs, the probability of penguin happiness is 64%. For those who choose to take the elevator, the probability of penguin happiness is 40%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.29
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.64
P(V2=1 | X=1) = 0.40
0.40 * (0.63 - 0.15)+ 0.64 * (0.77 - 0.29)= -0.12
-0.12 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 15%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 63%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 29%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 77%. For those who choose to take the stairs, the probability of penguin happiness is 64%. For those who choose to take the elevator, the probability of penguin happiness is 40%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.29
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.64
P(V2=1 | X=1) = 0.40
0.40 * (0.63 - 0.15)+ 0.64 * (0.77 - 0.29)= -0.12
-0.12 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 34%. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 48%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.34
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.48
0.34*0.48 - 0.66*0.46 = 0.46
0.46 > 0",mediation,penguin,1,marginal,P(Y)
2763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 34%. The probability of taking the stairs and large feet is 30%. The probability of taking the elevator and large feet is 16%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.34
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.16
0.16/0.34 - 0.30/0.66 = 0.02
0.02 > 0",mediation,penguin,1,correlation,P(Y | X)
2764,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 34%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.34
0.34 - 0.45 = -0.10
-0.10 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 34%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.34
0.34 - 0.45 = -0.10
-0.10 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2770,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 14%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 57%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 21%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 65%. For those who choose to take the stairs, the probability of penguin happiness is 70%. For those who choose to take the elevator, the probability of penguin happiness is 30%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.14
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.21
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.30
0.30 * (0.57 - 0.14)+ 0.70 * (0.65 - 0.21)= -0.18
-0.18 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 14%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 57%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 21%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 65%. For those who choose to take the stairs, the probability of penguin happiness is 70%. For those who choose to take the elevator, the probability of penguin happiness is 30%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.14
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.21
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.30
0.30 * (0.57 - 0.14)+ 0.70 * (0.65 - 0.21)= -0.18
-0.18 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 31%. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 34%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.34
0.31*0.34 - 0.69*0.45 = 0.41
0.41 > 0",mediation,penguin,1,marginal,P(Y)
2778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 57%. For those who choose to take the elevator, the probability of large feet is 34%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.34
0.34 - 0.57 = -0.24
-0.24 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 24%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 64%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 30%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 73%. For those who choose to take the stairs, the probability of penguin happiness is 83%. For those who choose to take the elevator, the probability of penguin happiness is 8%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.24
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.30
P(Y=1 | X=1, V2=1) = 0.73
P(V2=1 | X=0) = 0.83
P(V2=1 | X=1) = 0.08
0.83 * (0.73 - 0.30) + 0.08 * (0.64 - 0.24) = 0.09
0.09 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 36%. For those who choose to take the stairs, the probability of large feet is 57%. For those who choose to take the elevator, the probability of large feet is 34%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.34
0.36*0.34 - 0.64*0.57 = 0.49
0.49 > 0",mediation,penguin,1,marginal,P(Y)
2797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 49%. For those who choose to take the elevator, the probability of large feet is 41%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.41
0.41 - 0.49 = -0.08
-0.08 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 20%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 61%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 27%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 68%. For those who choose to take the stairs, the probability of penguin happiness is 70%. For those who choose to take the elevator, the probability of penguin happiness is 33%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.20
P(Y=1 | X=0, V2=1) = 0.61
P(Y=1 | X=1, V2=0) = 0.27
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.33
0.33 * (0.61 - 0.20)+ 0.70 * (0.68 - 0.27)= -0.15
-0.15 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 20%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 61%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 27%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 68%. For those who choose to take the stairs, the probability of penguin happiness is 70%. For those who choose to take the elevator, the probability of penguin happiness is 33%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.20
P(Y=1 | X=0, V2=1) = 0.61
P(Y=1 | X=1, V2=0) = 0.27
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.33
0.70 * (0.68 - 0.27) + 0.33 * (0.61 - 0.20) = 0.07
0.07 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 20%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 61%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 27%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 68%. For those who choose to take the stairs, the probability of penguin happiness is 70%. For those who choose to take the elevator, the probability of penguin happiness is 33%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.20
P(Y=1 | X=0, V2=1) = 0.61
P(Y=1 | X=1, V2=0) = 0.27
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.33
0.70 * (0.68 - 0.27) + 0.33 * (0.61 - 0.20) = 0.07
0.07 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 76%. For those who choose to take the stairs, the probability of large feet is 49%. For those who choose to take the elevator, the probability of large feet is 41%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.76
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.41
0.76*0.41 - 0.24*0.49 = 0.43
0.43 > 0",mediation,penguin,1,marginal,P(Y)
2804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 76%. The probability of taking the stairs and large feet is 12%. The probability of taking the elevator and large feet is 31%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.31
0.31/0.76 - 0.12/0.24 = -0.08
-0.08 < 0",mediation,penguin,1,correlation,P(Y | X)
2805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 76%. The probability of taking the stairs and large feet is 12%. The probability of taking the elevator and large feet is 31%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.31
0.31/0.76 - 0.12/0.24 = -0.08
-0.08 < 0",mediation,penguin,1,correlation,P(Y | X)
2806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 22%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.22
0.22 - 0.45 = -0.23
-0.23 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 22%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.22
0.22 - 0.45 = -0.23
-0.23 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 22%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.22
0.22 - 0.45 = -0.23
-0.23 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 22%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.22
0.22 - 0.45 = -0.23
-0.23 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 13%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 49%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 20%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 70%. For those who choose to take the stairs, the probability of penguin happiness is 89%. For those who choose to take the elevator, the probability of penguin happiness is 5%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.13
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.70
P(V2=1 | X=0) = 0.89
P(V2=1 | X=1) = 0.05
0.05 * (0.49 - 0.13)+ 0.89 * (0.70 - 0.20)= -0.30
-0.30 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 13%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 49%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 20%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 70%. For those who choose to take the stairs, the probability of penguin happiness is 89%. For those who choose to take the elevator, the probability of penguin happiness is 5%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.13
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.70
P(V2=1 | X=0) = 0.89
P(V2=1 | X=1) = 0.05
0.89 * (0.70 - 0.20) + 0.05 * (0.49 - 0.13) = 0.19
0.19 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 52%. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 22%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.22
0.52*0.22 - 0.48*0.45 = 0.36
0.36 > 0",mediation,penguin,1,marginal,P(Y)
2819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 52%. The probability of taking the stairs and large feet is 22%. The probability of taking the elevator and large feet is 12%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.12
0.12/0.52 - 0.22/0.48 = -0.23
-0.23 < 0",mediation,penguin,1,correlation,P(Y | X)
2821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 44%. For those who choose to take the elevator, the probability of large feet is 39%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.39
0.39 - 0.44 = -0.04
-0.04 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 44%. For those who choose to take the elevator, the probability of large feet is 39%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.39
0.39 - 0.44 = -0.04
-0.04 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 44%. For those who choose to take the elevator, the probability of large feet is 39%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.39
0.39 - 0.44 = -0.04
-0.04 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 5%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 67%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 17%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 77%. For those who choose to take the stairs, the probability of penguin happiness is 63%. For those who choose to take the elevator, the probability of penguin happiness is 38%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.05
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.17
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.63
P(V2=1 | X=1) = 0.38
0.63 * (0.77 - 0.17) + 0.38 * (0.67 - 0.05) = 0.11
0.11 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2834,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 43%. For those who choose to take the elevator, the probability of large feet is 35%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.35
0.35 - 0.43 = -0.08
-0.08 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 43%. The probability of taking the stairs and large feet is 24%. The probability of taking the elevator and large feet is 15%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.15
0.15/0.43 - 0.24/0.57 = -0.08
-0.08 < 0",mediation,penguin,1,correlation,P(Y | X)
2847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 43%. The probability of taking the stairs and large feet is 24%. The probability of taking the elevator and large feet is 15%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.15
0.15/0.43 - 0.24/0.57 = -0.08
-0.08 < 0",mediation,penguin,1,correlation,P(Y | X)
2849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 9%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 45%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 18%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 56%. For those who choose to take the stairs, the probability of penguin happiness is 54%. For those who choose to take the elevator, the probability of penguin happiness is 9%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.56
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.09
0.09 * (0.45 - 0.09)+ 0.54 * (0.56 - 0.18)= -0.16
-0.16 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 40%. For those who choose to take the stairs, the probability of large feet is 29%. For those who choose to take the elevator, the probability of large feet is 21%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.21
0.40*0.21 - 0.60*0.29 = 0.26
0.26 > 0",mediation,penguin,1,marginal,P(Y)
2863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 47%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.47
0.47 - 0.45 = 0.02
0.02 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 26%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 67%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 35%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 79%. For those who choose to take the stairs, the probability of penguin happiness is 46%. For those who choose to take the elevator, the probability of penguin happiness is 28%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.79
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.28
0.28 * (0.67 - 0.26)+ 0.46 * (0.79 - 0.35)= -0.08
-0.08 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 26%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 67%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 35%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 79%. For those who choose to take the stairs, the probability of penguin happiness is 46%. For those who choose to take the elevator, the probability of penguin happiness is 28%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.79
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.28
0.46 * (0.79 - 0.35) + 0.28 * (0.67 - 0.26) = 0.10
0.10 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 36%. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 47%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.47
0.36*0.47 - 0.64*0.45 = 0.46
0.46 > 0",mediation,penguin,1,marginal,P(Y)
2874,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 36%. The probability of taking the stairs and large feet is 29%. The probability of taking the elevator and large feet is 17%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.36
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.17
0.17/0.36 - 0.29/0.64 = 0.02
0.02 > 0",mediation,penguin,1,correlation,P(Y | X)
2883,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 28%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 60%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 35%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 74%. For those who choose to take the stairs, the probability of penguin happiness is 57%. For those who choose to take the elevator, the probability of penguin happiness is 22%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.28
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.74
P(V2=1 | X=0) = 0.57
P(V2=1 | X=1) = 0.22
0.22 * (0.60 - 0.28)+ 0.57 * (0.74 - 0.35)= -0.11
-0.11 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2884,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 28%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 60%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 35%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 74%. For those who choose to take the stairs, the probability of penguin happiness is 57%. For those who choose to take the elevator, the probability of penguin happiness is 22%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.28
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.74
P(V2=1 | X=0) = 0.57
P(V2=1 | X=1) = 0.22
0.57 * (0.74 - 0.35) + 0.22 * (0.60 - 0.28) = 0.10
0.10 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 68%. The probability of taking the stairs and large feet is 15%. The probability of taking the elevator and large feet is 29%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.68
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.29
0.29/0.68 - 0.15/0.32 = -0.03
-0.03 < 0",mediation,penguin,1,correlation,P(Y | X)
2893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 72%. For those who choose to take the elevator, the probability of large feet is 66%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.66
0.66 - 0.72 = -0.07
-0.07 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 72%. For those who choose to take the elevator, the probability of large feet is 66%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.66
0.66 - 0.72 = -0.07
-0.07 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 35%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 77%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 49%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 90%. For those who choose to take the stairs, the probability of penguin happiness is 89%. For those who choose to take the elevator, the probability of penguin happiness is 41%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.35
P(Y=1 | X=0, V2=1) = 0.77
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.90
P(V2=1 | X=0) = 0.89
P(V2=1 | X=1) = 0.41
0.41 * (0.77 - 0.35)+ 0.89 * (0.90 - 0.49)= -0.20
-0.20 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2901,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 32%. For those who choose to take the stairs, the probability of large feet is 72%. For those who choose to take the elevator, the probability of large feet is 66%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.66
0.32*0.66 - 0.68*0.72 = 0.70
0.70 > 0",mediation,penguin,1,marginal,P(Y)
2904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 67%. For those who choose to take the elevator, the probability of large feet is 67%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.67
0.67 - 0.67 = 0.01
0.01 > 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2907,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 67%. For those who choose to take the elevator, the probability of large feet is 67%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.67
0.67 - 0.67 = 0.01
0.01 > 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 67%. For those who choose to take the elevator, the probability of large feet is 67%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.67
0.67 - 0.67 = 0.01
0.01 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 30%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 82%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 46%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 95%. For those who choose to take the stairs, the probability of penguin happiness is 71%. For those who choose to take the elevator, the probability of penguin happiness is 43%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.30
P(Y=1 | X=0, V2=1) = 0.82
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.43
0.43 * (0.82 - 0.30)+ 0.71 * (0.95 - 0.46)= -0.14
-0.14 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 30%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 82%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 46%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 95%. For those who choose to take the stairs, the probability of penguin happiness is 71%. For those who choose to take the elevator, the probability of penguin happiness is 43%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.30
P(Y=1 | X=0, V2=1) = 0.82
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.43
0.71 * (0.95 - 0.46) + 0.43 * (0.82 - 0.30) = 0.14
0.14 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 67%. For those who choose to take the stairs, the probability of large feet is 67%. For those who choose to take the elevator, the probability of large feet is 67%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.67
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.67
0.67*0.67 - 0.33*0.67 = 0.67
0.67 > 0",mediation,penguin,1,marginal,P(Y)
2919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 27%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.27
0.27 - 0.45 = -0.18
-0.18 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 27%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.27
0.27 - 0.45 = -0.18
-0.18 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 9%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 52%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 17%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 58%. For those who choose to take the stairs, the probability of penguin happiness is 82%. For those who choose to take the elevator, the probability of penguin happiness is 24%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.09
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.17
P(Y=1 | X=1, V2=1) = 0.58
P(V2=1 | X=0) = 0.82
P(V2=1 | X=1) = 0.24
0.82 * (0.58 - 0.17) + 0.24 * (0.52 - 0.09) = 0.06
0.06 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 55%. For those who choose to take the stairs, the probability of large feet is 45%. For those who choose to take the elevator, the probability of large feet is 27%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.27
0.55*0.27 - 0.45*0.45 = 0.34
0.34 > 0",mediation,penguin,1,marginal,P(Y)
2931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 55%. The probability of taking the stairs and large feet is 20%. The probability of taking the elevator and large feet is 15%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.15
0.15/0.55 - 0.20/0.45 = -0.18
-0.18 < 0",mediation,penguin,1,correlation,P(Y | X)
2933,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 37%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 80%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 43%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 96%. For those who choose to take the stairs, the probability of penguin happiness is 71%. For those who choose to take the elevator, the probability of penguin happiness is 39%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.37
P(Y=1 | X=0, V2=1) = 0.80
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.96
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.39
0.71 * (0.96 - 0.43) + 0.39 * (0.80 - 0.37) = 0.14
0.14 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 37%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 80%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 43%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 96%. For those who choose to take the stairs, the probability of penguin happiness is 71%. For those who choose to take the elevator, the probability of penguin happiness is 39%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.37
P(Y=1 | X=0, V2=1) = 0.80
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.96
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.39
0.71 * (0.96 - 0.43) + 0.39 * (0.80 - 0.37) = 0.14
0.14 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 39%. The probability of taking the stairs and large feet is 41%. The probability of taking the elevator and large feet is 25%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.25
0.25/0.39 - 0.41/0.61 = -0.04
-0.04 < 0",mediation,penguin,1,correlation,P(Y | X)
2951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 61%. For those who choose to take the elevator, the probability of large feet is 63%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.63
0.63 - 0.61 = 0.02
0.02 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 18%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 67%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 23%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 85%. For those who choose to take the stairs, the probability of penguin happiness is 89%. For those who choose to take the elevator, the probability of penguin happiness is 66%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.18
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.85
P(V2=1 | X=0) = 0.89
P(V2=1 | X=1) = 0.66
0.66 * (0.67 - 0.18)+ 0.89 * (0.85 - 0.23)= -0.12
-0.12 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 41%. For those who choose to take the stairs, the probability of large feet is 61%. For those who choose to take the elevator, the probability of large feet is 63%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.63
0.41*0.63 - 0.59*0.61 = 0.63
0.63 > 0",mediation,penguin,1,marginal,P(Y)
2958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 41%. The probability of taking the stairs and large feet is 36%. The probability of taking the elevator and large feet is 26%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.26
0.26/0.41 - 0.36/0.59 = 0.02
0.02 > 0",mediation,penguin,1,correlation,P(Y | X)
2960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 20%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 62%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 35%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 78%. For those who choose to take the stairs, the probability of penguin happiness is 82%. For those who choose to take the elevator, the probability of penguin happiness is 45%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.20
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.78
P(V2=1 | X=0) = 0.82
P(V2=1 | X=1) = 0.45
0.82 * (0.78 - 0.35) + 0.45 * (0.62 - 0.20) = 0.16
0.16 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 32%. For those who choose to take the stairs, the probability of large feet is 55%. For those who choose to take the elevator, the probability of large feet is 55%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.55
0.32*0.55 - 0.68*0.55 = 0.55
0.55 > 0",mediation,penguin,1,marginal,P(Y)
2972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 32%. The probability of taking the stairs and large feet is 37%. The probability of taking the elevator and large feet is 18%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.32
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.18
0.18/0.32 - 0.37/0.68 = 0.00
0.00 = 0",mediation,penguin,1,correlation,P(Y | X)
2977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 50%. For those who choose to take the elevator, the probability of large feet is 41%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.41
0.41 - 0.50 = -0.09
-0.09 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
2978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 50%. For those who choose to take the elevator, the probability of large feet is 41%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.41
0.41 - 0.50 = -0.09
-0.09 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 11%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 57%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 25%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 66%. For those who choose to take the stairs, the probability of penguin happiness is 86%. For those who choose to take the elevator, the probability of penguin happiness is 39%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.11
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.25
P(Y=1 | X=1, V2=1) = 0.66
P(V2=1 | X=0) = 0.86
P(V2=1 | X=1) = 0.39
0.39 * (0.57 - 0.11)+ 0.86 * (0.66 - 0.25)= -0.22
-0.22 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
2982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 11%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 57%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 25%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 66%. For those who choose to take the stairs, the probability of penguin happiness is 86%. For those who choose to take the elevator, the probability of penguin happiness is 39%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.11
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.25
P(Y=1 | X=1, V2=1) = 0.66
P(V2=1 | X=0) = 0.86
P(V2=1 | X=1) = 0.39
0.86 * (0.66 - 0.25) + 0.39 * (0.57 - 0.11) = 0.10
0.10 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 72%. For those who choose to take the stairs, the probability of large feet is 50%. For those who choose to take the elevator, the probability of large feet is 41%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.72
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.41
0.72*0.41 - 0.28*0.50 = 0.43
0.43 > 0",mediation,penguin,1,marginal,P(Y)
2986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 72%. The probability of taking the stairs and large feet is 14%. The probability of taking the elevator and large feet is 30%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.72
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.30
0.30/0.72 - 0.14/0.28 = -0.09
-0.09 < 0",mediation,penguin,1,correlation,P(Y | X)
2988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
2993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 57%. For those who choose to take the elevator, the probability of large feet is 59%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.59
0.59 - 0.57 = 0.01
0.01 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
2996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 29%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 73%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 45%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 86%. For those who choose to take the stairs, the probability of penguin happiness is 65%. For those who choose to take the elevator, the probability of penguin happiness is 33%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.29
P(Y=1 | X=0, V2=1) = 0.73
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.33
0.65 * (0.86 - 0.45) + 0.33 * (0.73 - 0.29) = 0.14
0.14 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
2997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 29%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 73%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 45%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 86%. For those who choose to take the stairs, the probability of penguin happiness is 65%. For those who choose to take the elevator, the probability of penguin happiness is 33%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.29
P(Y=1 | X=0, V2=1) = 0.73
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.33
0.65 * (0.86 - 0.45) + 0.33 * (0.73 - 0.29) = 0.14
0.14 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 41%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.41
0.41 - 0.46 = -0.04
-0.04 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 41%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.41
0.41 - 0.46 = -0.04
-0.04 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3006,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 41%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.41
0.41 - 0.46 = -0.04
-0.04 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 41%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.41
0.41 - 0.46 = -0.04
-0.04 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 8%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 57%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 19%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 71%. For those who choose to take the stairs, the probability of penguin happiness is 77%. For those who choose to take the elevator, the probability of penguin happiness is 42%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.08
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.19
P(Y=1 | X=1, V2=1) = 0.71
P(V2=1 | X=0) = 0.77
P(V2=1 | X=1) = 0.42
0.77 * (0.71 - 0.19) + 0.42 * (0.57 - 0.08) = 0.14
0.14 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3012,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 67%. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 41%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.67
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.41
0.67*0.41 - 0.33*0.46 = 0.43
0.43 > 0",mediation,penguin,1,marginal,P(Y)
3013,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 67%. For those who choose to take the stairs, the probability of large feet is 46%. For those who choose to take the elevator, the probability of large feet is 41%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.67
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.41
0.67*0.41 - 0.33*0.46 = 0.43
0.43 > 0",mediation,penguin,1,marginal,P(Y)
3014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 67%. The probability of taking the stairs and large feet is 15%. The probability of taking the elevator and large feet is 27%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.67
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.27
0.27/0.67 - 0.15/0.33 = -0.04
-0.04 < 0",mediation,penguin,1,correlation,P(Y | X)
3016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
3018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 60%. For those who choose to take the elevator, the probability of large feet is 59%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.59
0.59 - 0.60 = -0.00
0.00 = 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 33%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 65%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 39%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 78%. For those who choose to take the stairs, the probability of penguin happiness is 83%. For those who choose to take the elevator, the probability of penguin happiness is 51%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.33
P(Y=1 | X=0, V2=1) = 0.65
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.78
P(V2=1 | X=0) = 0.83
P(V2=1 | X=1) = 0.51
0.51 * (0.65 - 0.33)+ 0.83 * (0.78 - 0.39)= -0.10
-0.10 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look directly at how my decision correlates with foot size in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
3033,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 36%. For those who choose to take the elevator, the probability of large feet is 41%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.41
0.41 - 0.36 = 0.04
0.04 > 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 36%. For those who choose to take the elevator, the probability of large feet is 41%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.41
0.41 - 0.36 = 0.04
0.04 > 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 2%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 54%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 20%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 65%. For those who choose to take the stairs, the probability of penguin happiness is 65%. For those who choose to take the elevator, the probability of penguin happiness is 46%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.02
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.46
0.46 * (0.54 - 0.02)+ 0.65 * (0.65 - 0.20)= -0.10
-0.10 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 2%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 54%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 20%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 65%. For those who choose to take the stairs, the probability of penguin happiness is 65%. For those who choose to take the elevator, the probability of penguin happiness is 46%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.02
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.46
0.65 * (0.65 - 0.20) + 0.46 * (0.54 - 0.02) = 0.13
0.13 > 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 33%. For those who choose to take the stairs, the probability of large feet is 36%. For those who choose to take the elevator, the probability of large feet is 41%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.33
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.41
0.33*0.41 - 0.67*0.36 = 0.37
0.37 > 0",mediation,penguin,1,marginal,P(Y)
3044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. Method 1: We look at how my decision correlates with foot size case by case according to penguin mood. Method 2: We look directly at how my decision correlates with foot size in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
3046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 66%. For those who choose to take the elevator, the probability of large feet is 59%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.59
0.59 - 0.66 = -0.07
-0.07 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 66%. For those who choose to take the elevator, the probability of large feet is 59%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.59
0.59 - 0.66 = -0.07
-0.07 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs, the probability of large feet is 66%. For those who choose to take the elevator, the probability of large feet is 59%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.59
0.59 - 0.66 = -0.07
-0.07 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. For those who choose to take the stairs and penguins who are sad, the probability of large feet is 31%. For those who choose to take the stairs and penguins who are happy, the probability of large feet is 78%. For those who choose to take the elevator and penguins who are sad, the probability of large feet is 48%. For those who choose to take the elevator and penguins who are happy, the probability of large feet is 85%. For those who choose to take the stairs, the probability of penguin happiness is 74%. For those who choose to take the elevator, the probability of penguin happiness is 29%.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.31
P(Y=1 | X=0, V2=1) = 0.78
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.85
P(V2=1 | X=0) = 0.74
P(V2=1 | X=1) = 0.29
0.29 * (0.78 - 0.31)+ 0.74 * (0.85 - 0.48)= -0.22
-0.22 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3055,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 66%. For those who choose to take the stairs, the probability of large feet is 66%. For those who choose to take the elevator, the probability of large feet is 59%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.59
0.66*0.59 - 0.34*0.66 = 0.60
0.60 > 0",mediation,penguin,1,marginal,P(Y)
3056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. The overall probability of taking the elevator is 66%. The probability of taking the stairs and large feet is 23%. The probability of taking the elevator and large feet is 38%.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.38
0.38/0.66 - 0.23/0.34 = -0.07
-0.07 < 0",mediation,penguin,1,correlation,P(Y | X)
3061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 42%. For people who have a brother, the probability of smallpox survival is 54%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.54
0.54 - 0.42 = 0.11
0.11 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 42%. For people who have a brother, the probability of smallpox survival is 54%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.54
0.54 - 0.42 = 0.11
0.11 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 42%. For people who have a brother, the probability of smallpox survival is 54%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.54
0.54 - 0.42 = 0.11
0.11 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 97%. The probability of not having a brother and smallpox survival is 1%. The probability of having a brother and smallpox survival is 52%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.52
0.52/0.97 - 0.01/0.03 = 0.11
0.11 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 97%. The probability of not having a brother and smallpox survival is 1%. The probability of having a brother and smallpox survival is 52%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.52
0.52/0.97 - 0.01/0.03 = 0.11
0.11 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3070,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 46%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.46
0.46 - 0.39 = 0.08
0.08 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3074,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 46%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.46
0.46 - 0.39 = 0.08
0.08 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 46%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.46
0.46 - 0.39 = 0.08
0.08 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 46%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.46
0.46 - 0.39 = 0.08
0.08 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 78%. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 46%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.78
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.46
0.78*0.46 - 0.22*0.39 = 0.44
0.44 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3079,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 78%. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 46%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.78
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.46
0.78*0.46 - 0.22*0.39 = 0.44
0.44 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 49%. For people who have a brother, the probability of smallpox survival is 45%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.45
0.45 - 0.49 = -0.05
-0.05 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 82%. For people who do not have a brother, the probability of smallpox survival is 49%. For people who have a brother, the probability of smallpox survival is 45%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.45
0.82*0.45 - 0.18*0.49 = 0.46
0.46 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 58%. For people who have a brother, the probability of smallpox survival is 48%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.48
0.48 - 0.58 = -0.10
-0.10 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 58%. For people who have a brother, the probability of smallpox survival is 48%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.48
0.48 - 0.58 = -0.10
-0.10 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3103,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 100%. For people who do not have a brother, the probability of smallpox survival is 58%. For people who have a brother, the probability of smallpox survival is 48%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 1.00
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.48
1.00*0.48 - 0.00*0.58 = 0.48
0.48 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 71%. For people who have a brother, the probability of smallpox survival is 65%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.65
0.65 - 0.71 = -0.06
-0.06 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3111,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 71%. For people who have a brother, the probability of smallpox survival is 65%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.65
0.65 - 0.71 = -0.06
-0.06 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 71%. For people who have a brother, the probability of smallpox survival is 65%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.65
0.65 - 0.71 = -0.06
-0.06 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 71%. For people who have a brother, the probability of smallpox survival is 65%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.65
0.65 - 0.71 = -0.06
-0.06 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 89%. The probability of not having a brother and smallpox survival is 8%. The probability of having a brother and smallpox survival is 58%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.58
0.58/0.89 - 0.08/0.11 = -0.06
-0.06 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 68%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.68
0.68 - 0.55 = 0.13
0.13 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 68%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.68
0.68 - 0.55 = 0.13
0.13 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 68%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.68
0.68 - 0.55 = 0.13
0.13 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 68%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.68
0.68 - 0.55 = 0.13
0.13 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3125,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 68%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.68
0.68 - 0.55 = 0.13
0.13 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 74%. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 68%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.74
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.68
0.74*0.68 - 0.26*0.55 = 0.65
0.65 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 74%. The probability of not having a brother and smallpox survival is 14%. The probability of having a brother and smallpox survival is 50%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.74
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.50
0.50/0.74 - 0.14/0.26 = 0.13
0.13 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 46%. For people who have a brother, the probability of smallpox survival is 54%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.54
0.54 - 0.46 = 0.07
0.07 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 75%. The probability of not having a brother and smallpox survival is 11%. The probability of having a brother and smallpox survival is 40%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.75
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.40
0.40/0.75 - 0.11/0.25 = 0.07
0.07 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3143,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 57%. For people who have a brother, the probability of smallpox survival is 52%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.52
0.52 - 0.57 = -0.05
-0.05 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 57%. For people who have a brother, the probability of smallpox survival is 52%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.52
0.52 - 0.57 = -0.05
-0.05 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 78%. For people who do not have a brother, the probability of smallpox survival is 57%. For people who have a brother, the probability of smallpox survival is 52%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.78
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.52
0.78*0.52 - 0.22*0.57 = 0.53
0.53 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 78%. The probability of not having a brother and smallpox survival is 13%. The probability of having a brother and smallpox survival is 40%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.78
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.40
0.40/0.78 - 0.13/0.22 = -0.05
-0.05 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 31%. For people who have a brother, the probability of smallpox survival is 41%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.41
0.41 - 0.31 = 0.10
0.10 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 31%. For people who have a brother, the probability of smallpox survival is 41%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.41
0.41 - 0.31 = 0.10
0.10 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3160,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 31%. For people who have a brother, the probability of smallpox survival is 41%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.41
0.41 - 0.31 = 0.10
0.10 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3166,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 44%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.44
0.44 - 0.39 = 0.05
0.05 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 94%. The probability of not having a brother and smallpox survival is 2%. The probability of having a brother and smallpox survival is 42%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.94
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.42
0.42/0.94 - 0.02/0.06 = 0.05
0.05 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 54%. For people who have a brother, the probability of smallpox survival is 56%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.56
0.56 - 0.54 = 0.02
0.02 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 54%. For people who have a brother, the probability of smallpox survival is 56%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.56
0.56 - 0.54 = 0.02
0.02 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 71%. For people who do not have a brother, the probability of smallpox survival is 54%. For people who have a brother, the probability of smallpox survival is 56%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.56
0.71*0.56 - 0.29*0.54 = 0.55
0.55 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 71%. The probability of not having a brother and smallpox survival is 16%. The probability of having a brother and smallpox survival is 39%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.71
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.39
0.39/0.71 - 0.16/0.29 = 0.02
0.02 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 71%. The probability of not having a brother and smallpox survival is 16%. The probability of having a brother and smallpox survival is 39%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.71
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.39
0.39/0.71 - 0.16/0.29 = 0.02
0.02 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 49%. For people who have a brother, the probability of smallpox survival is 50%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.50
0.50 - 0.49 = 0.00
0.00 = 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 49%. For people who have a brother, the probability of smallpox survival is 50%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.50
0.50 - 0.49 = 0.00
0.00 = 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 49%. For people who have a brother, the probability of smallpox survival is 50%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.50
0.50 - 0.49 = 0.00
0.00 = 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3198,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 87%. For people who do not have a brother, the probability of smallpox survival is 49%. For people who have a brother, the probability of smallpox survival is 50%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.50
0.87*0.50 - 0.13*0.49 = 0.49
0.49 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 87%. For people who do not have a brother, the probability of smallpox survival is 49%. For people who have a brother, the probability of smallpox survival is 50%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.50
0.87*0.50 - 0.13*0.49 = 0.49
0.49 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 87%. The probability of not having a brother and smallpox survival is 6%. The probability of having a brother and smallpox survival is 43%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.87
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.43
0.43/0.87 - 0.06/0.13 = 0.00
0.00 = 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3203,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 33%. For people who have a brother, the probability of smallpox survival is 34%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.34
0.34 - 0.33 = 0.01
0.01 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 33%. For people who have a brother, the probability of smallpox survival is 34%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.34
0.34 - 0.33 = 0.01
0.01 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 76%. For people who do not have a brother, the probability of smallpox survival is 33%. For people who have a brother, the probability of smallpox survival is 34%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.76
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.34
0.76*0.34 - 0.24*0.33 = 0.34
0.34 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 76%. The probability of not having a brother and smallpox survival is 8%. The probability of having a brother and smallpox survival is 26%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.26
0.26/0.76 - 0.08/0.24 = 0.01
0.01 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 50%. For people who have a brother, the probability of smallpox survival is 59%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.59
0.59 - 0.50 = 0.08
0.08 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 50%. For people who have a brother, the probability of smallpox survival is 59%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.59
0.59 - 0.50 = 0.08
0.08 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3219,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 50%. For people who have a brother, the probability of smallpox survival is 59%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.59
0.59 - 0.50 = 0.08
0.08 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 77%. For people who do not have a brother, the probability of smallpox survival is 50%. For people who have a brother, the probability of smallpox survival is 59%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.59
0.77*0.59 - 0.23*0.50 = 0.57
0.57 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 77%. The probability of not having a brother and smallpox survival is 11%. The probability of having a brother and smallpox survival is 46%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.46
0.46/0.77 - 0.11/0.23 = 0.08
0.08 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 77%. The probability of not having a brother and smallpox survival is 11%. The probability of having a brother and smallpox survival is 46%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.46
0.46/0.77 - 0.11/0.23 = 0.08
0.08 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 43%. For people who have a brother, the probability of smallpox survival is 51%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.51
0.51 - 0.43 = 0.07
0.07 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 43%. For people who have a brother, the probability of smallpox survival is 51%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.51
0.51 - 0.43 = 0.07
0.07 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 43%. For people who have a brother, the probability of smallpox survival is 51%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.51
0.51 - 0.43 = 0.07
0.07 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 43%. For people who have a brother, the probability of smallpox survival is 51%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.51
0.51 - 0.43 = 0.07
0.07 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 86%. The probability of not having a brother and smallpox survival is 6%. The probability of having a brother and smallpox survival is 43%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.86
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.43
0.43/0.86 - 0.06/0.14 = 0.07
0.07 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 86%. The probability of not having a brother and smallpox survival is 6%. The probability of having a brother and smallpox survival is 43%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.86
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.43
0.43/0.86 - 0.06/0.14 = 0.07
0.07 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 45%. For people who have a brother, the probability of smallpox survival is 58%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.58
0.58 - 0.45 = 0.13
0.13 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 45%. For people who have a brother, the probability of smallpox survival is 58%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.58
0.58 - 0.45 = 0.13
0.13 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 45%. For people who have a brother, the probability of smallpox survival is 58%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.58
0.58 - 0.45 = 0.13
0.13 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 45%. For people who have a brother, the probability of smallpox survival is 58%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.58
0.58 - 0.45 = 0.13
0.13 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 76%. For people who do not have a brother, the probability of smallpox survival is 45%. For people who have a brother, the probability of smallpox survival is 58%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.76
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.58
0.76*0.58 - 0.24*0.45 = 0.55
0.55 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 76%. The probability of not having a brother and smallpox survival is 11%. The probability of having a brother and smallpox survival is 44%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.44
0.44/0.76 - 0.11/0.24 = 0.13
0.13 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 40%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.40
0.40 - 0.39 = 0.01
0.01 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 40%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.40
0.40 - 0.39 = 0.01
0.01 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 91%. The probability of not having a brother and smallpox survival is 4%. The probability of having a brother and smallpox survival is 36%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.36
0.36/0.91 - 0.04/0.09 = 0.01
0.01 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 56%. For people who have a brother, the probability of smallpox survival is 49%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.49
0.49 - 0.56 = -0.07
-0.07 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 56%. For people who have a brother, the probability of smallpox survival is 49%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.49
0.49 - 0.56 = -0.07
-0.07 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 71%. For people who do not have a brother, the probability of smallpox survival is 56%. For people who have a brother, the probability of smallpox survival is 49%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.49
0.71*0.49 - 0.29*0.56 = 0.51
0.51 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 71%. The probability of not having a brother and smallpox survival is 16%. The probability of having a brother and smallpox survival is 35%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.71
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.35
0.35/0.71 - 0.16/0.29 = -0.07
-0.07 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 33%. For people who have a brother, the probability of smallpox survival is 34%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.34
0.34 - 0.33 = 0.01
0.01 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 33%. For people who have a brother, the probability of smallpox survival is 34%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.34
0.34 - 0.33 = 0.01
0.01 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3282,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 71%. For people who do not have a brother, the probability of smallpox survival is 33%. For people who have a brother, the probability of smallpox survival is 34%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.34
0.71*0.34 - 0.29*0.33 = 0.34
0.34 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 71%. For people who do not have a brother, the probability of smallpox survival is 33%. For people who have a brother, the probability of smallpox survival is 34%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.34
0.71*0.34 - 0.29*0.33 = 0.34
0.34 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 39%. For people who have a brother, the probability of smallpox survival is 36%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.36
0.36 - 0.39 = -0.03
-0.03 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 79%. The probability of not having a brother and smallpox survival is 8%. The probability of having a brother and smallpox survival is 29%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.79
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.29
0.29/0.79 - 0.08/0.21 = -0.03
-0.03 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 65%. For people who have a brother, the probability of smallpox survival is 73%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.73
0.73 - 0.65 = 0.08
0.08 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3303,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 65%. For people who have a brother, the probability of smallpox survival is 73%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.73
0.73 - 0.65 = 0.08
0.08 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 65%. For people who have a brother, the probability of smallpox survival is 73%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.73
0.73 - 0.65 = 0.08
0.08 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 65%. For people who have a brother, the probability of smallpox survival is 73%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.73
0.73 - 0.65 = 0.08
0.08 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 73%. The probability of not having a brother and smallpox survival is 18%. The probability of having a brother and smallpox survival is 53%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.53
0.53/0.73 - 0.18/0.27 = 0.08
0.08 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 36%. For people who have a brother, the probability of smallpox survival is 56%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.56
0.56 - 0.36 = 0.20
0.20 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3315,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 36%. For people who have a brother, the probability of smallpox survival is 56%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.56
0.56 - 0.36 = 0.20
0.20 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3317,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 36%. For people who have a brother, the probability of smallpox survival is 56%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.56
0.56 - 0.36 = 0.20
0.20 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 62%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.62
0.62 - 0.55 = 0.07
0.07 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 62%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.62
0.62 - 0.55 = 0.07
0.07 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 93%. For people who do not have a brother, the probability of smallpox survival is 55%. For people who have a brother, the probability of smallpox survival is 62%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.62
0.93*0.62 - 0.07*0.55 = 0.61
0.61 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 93%. The probability of not having a brother and smallpox survival is 4%. The probability of having a brother and smallpox survival is 58%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.58
0.58/0.93 - 0.04/0.07 = 0.07
0.07 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 44%. For people who have a brother, the probability of smallpox survival is 36%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.36
0.36 - 0.44 = -0.09
-0.09 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 44%. For people who have a brother, the probability of smallpox survival is 36%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.36
0.36 - 0.44 = -0.09
-0.09 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 92%. The probability of not having a brother and smallpox survival is 2%. The probability of having a brother and smallpox survival is 27%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.27
0.27/0.92 - 0.02/0.08 = 0.03
0.03 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3360,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 30%. For people who have a brother, the probability of smallpox survival is 50%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.50
0.50 - 0.30 = 0.20
0.20 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 30%. For people who have a brother, the probability of smallpox survival is 50%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.50
0.50 - 0.30 = 0.20
0.20 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 70%. The probability of not having a brother and smallpox survival is 9%. The probability of having a brother and smallpox survival is 35%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.70
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.35
0.35/0.70 - 0.09/0.30 = 0.20
0.20 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 51%. For people who have a brother, the probability of smallpox survival is 62%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.62
0.62 - 0.51 = 0.10
0.10 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3378,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 77%. For people who do not have a brother, the probability of smallpox survival is 51%. For people who have a brother, the probability of smallpox survival is 62%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.62
0.77*0.62 - 0.23*0.51 = 0.59
0.59 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 77%. For people who do not have a brother, the probability of smallpox survival is 51%. For people who have a brother, the probability of smallpox survival is 62%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.62
0.77*0.62 - 0.23*0.51 = 0.59
0.59 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 58%. For people who have a brother, the probability of smallpox survival is 69%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.69
0.69 - 0.58 = 0.11
0.11 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 58%. For people who have a brother, the probability of smallpox survival is 69%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.69
0.69 - 0.58 = 0.11
0.11 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3390,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 86%. For people who do not have a brother, the probability of smallpox survival is 58%. For people who have a brother, the probability of smallpox survival is 69%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.69
0.86*0.69 - 0.14*0.58 = 0.67
0.67 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 86%. For people who do not have a brother, the probability of smallpox survival is 58%. For people who have a brother, the probability of smallpox survival is 69%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.69
0.86*0.69 - 0.14*0.58 = 0.67
0.67 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look directly at how having a brother correlates with smallpox survival in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 44%. For people who have a brother, the probability of smallpox survival is 43%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.43
0.43 - 0.44 = -0.01
-0.01 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 44%. For people who have a brother, the probability of smallpox survival is 43%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.43
0.43 - 0.44 = -0.01
-0.01 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3400,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 44%. For people who have a brother, the probability of smallpox survival is 43%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.43
0.43 - 0.44 = -0.01
-0.01 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 44%. For people who have a brother, the probability of smallpox survival is 43%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.43
0.43 - 0.44 = -0.01
-0.01 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 88%. For people who do not have a brother, the probability of smallpox survival is 44%. For people who have a brother, the probability of smallpox survival is 43%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.43
0.88*0.43 - 0.12*0.44 = 0.43
0.43 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 88%. For people who do not have a brother, the probability of smallpox survival is 44%. For people who have a brother, the probability of smallpox survival is 43%.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.43
0.88*0.43 - 0.12*0.44 = 0.43
0.43 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 88%. The probability of not having a brother and smallpox survival is 5%. The probability of having a brother and smallpox survival is 38%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.38
0.38/0.88 - 0.05/0.12 = -0.01
-0.01 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
3410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 42%. For people who have a brother, the probability of smallpox survival is 41%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.41
0.41 - 0.42 = -0.00
0.00 = 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. For people who do not have a brother, the probability of smallpox survival is 42%. For people who have a brother, the probability of smallpox survival is 41%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.41
0.41 - 0.42 = -0.00
0.00 = 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
3414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. The overall probability of having a brother is 80%. For people who do not have a brother, the probability of smallpox survival is 42%. For people who have a brother, the probability of smallpox survival is 41%.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.41
0.80*0.41 - 0.20*0.42 = 0.41
0.41 > 0",diamond,vaccine_kills,1,marginal,P(Y)
3418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. Method 1: We look at how having a brother correlates with smallpox survival case by case according to vaccination reaction. Method 2: We look directly at how having a brother correlates with smallpox survival in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
3420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 10%. For people who have a sister, the probability of healthy heart is 54%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.54
0.54 - 0.10 = 0.44
0.44 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 10%. For people who have a sister, the probability of healthy heart is 54%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.54
0.54 - 0.10 = 0.44
0.44 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 85%. For people who do not have a sister, the probability of healthy heart is 10%. For people who have a sister, the probability of healthy heart is 54%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.54
0.85*0.54 - 0.15*0.10 = 0.48
0.48 > 0",mediation,blood_pressure,1,marginal,P(Y)
3430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 85%. The probability of not having a sister and healthy heart is 2%. The probability of having a sister and healthy heart is 46%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.46
0.46/0.85 - 0.02/0.15 = 0.44
0.44 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3434,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 46%. For people who have a sister, the probability of healthy heart is 88%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.88
0.88 - 0.46 = 0.42
0.42 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 46%. For people who have a sister, the probability of healthy heart is 88%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.88
0.88 - 0.46 = 0.42
0.42 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 46%. For people who have a sister, the probability of healthy heart is 88%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.88
0.88 - 0.46 = 0.42
0.42 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 77%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 36%. For people who have a sister and with low blood pressure, the probability of healthy heart is 90%. For people who have a sister and with high blood pressure, the probability of healthy heart is 44%. For people who do not have a sister, the probability of high blood pressure is 75%. For people who have a sister, the probability of high blood pressure is 3%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.77
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.90
P(Y=1 | X=1, V2=1) = 0.44
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.03
0.75 * (0.44 - 0.90) + 0.03 * (0.36 - 0.77) = 0.10
0.10 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 57%. For people who do not have a sister, the probability of healthy heart is 46%. For people who have a sister, the probability of healthy heart is 88%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.88
0.57*0.88 - 0.43*0.46 = 0.69
0.69 > 0",mediation,blood_pressure,1,marginal,P(Y)
3446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 61%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.61
0.61 - 0.38 = 0.23
0.23 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 51%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 23%. For people who have a sister and with low blood pressure, the probability of healthy heart is 81%. For people who have a sister and with high blood pressure, the probability of healthy heart is 47%. For people who do not have a sister, the probability of high blood pressure is 46%. For people who have a sister, the probability of high blood pressure is 59%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.23
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.59
0.59 * (0.23 - 0.51)+ 0.46 * (0.47 - 0.81)= -0.04
-0.04 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 51%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 23%. For people who have a sister and with low blood pressure, the probability of healthy heart is 81%. For people who have a sister and with high blood pressure, the probability of healthy heart is 47%. For people who do not have a sister, the probability of high blood pressure is 46%. For people who have a sister, the probability of high blood pressure is 59%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.23
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.59
0.46 * (0.47 - 0.81) + 0.59 * (0.23 - 0.51) = 0.27
0.27 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 51%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 23%. For people who have a sister and with low blood pressure, the probability of healthy heart is 81%. For people who have a sister and with high blood pressure, the probability of healthy heart is 47%. For people who do not have a sister, the probability of high blood pressure is 46%. For people who have a sister, the probability of high blood pressure is 59%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.23
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.59
0.46 * (0.47 - 0.81) + 0.59 * (0.23 - 0.51) = 0.27
0.27 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 26%. For people who have a sister, the probability of healthy heart is 49%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.49
0.49 - 0.26 = 0.23
0.23 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 26%. For people who have a sister, the probability of healthy heart is 49%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.49
0.49 - 0.26 = 0.23
0.23 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 96%. For people who do not have a sister, the probability of healthy heart is 26%. For people who have a sister, the probability of healthy heart is 49%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.49
0.96*0.49 - 0.04*0.26 = 0.48
0.48 > 0",mediation,blood_pressure,1,marginal,P(Y)
3471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 96%. For people who do not have a sister, the probability of healthy heart is 26%. For people who have a sister, the probability of healthy heart is 49%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.49
0.96*0.49 - 0.04*0.26 = 0.48
0.48 > 0",mediation,blood_pressure,1,marginal,P(Y)
3472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 96%. The probability of not having a sister and healthy heart is 1%. The probability of having a sister and healthy heart is 47%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.47
0.47/0.96 - 0.01/0.04 = 0.23
0.23 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 47%. For people who have a sister, the probability of healthy heart is 88%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.88
0.88 - 0.47 = 0.41
0.41 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 47%. For people who have a sister, the probability of healthy heart is 88%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.88
0.88 - 0.47 = 0.41
0.41 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 66%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 36%. For people who have a sister and with low blood pressure, the probability of healthy heart is 92%. For people who have a sister and with high blood pressure, the probability of healthy heart is 70%. For people who do not have a sister, the probability of high blood pressure is 63%. For people who have a sister, the probability of high blood pressure is 22%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.66
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.92
P(Y=1 | X=1, V2=1) = 0.70
P(V2=1 | X=0) = 0.63
P(V2=1 | X=1) = 0.22
0.63 * (0.70 - 0.92) + 0.22 * (0.36 - 0.66) = 0.31
0.31 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 82%. For people who do not have a sister, the probability of healthy heart is 47%. For people who have a sister, the probability of healthy heart is 88%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.88
0.82*0.88 - 0.18*0.47 = 0.81
0.81 > 0",mediation,blood_pressure,1,marginal,P(Y)
3489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3496,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 59%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 19%. For people who have a sister and with low blood pressure, the probability of healthy heart is 49%. For people who have a sister and with high blood pressure, the probability of healthy heart is 9%. For people who do not have a sister, the probability of high blood pressure is 95%. For people who have a sister, the probability of high blood pressure is 21%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.19
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.09
P(V2=1 | X=0) = 0.95
P(V2=1 | X=1) = 0.21
0.95 * (0.09 - 0.49) + 0.21 * (0.19 - 0.59) = -0.10
-0.10 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 59%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.59
0.59 - 0.38 = 0.21
0.21 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 59%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.59
0.59 - 0.38 = 0.21
0.21 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 20%. For people who have a sister and with low blood pressure, the probability of healthy heart is 77%. For people who have a sister and with high blood pressure, the probability of healthy heart is 46%. For people who do not have a sister, the probability of high blood pressure is 37%. For people who have a sister, the probability of high blood pressure is 60%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.20
P(Y=1 | X=1, V2=0) = 0.77
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.60
0.60 * (0.20 - 0.48)+ 0.37 * (0.46 - 0.77)= -0.06
-0.06 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 20%. For people who have a sister and with low blood pressure, the probability of healthy heart is 77%. For people who have a sister and with high blood pressure, the probability of healthy heart is 46%. For people who do not have a sister, the probability of high blood pressure is 37%. For people who have a sister, the probability of high blood pressure is 60%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.20
P(Y=1 | X=1, V2=0) = 0.77
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.60
0.37 * (0.46 - 0.77) + 0.60 * (0.20 - 0.48) = 0.28
0.28 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3512,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 41%. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 59%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.59
0.41*0.59 - 0.59*0.38 = 0.47
0.47 > 0",mediation,blood_pressure,1,marginal,P(Y)
3515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 41%. The probability of not having a sister and healthy heart is 22%. The probability of having a sister and healthy heart is 24%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.24
0.24/0.41 - 0.22/0.59 = 0.21
0.21 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 52%. For people who have a sister, the probability of healthy heart is 66%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.66
0.66 - 0.52 = 0.15
0.15 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 71%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 46%. For people who have a sister and with low blood pressure, the probability of healthy heart is 81%. For people who have a sister and with high blood pressure, the probability of healthy heart is 33%. For people who do not have a sister, the probability of high blood pressure is 75%. For people who have a sister, the probability of high blood pressure is 31%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.46
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.33
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.31
0.31 * (0.46 - 0.71)+ 0.75 * (0.33 - 0.81)= 0.11
0.11 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 71%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 46%. For people who have a sister and with low blood pressure, the probability of healthy heart is 81%. For people who have a sister and with high blood pressure, the probability of healthy heart is 33%. For people who do not have a sister, the probability of high blood pressure is 75%. For people who have a sister, the probability of high blood pressure is 31%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.46
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.33
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.31
0.31 * (0.46 - 0.71)+ 0.75 * (0.33 - 0.81)= 0.11
0.11 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 36%. For people who have a sister, the probability of healthy heart is 77%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.77
0.77 - 0.36 = 0.41
0.41 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3542,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 88%. The probability of not having a sister and healthy heart is 4%. The probability of having a sister and healthy heart is 68%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.68
0.68/0.88 - 0.04/0.12 = 0.41
0.41 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 88%. The probability of not having a sister and healthy heart is 4%. The probability of having a sister and healthy heart is 68%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.68
0.68/0.88 - 0.04/0.12 = 0.41
0.41 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 60%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 8%. For people who have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who have a sister and with high blood pressure, the probability of healthy heart is 20%. For people who do not have a sister, the probability of high blood pressure is 94%. For people who have a sister, the probability of high blood pressure is 28%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.60
P(Y=1 | X=0, V2=1) = 0.08
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.20
P(V2=1 | X=0) = 0.94
P(V2=1 | X=1) = 0.28
0.28 * (0.08 - 0.60)+ 0.94 * (0.20 - 0.48)= 0.34
0.34 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 60%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 8%. For people who have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who have a sister and with high blood pressure, the probability of healthy heart is 20%. For people who do not have a sister, the probability of high blood pressure is 94%. For people who have a sister, the probability of high blood pressure is 28%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.60
P(Y=1 | X=0, V2=1) = 0.08
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.20
P(V2=1 | X=0) = 0.94
P(V2=1 | X=1) = 0.28
0.94 * (0.20 - 0.48) + 0.28 * (0.08 - 0.60) = 0.11
0.11 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3554,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 41%. For people who do not have a sister, the probability of healthy heart is 11%. For people who have a sister, the probability of healthy heart is 40%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.40
0.41*0.40 - 0.59*0.11 = 0.27
0.27 > 0",mediation,blood_pressure,1,marginal,P(Y)
3557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 41%. The probability of not having a sister and healthy heart is 7%. The probability of having a sister and healthy heart is 17%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.17
0.17/0.41 - 0.07/0.59 = 0.29
0.29 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 62%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 37%. For people who have a sister and with low blood pressure, the probability of healthy heart is 92%. For people who have a sister and with high blood pressure, the probability of healthy heart is 66%. For people who do not have a sister, the probability of high blood pressure is 48%. For people who have a sister, the probability of high blood pressure is 55%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.62
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.92
P(Y=1 | X=1, V2=1) = 0.66
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.55
0.55 * (0.37 - 0.62)+ 0.48 * (0.66 - 0.92)= -0.02
-0.02 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 62%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 37%. For people who have a sister and with low blood pressure, the probability of healthy heart is 92%. For people who have a sister and with high blood pressure, the probability of healthy heart is 66%. For people who do not have a sister, the probability of high blood pressure is 48%. For people who have a sister, the probability of high blood pressure is 55%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.62
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.92
P(Y=1 | X=1, V2=1) = 0.66
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.55
0.55 * (0.37 - 0.62)+ 0.48 * (0.66 - 0.92)= -0.02
-0.02 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 62%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 37%. For people who have a sister and with low blood pressure, the probability of healthy heart is 92%. For people who have a sister and with high blood pressure, the probability of healthy heart is 66%. For people who do not have a sister, the probability of high blood pressure is 48%. For people who have a sister, the probability of high blood pressure is 55%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.62
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.92
P(Y=1 | X=1, V2=1) = 0.66
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.55
0.48 * (0.66 - 0.92) + 0.55 * (0.37 - 0.62) = 0.30
0.30 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 59%. For people who do not have a sister, the probability of healthy heart is 50%. For people who have a sister, the probability of healthy heart is 78%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.78
0.59*0.78 - 0.41*0.50 = 0.66
0.66 > 0",mediation,blood_pressure,1,marginal,P(Y)
3571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 59%. The probability of not having a sister and healthy heart is 21%. The probability of having a sister and healthy heart is 46%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.46
0.46/0.59 - 0.21/0.41 = 0.28
0.28 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 59%. For people who have a sister, the probability of healthy heart is 49%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.49
0.49 - 0.59 = -0.11
-0.11 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 59%. For people who have a sister, the probability of healthy heart is 49%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.49
0.49 - 0.59 = -0.11
-0.11 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 76%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 25%. For people who have a sister and with low blood pressure, the probability of healthy heart is 63%. For people who have a sister and with high blood pressure, the probability of healthy heart is 40%. For people who do not have a sister, the probability of high blood pressure is 33%. For people who have a sister, the probability of high blood pressure is 62%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.25
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.40
P(V2=1 | X=0) = 0.33
P(V2=1 | X=1) = 0.62
0.33 * (0.40 - 0.63) + 0.62 * (0.25 - 0.76) = -0.04
-0.04 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 88%. For people who do not have a sister, the probability of healthy heart is 59%. For people who have a sister, the probability of healthy heart is 49%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.49
0.88*0.49 - 0.12*0.59 = 0.49
0.49 > 0",mediation,blood_pressure,1,marginal,P(Y)
3583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 88%. For people who do not have a sister, the probability of healthy heart is 59%. For people who have a sister, the probability of healthy heart is 49%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.49
0.88*0.49 - 0.12*0.59 = 0.49
0.49 > 0",mediation,blood_pressure,1,marginal,P(Y)
3584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 88%. The probability of not having a sister and healthy heart is 7%. The probability of having a sister and healthy heart is 43%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.43
0.43/0.88 - 0.07/0.12 = -0.11
-0.11 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
3588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 24%. For people who have a sister, the probability of healthy heart is 69%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.69
0.69 - 0.24 = 0.45
0.45 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 24%. For people who have a sister, the probability of healthy heart is 69%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.69
0.69 - 0.24 = 0.45
0.45 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 24%. For people who have a sister, the probability of healthy heart is 69%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.69
0.69 - 0.24 = 0.45
0.45 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 24%. For people who have a sister, the probability of healthy heart is 69%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.69
0.69 - 0.24 = 0.45
0.45 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 59%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 19%. For people who have a sister and with low blood pressure, the probability of healthy heart is 94%. For people who have a sister and with high blood pressure, the probability of healthy heart is 45%. For people who do not have a sister, the probability of high blood pressure is 89%. For people who have a sister, the probability of high blood pressure is 51%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.19
P(Y=1 | X=1, V2=0) = 0.94
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.89
P(V2=1 | X=1) = 0.51
0.51 * (0.19 - 0.59)+ 0.89 * (0.45 - 0.94)= 0.15
0.15 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 59%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 19%. For people who have a sister and with low blood pressure, the probability of healthy heart is 94%. For people who have a sister and with high blood pressure, the probability of healthy heart is 45%. For people who do not have a sister, the probability of high blood pressure is 89%. For people who have a sister, the probability of high blood pressure is 51%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.19
P(Y=1 | X=1, V2=0) = 0.94
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.89
P(V2=1 | X=1) = 0.51
0.89 * (0.45 - 0.94) + 0.51 * (0.19 - 0.59) = 0.27
0.27 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3595,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 59%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 19%. For people who have a sister and with low blood pressure, the probability of healthy heart is 94%. For people who have a sister and with high blood pressure, the probability of healthy heart is 45%. For people who do not have a sister, the probability of high blood pressure is 89%. For people who have a sister, the probability of high blood pressure is 51%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.19
P(Y=1 | X=1, V2=0) = 0.94
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.89
P(V2=1 | X=1) = 0.51
0.89 * (0.45 - 0.94) + 0.51 * (0.19 - 0.59) = 0.27
0.27 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 81%. For people who do not have a sister, the probability of healthy heart is 24%. For people who have a sister, the probability of healthy heart is 69%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.69
0.81*0.69 - 0.19*0.24 = 0.60
0.60 > 0",mediation,blood_pressure,1,marginal,P(Y)
3598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 81%. The probability of not having a sister and healthy heart is 4%. The probability of having a sister and healthy heart is 56%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.56
0.56/0.81 - 0.04/0.19 = 0.45
0.45 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3603,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 42%. For people who have a sister, the probability of healthy heart is 60%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.60
0.60 - 0.42 = 0.18
0.18 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3605,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 42%. For people who have a sister, the probability of healthy heart is 60%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.60
0.60 - 0.42 = 0.18
0.18 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 63%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 31%. For people who have a sister and with low blood pressure, the probability of healthy heart is 72%. For people who have a sister and with high blood pressure, the probability of healthy heart is 41%. For people who do not have a sister, the probability of high blood pressure is 66%. For people who have a sister, the probability of high blood pressure is 38%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.31
P(Y=1 | X=1, V2=0) = 0.72
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.66
P(V2=1 | X=1) = 0.38
0.38 * (0.31 - 0.63)+ 0.66 * (0.41 - 0.72)= 0.09
0.09 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 63%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 31%. For people who have a sister and with low blood pressure, the probability of healthy heart is 72%. For people who have a sister and with high blood pressure, the probability of healthy heart is 41%. For people who do not have a sister, the probability of high blood pressure is 66%. For people who have a sister, the probability of high blood pressure is 38%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.31
P(Y=1 | X=1, V2=0) = 0.72
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.66
P(V2=1 | X=1) = 0.38
0.66 * (0.41 - 0.72) + 0.38 * (0.31 - 0.63) = 0.10
0.10 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 54%. For people who do not have a sister, the probability of healthy heart is 42%. For people who have a sister, the probability of healthy heart is 60%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.60
0.54*0.60 - 0.46*0.42 = 0.52
0.52 > 0",mediation,blood_pressure,1,marginal,P(Y)
3611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 54%. For people who do not have a sister, the probability of healthy heart is 42%. For people who have a sister, the probability of healthy heart is 60%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.60
0.54*0.60 - 0.46*0.42 = 0.52
0.52 > 0",mediation,blood_pressure,1,marginal,P(Y)
3614,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3615,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 29%. For people who have a sister, the probability of healthy heart is 65%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.65
0.65 - 0.29 = 0.36
0.36 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 29%. For people who have a sister, the probability of healthy heart is 65%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.65
0.65 - 0.29 = 0.36
0.36 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3620,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 41%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 18%. For people who have a sister and with low blood pressure, the probability of healthy heart is 73%. For people who have a sister and with high blood pressure, the probability of healthy heart is 44%. For people who do not have a sister, the probability of high blood pressure is 50%. For people who have a sister, the probability of high blood pressure is 26%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.41
P(Y=1 | X=0, V2=1) = 0.18
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.44
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.26
0.26 * (0.18 - 0.41)+ 0.50 * (0.44 - 0.73)= 0.05
0.05 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 41%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 18%. For people who have a sister and with low blood pressure, the probability of healthy heart is 73%. For people who have a sister and with high blood pressure, the probability of healthy heart is 44%. For people who do not have a sister, the probability of high blood pressure is 50%. For people who have a sister, the probability of high blood pressure is 26%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.41
P(Y=1 | X=0, V2=1) = 0.18
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.44
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.26
0.50 * (0.44 - 0.73) + 0.26 * (0.18 - 0.41) = 0.29
0.29 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 41%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 18%. For people who have a sister and with low blood pressure, the probability of healthy heart is 73%. For people who have a sister and with high blood pressure, the probability of healthy heart is 44%. For people who do not have a sister, the probability of high blood pressure is 50%. For people who have a sister, the probability of high blood pressure is 26%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.41
P(Y=1 | X=0, V2=1) = 0.18
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.44
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.26
0.50 * (0.44 - 0.73) + 0.26 * (0.18 - 0.41) = 0.29
0.29 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 47%. For people who do not have a sister, the probability of healthy heart is 29%. For people who have a sister, the probability of healthy heart is 65%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.65
0.47*0.65 - 0.53*0.29 = 0.46
0.46 > 0",mediation,blood_pressure,1,marginal,P(Y)
3625,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 47%. For people who do not have a sister, the probability of healthy heart is 29%. For people who have a sister, the probability of healthy heart is 65%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.65
0.47*0.65 - 0.53*0.29 = 0.46
0.46 > 0",mediation,blood_pressure,1,marginal,P(Y)
3626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 47%. The probability of not having a sister and healthy heart is 16%. The probability of having a sister and healthy heart is 30%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.30
0.30/0.47 - 0.16/0.53 = 0.36
0.36 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 25%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.25
0.25 - 0.38 = -0.13
-0.13 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 51%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 0%. For people who have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who have a sister and with high blood pressure, the probability of healthy heart is 18%. For people who do not have a sister, the probability of high blood pressure is 26%. For people who have a sister, the probability of high blood pressure is 75%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.00
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.18
P(V2=1 | X=0) = 0.26
P(V2=1 | X=1) = 0.75
0.75 * (0.00 - 0.51)+ 0.26 * (0.18 - 0.48)= -0.25
-0.25 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3639,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 91%. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 25%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.25
0.91*0.25 - 0.09*0.38 = 0.26
0.26 > 0",mediation,blood_pressure,1,marginal,P(Y)
3640,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 91%. The probability of not having a sister and healthy heart is 3%. The probability of having a sister and healthy heart is 23%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.23
0.23/0.91 - 0.03/0.09 = -0.13
-0.13 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
3642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3646,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 20%. For people who have a sister, the probability of healthy heart is 53%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.53
0.53 - 0.20 = 0.32
0.32 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 44%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 11%. For people who have a sister and with low blood pressure, the probability of healthy heart is 68%. For people who have a sister and with high blood pressure, the probability of healthy heart is 38%. For people who do not have a sister, the probability of high blood pressure is 73%. For people who have a sister, the probability of high blood pressure is 52%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.11
P(Y=1 | X=1, V2=0) = 0.68
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.73
P(V2=1 | X=1) = 0.52
0.52 * (0.11 - 0.44)+ 0.73 * (0.38 - 0.68)= 0.07
0.07 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 44%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 11%. For people who have a sister and with low blood pressure, the probability of healthy heart is 68%. For people who have a sister and with high blood pressure, the probability of healthy heart is 38%. For people who do not have a sister, the probability of high blood pressure is 73%. For people who have a sister, the probability of high blood pressure is 52%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.11
P(Y=1 | X=1, V2=0) = 0.68
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.73
P(V2=1 | X=1) = 0.52
0.73 * (0.38 - 0.68) + 0.52 * (0.11 - 0.44) = 0.26
0.26 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 44%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 11%. For people who have a sister and with low blood pressure, the probability of healthy heart is 68%. For people who have a sister and with high blood pressure, the probability of healthy heart is 38%. For people who do not have a sister, the probability of high blood pressure is 73%. For people who have a sister, the probability of high blood pressure is 52%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.11
P(Y=1 | X=1, V2=0) = 0.68
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.73
P(V2=1 | X=1) = 0.52
0.73 * (0.38 - 0.68) + 0.52 * (0.11 - 0.44) = 0.26
0.26 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3654,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 93%. The probability of not having a sister and healthy heart is 2%. The probability of having a sister and healthy heart is 49%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.49
0.49/0.93 - 0.02/0.07 = 0.32
0.32 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3656,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3663,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 64%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 20%. For people who have a sister and with low blood pressure, the probability of healthy heart is 50%. For people who have a sister and with high blood pressure, the probability of healthy heart is 18%. For people who do not have a sister, the probability of high blood pressure is 91%. For people who have a sister, the probability of high blood pressure is 42%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.64
P(Y=1 | X=0, V2=1) = 0.20
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.18
P(V2=1 | X=0) = 0.91
P(V2=1 | X=1) = 0.42
0.42 * (0.20 - 0.64)+ 0.91 * (0.18 - 0.50)= 0.22
0.22 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 59%. For people who do not have a sister, the probability of healthy heart is 23%. For people who have a sister, the probability of healthy heart is 37%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.37
0.59*0.37 - 0.41*0.23 = 0.33
0.33 > 0",mediation,blood_pressure,1,marginal,P(Y)
3668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 59%. The probability of not having a sister and healthy heart is 10%. The probability of having a sister and healthy heart is 22%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.22
0.22/0.59 - 0.10/0.41 = 0.13
0.13 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 59%. The probability of not having a sister and healthy heart is 10%. The probability of having a sister and healthy heart is 22%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.22
0.22/0.59 - 0.10/0.41 = 0.13
0.13 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3672,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 16%. For people who have a sister, the probability of healthy heart is 50%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.50
0.50 - 0.16 = 0.34
0.34 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 16%. For people who have a sister, the probability of healthy heart is 50%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.50
0.50 - 0.16 = 0.34
0.34 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 39%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 2%. For people who have a sister and with low blood pressure, the probability of healthy heart is 66%. For people who have a sister and with high blood pressure, the probability of healthy heart is 27%. For people who do not have a sister, the probability of high blood pressure is 62%. For people who have a sister, the probability of high blood pressure is 41%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.39
P(Y=1 | X=0, V2=1) = 0.02
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.27
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.41
0.41 * (0.02 - 0.39)+ 0.62 * (0.27 - 0.66)= 0.08
0.08 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 39%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 2%. For people who have a sister and with low blood pressure, the probability of healthy heart is 66%. For people who have a sister and with high blood pressure, the probability of healthy heart is 27%. For people who do not have a sister, the probability of high blood pressure is 62%. For people who have a sister, the probability of high blood pressure is 41%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.39
P(Y=1 | X=0, V2=1) = 0.02
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.27
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.41
0.62 * (0.27 - 0.66) + 0.41 * (0.02 - 0.39) = 0.26
0.26 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3687,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 50%. For people who have a sister, the probability of healthy heart is 73%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.73 - 0.50 = 0.23
0.23 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 50%. For people who have a sister, the probability of healthy heart is 73%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.73 - 0.50 = 0.23
0.23 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 83%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 43%. For people who have a sister and with low blood pressure, the probability of healthy heart is 73%. For people who have a sister and with high blood pressure, the probability of healthy heart is 50%. For people who do not have a sister, the probability of high blood pressure is 82%. For people who have a sister, the probability of high blood pressure is 1%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.83
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.50
P(V2=1 | X=0) = 0.82
P(V2=1 | X=1) = 0.01
0.01 * (0.43 - 0.83)+ 0.82 * (0.50 - 0.73)= 0.33
0.33 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 92%. The probability of not having a sister and healthy heart is 4%. The probability of having a sister and healthy heart is 67%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.67
0.67/0.92 - 0.04/0.08 = 0.23
0.23 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 92%. The probability of not having a sister and healthy heart is 4%. The probability of having a sister and healthy heart is 67%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.67
0.67/0.92 - 0.04/0.08 = 0.23
0.23 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 38%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 7%. For people who have a sister and with low blood pressure, the probability of healthy heart is 81%. For people who have a sister and with high blood pressure, the probability of healthy heart is 50%. For people who do not have a sister, the probability of high blood pressure is 70%. For people who have a sister, the probability of high blood pressure is 23%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.07
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.50
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.23
0.23 * (0.07 - 0.38)+ 0.70 * (0.50 - 0.81)= 0.14
0.14 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 38%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 7%. For people who have a sister and with low blood pressure, the probability of healthy heart is 81%. For people who have a sister and with high blood pressure, the probability of healthy heart is 50%. For people who do not have a sister, the probability of high blood pressure is 70%. For people who have a sister, the probability of high blood pressure is 23%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.07
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.50
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.23
0.23 * (0.07 - 0.38)+ 0.70 * (0.50 - 0.81)= 0.14
0.14 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 98%. For people who do not have a sister, the probability of healthy heart is 16%. For people who have a sister, the probability of healthy heart is 74%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.74
0.98*0.74 - 0.02*0.16 = 0.73
0.73 > 0",mediation,blood_pressure,1,marginal,P(Y)
3712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 47%. For people who have a sister, the probability of healthy heart is 64%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.64
0.64 - 0.47 = 0.17
0.17 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 47%. For people who have a sister, the probability of healthy heart is 64%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.64
0.64 - 0.47 = 0.17
0.17 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 78%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 30%. For people who have a sister and with low blood pressure, the probability of healthy heart is 73%. For people who have a sister and with high blood pressure, the probability of healthy heart is 41%. For people who do not have a sister, the probability of high blood pressure is 65%. For people who have a sister, the probability of high blood pressure is 29%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.30
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.29
0.29 * (0.30 - 0.78)+ 0.65 * (0.41 - 0.73)= 0.17
0.17 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 78%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 30%. For people who have a sister and with low blood pressure, the probability of healthy heart is 73%. For people who have a sister and with high blood pressure, the probability of healthy heart is 41%. For people who do not have a sister, the probability of high blood pressure is 65%. For people who have a sister, the probability of high blood pressure is 29%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.30
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.29
0.29 * (0.30 - 0.78)+ 0.65 * (0.41 - 0.73)= 0.17
0.17 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 78%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 30%. For people who have a sister and with low blood pressure, the probability of healthy heart is 73%. For people who have a sister and with high blood pressure, the probability of healthy heart is 41%. For people who do not have a sister, the probability of high blood pressure is 65%. For people who have a sister, the probability of high blood pressure is 29%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.30
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.29
0.65 * (0.41 - 0.73) + 0.29 * (0.30 - 0.78) = 0.05
0.05 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3721,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 78%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 30%. For people who have a sister and with low blood pressure, the probability of healthy heart is 73%. For people who have a sister and with high blood pressure, the probability of healthy heart is 41%. For people who do not have a sister, the probability of high blood pressure is 65%. For people who have a sister, the probability of high blood pressure is 29%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.30
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.29
0.65 * (0.41 - 0.73) + 0.29 * (0.30 - 0.78) = 0.05
0.05 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 46%. For people who do not have a sister, the probability of healthy heart is 47%. For people who have a sister, the probability of healthy heart is 64%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.64
0.46*0.64 - 0.54*0.47 = 0.56
0.56 > 0",mediation,blood_pressure,1,marginal,P(Y)
3725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 46%. The probability of not having a sister and healthy heart is 25%. The probability of having a sister and healthy heart is 30%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.30
0.30/0.46 - 0.25/0.54 = 0.17
0.17 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 21%. For people who have a sister, the probability of healthy heart is 55%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.55
0.55 - 0.21 = 0.34
0.34 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 21%. For people who have a sister, the probability of healthy heart is 55%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.55
0.55 - 0.21 = 0.34
0.34 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 21%. For people who have a sister, the probability of healthy heart is 55%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.55
0.55 - 0.21 = 0.34
0.34 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3735,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 43%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 18%. For people who have a sister and with low blood pressure, the probability of healthy heart is 63%. For people who have a sister and with high blood pressure, the probability of healthy heart is 40%. For people who do not have a sister, the probability of high blood pressure is 85%. For people who have a sister, the probability of high blood pressure is 35%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.18
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.40
P(V2=1 | X=0) = 0.85
P(V2=1 | X=1) = 0.35
0.85 * (0.40 - 0.63) + 0.35 * (0.18 - 0.43) = 0.22
0.22 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 47%. The probability of not having a sister and healthy heart is 11%. The probability of having a sister and healthy heart is 26%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.26
0.26/0.47 - 0.11/0.53 = 0.34
0.34 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3740,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3742,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 49%. For people who have a sister, the probability of healthy heart is 69%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.69
0.69 - 0.49 = 0.19
0.19 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 61%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 41%. For people who have a sister and with low blood pressure, the probability of healthy heart is 84%. For people who have a sister and with high blood pressure, the probability of healthy heart is 24%. For people who do not have a sister, the probability of high blood pressure is 58%. For people who have a sister, the probability of high blood pressure is 26%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.61
P(Y=1 | X=0, V2=1) = 0.41
P(Y=1 | X=1, V2=0) = 0.84
P(Y=1 | X=1, V2=1) = 0.24
P(V2=1 | X=0) = 0.58
P(V2=1 | X=1) = 0.26
0.26 * (0.41 - 0.61)+ 0.58 * (0.24 - 0.84)= 0.07
0.07 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 61%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 41%. For people who have a sister and with low blood pressure, the probability of healthy heart is 84%. For people who have a sister and with high blood pressure, the probability of healthy heart is 24%. For people who do not have a sister, the probability of high blood pressure is 58%. For people who have a sister, the probability of high blood pressure is 26%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.61
P(Y=1 | X=0, V2=1) = 0.41
P(Y=1 | X=1, V2=0) = 0.84
P(Y=1 | X=1, V2=1) = 0.24
P(V2=1 | X=0) = 0.58
P(V2=1 | X=1) = 0.26
0.58 * (0.24 - 0.84) + 0.26 * (0.41 - 0.61) = 0.00
0.00 = 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 94%. For people who do not have a sister, the probability of healthy heart is 49%. For people who have a sister, the probability of healthy heart is 69%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.69
0.94*0.69 - 0.06*0.49 = 0.67
0.67 > 0",mediation,blood_pressure,1,marginal,P(Y)
3760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 57%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 23%. For people who have a sister and with low blood pressure, the probability of healthy heart is 87%. For people who have a sister and with high blood pressure, the probability of healthy heart is 59%. For people who do not have a sister, the probability of high blood pressure is 76%. For people who have a sister, the probability of high blood pressure is 7%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.57
P(Y=1 | X=0, V2=1) = 0.23
P(Y=1 | X=1, V2=0) = 0.87
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.76
P(V2=1 | X=1) = 0.07
0.07 * (0.23 - 0.57)+ 0.76 * (0.59 - 0.87)= 0.24
0.24 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 57%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 23%. For people who have a sister and with low blood pressure, the probability of healthy heart is 87%. For people who have a sister and with high blood pressure, the probability of healthy heart is 59%. For people who do not have a sister, the probability of high blood pressure is 76%. For people who have a sister, the probability of high blood pressure is 7%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.57
P(Y=1 | X=0, V2=1) = 0.23
P(Y=1 | X=1, V2=0) = 0.87
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.76
P(V2=1 | X=1) = 0.07
0.07 * (0.23 - 0.57)+ 0.76 * (0.59 - 0.87)= 0.24
0.24 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3764,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 92%. For people who do not have a sister, the probability of healthy heart is 31%. For people who have a sister, the probability of healthy heart is 85%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.85
0.92*0.85 - 0.08*0.31 = 0.82
0.82 > 0",mediation,blood_pressure,1,marginal,P(Y)
3776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 87%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 64%. For people who have a sister and with low blood pressure, the probability of healthy heart is 89%. For people who have a sister and with high blood pressure, the probability of healthy heart is 40%. For people who do not have a sister, the probability of high blood pressure is 75%. For people who have a sister, the probability of high blood pressure is 29%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.87
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.89
P(Y=1 | X=1, V2=1) = 0.40
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.29
0.75 * (0.40 - 0.89) + 0.29 * (0.64 - 0.87) = -0.17
-0.17 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 47%. The probability of not having a sister and healthy heart is 37%. The probability of having a sister and healthy heart is 35%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.35
0.35/0.47 - 0.37/0.53 = 0.05
0.05 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3782,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 80%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.80 - 0.38 = 0.42
0.42 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 80%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.80 - 0.38 = 0.42
0.42 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3792,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 59%. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 80%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.59*0.80 - 0.41*0.38 = 0.63
0.63 > 0",mediation,blood_pressure,1,marginal,P(Y)
3793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 59%. For people who do not have a sister, the probability of healthy heart is 38%. For people who have a sister, the probability of healthy heart is 80%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.59*0.80 - 0.41*0.38 = 0.63
0.63 > 0",mediation,blood_pressure,1,marginal,P(Y)
3795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 59%. The probability of not having a sister and healthy heart is 16%. The probability of having a sister and healthy heart is 47%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.47
0.47/0.59 - 0.16/0.41 = 0.42
0.42 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 50%. For people who have a sister, the probability of healthy heart is 56%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.56
0.56 - 0.50 = 0.06
0.06 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 50%. For people who have a sister, the probability of healthy heart is 56%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.56
0.56 - 0.50 = 0.06
0.06 > 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 79%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 15%. For people who have a sister and with low blood pressure, the probability of healthy heart is 62%. For people who have a sister and with high blood pressure, the probability of healthy heart is 10%. For people who do not have a sister, the probability of high blood pressure is 46%. For people who have a sister, the probability of high blood pressure is 11%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.79
P(Y=1 | X=0, V2=1) = 0.15
P(Y=1 | X=1, V2=0) = 0.62
P(Y=1 | X=1, V2=1) = 0.10
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.11
0.11 * (0.15 - 0.79)+ 0.46 * (0.10 - 0.62)= 0.22
0.22 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 79%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 15%. For people who have a sister and with low blood pressure, the probability of healthy heart is 62%. For people who have a sister and with high blood pressure, the probability of healthy heart is 10%. For people who do not have a sister, the probability of high blood pressure is 46%. For people who have a sister, the probability of high blood pressure is 11%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.79
P(Y=1 | X=0, V2=1) = 0.15
P(Y=1 | X=1, V2=0) = 0.62
P(Y=1 | X=1, V2=1) = 0.10
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.11
0.46 * (0.10 - 0.62) + 0.11 * (0.15 - 0.79) = -0.12
-0.12 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 99%. For people who do not have a sister, the probability of healthy heart is 50%. For people who have a sister, the probability of healthy heart is 56%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.56
0.99*0.56 - 0.01*0.50 = 0.56
0.56 > 0",mediation,blood_pressure,1,marginal,P(Y)
3808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 99%. The probability of not having a sister and healthy heart is 1%. The probability of having a sister and healthy heart is 55%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.55
0.55/0.99 - 0.01/0.01 = 0.06
0.06 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 99%. The probability of not having a sister and healthy heart is 1%. The probability of having a sister and healthy heart is 55%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.55
0.55/0.99 - 0.01/0.01 = 0.06
0.06 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 39%. For people who have a sister, the probability of healthy heart is 79%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.79
0.79 - 0.39 = 0.39
0.39 > 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
3816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 66%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 9%. For people who have a sister and with low blood pressure, the probability of healthy heart is 91%. For people who have a sister and with high blood pressure, the probability of healthy heart is 25%. For people who do not have a sister, the probability of high blood pressure is 47%. For people who have a sister, the probability of high blood pressure is 19%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.66
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.91
P(Y=1 | X=1, V2=1) = 0.25
P(V2=1 | X=0) = 0.47
P(V2=1 | X=1) = 0.19
0.19 * (0.09 - 0.66)+ 0.47 * (0.25 - 0.91)= 0.16
0.16 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 66%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 9%. For people who have a sister and with low blood pressure, the probability of healthy heart is 91%. For people who have a sister and with high blood pressure, the probability of healthy heart is 25%. For people who do not have a sister, the probability of high blood pressure is 47%. For people who have a sister, the probability of high blood pressure is 19%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.66
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.91
P(Y=1 | X=1, V2=1) = 0.25
P(V2=1 | X=0) = 0.47
P(V2=1 | X=1) = 0.19
0.19 * (0.09 - 0.66)+ 0.47 * (0.25 - 0.91)= 0.16
0.16 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
3819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 66%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 9%. For people who have a sister and with low blood pressure, the probability of healthy heart is 91%. For people who have a sister and with high blood pressure, the probability of healthy heart is 25%. For people who do not have a sister, the probability of high blood pressure is 47%. For people who have a sister, the probability of high blood pressure is 19%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.66
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.91
P(Y=1 | X=1, V2=1) = 0.25
P(V2=1 | X=0) = 0.47
P(V2=1 | X=1) = 0.19
0.47 * (0.25 - 0.91) + 0.19 * (0.09 - 0.66) = 0.21
0.21 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 57%. For people who do not have a sister, the probability of healthy heart is 39%. For people who have a sister, the probability of healthy heart is 79%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.79
0.57*0.79 - 0.43*0.39 = 0.61
0.61 > 0",mediation,blood_pressure,1,marginal,P(Y)
3822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 57%. The probability of not having a sister and healthy heart is 17%. The probability of having a sister and healthy heart is 44%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.44
0.44/0.57 - 0.17/0.43 = 0.39
0.39 > 0",mediation,blood_pressure,1,correlation,P(Y | X)
3824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 74%. For people who have a sister, the probability of healthy heart is 37%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.37
0.37 - 0.74 = -0.37
-0.37 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 74%. For people who have a sister, the probability of healthy heart is 37%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.37
0.37 - 0.74 = -0.37
-0.37 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
3832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 80%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 31%. For people who have a sister and with low blood pressure, the probability of healthy heart is 89%. For people who have a sister and with high blood pressure, the probability of healthy heart is 25%. For people who do not have a sister, the probability of high blood pressure is 12%. For people who have a sister, the probability of high blood pressure is 82%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.80
P(Y=1 | X=0, V2=1) = 0.31
P(Y=1 | X=1, V2=0) = 0.89
P(Y=1 | X=1, V2=1) = 0.25
P(V2=1 | X=0) = 0.12
P(V2=1 | X=1) = 0.82
0.12 * (0.25 - 0.89) + 0.82 * (0.31 - 0.80) = 0.07
0.07 > 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
3837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 97%. The probability of not having a sister and healthy heart is 2%. The probability of having a sister and healthy heart is 36%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.36
0.36/0.97 - 0.02/0.03 = -0.37
-0.37 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
3838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
3848,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 58%. For people considered unattractive and are not famous, the probability of thick lips is 6%. For people considered unattractive and are famous, the probability of thick lips is 25%. For people considered attractive and are not famous, the probability of thick lips is 3%. For people considered attractive and are famous, the probability of thick lips is 16%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.25
P(Y=1 | X=1, V3=0) = 0.03
P(Y=1 | X=1, V3=1) = 0.16
0.16 - (0.58*0.16 + 0.42*0.25) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 58%. For people considered unattractive and are not famous, the probability of thick lips is 6%. For people considered unattractive and are famous, the probability of thick lips is 25%. For people considered attractive and are not famous, the probability of thick lips is 3%. For people considered attractive and are famous, the probability of thick lips is 16%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.25
P(Y=1 | X=1, V3=0) = 0.03
P(Y=1 | X=1, V3=1) = 0.16
0.16 - (0.58*0.16 + 0.42*0.25) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3857,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.08.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 46%. For people considered unattractive and are not famous, the probability of thick lips is 9%. For people considered unattractive and are famous, the probability of thick lips is 30%. For people considered attractive and are not famous, the probability of thick lips is 5%. For people considered attractive and are famous, the probability of thick lips is 22%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.46
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.30
P(Y=1 | X=1, V3=0) = 0.05
P(Y=1 | X=1, V3=1) = 0.22
0.22 - (0.46*0.22 + 0.54*0.30) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 43%. For people considered unattractive, the probability of thick lips is 11%. For people considered attractive, the probability of thick lips is 11%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.11
0.43*0.11 - 0.57*0.11 = 0.11
0.11 > 0",collision,celebrity,1,marginal,P(Y)
3861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 43%. For people considered unattractive, the probability of thick lips is 11%. For people considered attractive, the probability of thick lips is 11%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.11
0.43*0.11 - 0.57*0.11 = 0.11
0.11 > 0",collision,celebrity,1,marginal,P(Y)
3865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 43%. For people considered unattractive and are not famous, the probability of thick lips is 7%. For people considered unattractive and are famous, the probability of thick lips is 19%. For people considered attractive and are not famous, the probability of thick lips is 4%. For people considered attractive and are famous, the probability of thick lips is 15%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.43
P(Y=1 | X=0, V3=0) = 0.07
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.15
0.15 - (0.43*0.15 + 0.57*0.19) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 43%. For people considered unattractive and are not famous, the probability of thick lips is 9%. For people considered unattractive and are famous, the probability of thick lips is 35%. For people considered attractive and are not famous, the probability of thick lips is 2%. For people considered attractive and are famous, the probability of thick lips is 25%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.43
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.25
0.25 - (0.43*0.25 + 0.57*0.35) = -0.04
-0.04 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3884,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.19.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.19.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 43%. For people considered unattractive and are not famous, the probability of thick lips is 4%. For people considered unattractive and are famous, the probability of thick lips is 27%. For people considered attractive and are not famous, the probability of thick lips is 4%. For people considered attractive and are famous, the probability of thick lips is 11%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.43
P(Y=1 | X=0, V3=0) = 0.04
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.11
0.11 - (0.43*0.11 + 0.57*0.27) = -0.04
-0.04 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 55%. For people considered unattractive, the probability of thick lips is 17%. For people considered attractive, the probability of thick lips is 17%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.17
0.55*0.17 - 0.45*0.17 = 0.17
0.17 > 0",collision,celebrity,1,marginal,P(Y)
3891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 55%. For people considered unattractive, the probability of thick lips is 17%. For people considered attractive, the probability of thick lips is 17%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.17
0.55*0.17 - 0.45*0.17 = 0.17
0.17 > 0",collision,celebrity,1,marginal,P(Y)
3907,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.27.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 58%. For people considered unattractive and are not famous, the probability of thick lips is 10%. For people considered unattractive and are famous, the probability of thick lips is 62%. For people considered attractive and are not famous, the probability of thick lips is 9%. For people considered attractive and are famous, the probability of thick lips is 29%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.10
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.09
P(Y=1 | X=1, V3=1) = 0.29
0.29 - (0.58*0.29 + 0.42*0.62) = -0.06
-0.06 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 58%. For people considered unattractive and are not famous, the probability of thick lips is 10%. For people considered unattractive and are famous, the probability of thick lips is 62%. For people considered attractive and are not famous, the probability of thick lips is 9%. For people considered attractive and are famous, the probability of thick lips is 29%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.10
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.09
P(Y=1 | X=1, V3=1) = 0.29
0.29 - (0.58*0.29 + 0.42*0.62) = -0.06
-0.06 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 52%. For people considered unattractive, the probability of thick lips is 16%. For people considered attractive, the probability of thick lips is 16%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.16
0.52*0.16 - 0.48*0.16 = 0.16
0.16 > 0",collision,celebrity,1,marginal,P(Y)
3915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3916,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.38.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.08.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3930,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 45%. For people considered unattractive, the probability of thick lips is 4%. For people considered attractive, the probability of thick lips is 4%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.04
P(Y=1 | X=1) = 0.04
0.45*0.04 - 0.55*0.04 = 0.04
0.04 > 0",collision,celebrity,1,marginal,P(Y)
3931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 45%. For people considered unattractive, the probability of thick lips is 4%. For people considered attractive, the probability of thick lips is 4%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.04
P(Y=1 | X=1) = 0.04
0.45*0.04 - 0.55*0.04 = 0.04
0.04 > 0",collision,celebrity,1,marginal,P(Y)
3935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.06.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 45%. For people considered unattractive and are not famous, the probability of thick lips is 2%. For people considered unattractive and are famous, the probability of thick lips is 11%. For people considered attractive and are not famous, the probability of thick lips is 0%. For people considered attractive and are famous, the probability of thick lips is 7%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.02
P(Y=1 | X=0, V3=1) = 0.11
P(Y=1 | X=1, V3=0) = 0.00
P(Y=1 | X=1, V3=1) = 0.07
0.07 - (0.45*0.07 + 0.55*0.11) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 49%. For people considered unattractive, the probability of thick lips is 12%. For people considered attractive, the probability of thick lips is 12%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.12
0.49*0.12 - 0.51*0.12 = 0.12
0.12 > 0",collision,celebrity,1,marginal,P(Y)
3944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3947,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.09.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 49%. For people considered unattractive and are not famous, the probability of thick lips is 9%. For people considered unattractive and are famous, the probability of thick lips is 29%. For people considered attractive and are not famous, the probability of thick lips is 6%. For people considered attractive and are famous, the probability of thick lips is 21%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.49
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.21
0.21 - (0.49*0.21 + 0.51*0.29) = -0.03
-0.03 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 47%. For people considered unattractive, the probability of thick lips is 19%. For people considered attractive, the probability of thick lips is 19%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.19
0.47*0.19 - 0.53*0.19 = 0.19
0.19 > 0",collision,celebrity,1,marginal,P(Y)
3964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.06.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
3978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 48%. For people considered unattractive and are not famous, the probability of thick lips is 3%. For people considered unattractive and are famous, the probability of thick lips is 9%. For people considered attractive and are not famous, the probability of thick lips is 2%. For people considered attractive and are famous, the probability of thick lips is 6%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.48
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.09
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.06
0.06 - (0.48*0.06 + 0.52*0.09) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 48%. For people considered unattractive and are not famous, the probability of thick lips is 3%. For people considered unattractive and are famous, the probability of thick lips is 9%. For people considered attractive and are not famous, the probability of thick lips is 2%. For people considered attractive and are famous, the probability of thick lips is 6%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.48
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.09
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.06
0.06 - (0.48*0.06 + 0.52*0.09) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
3980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 52%. For people considered unattractive, the probability of thick lips is 3%. For people considered attractive, the probability of thick lips is 3%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.03
P(Y=1 | X=1) = 0.03
0.52*0.03 - 0.48*0.03 = 0.03
0.03 > 0",collision,celebrity,1,marginal,P(Y)
3984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
3986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.03.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 60%. For people considered unattractive, the probability of thick lips is 18%. For people considered attractive, the probability of thick lips is 18%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.18
0.60*0.18 - 0.40*0.18 = 0.18
0.18 > 0",collision,celebrity,1,marginal,P(Y)
4004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 60%. For people considered unattractive and are not famous, the probability of thick lips is 12%. For people considered unattractive and are famous, the probability of thick lips is 31%. For people considered attractive and are not famous, the probability of thick lips is 9%. For people considered attractive and are famous, the probability of thick lips is 23%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.60
P(Y=1 | X=0, V3=0) = 0.12
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.09
P(Y=1 | X=1, V3=1) = 0.23
0.23 - (0.60*0.23 + 0.40*0.31) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 60%. For people considered unattractive and are not famous, the probability of thick lips is 12%. For people considered unattractive and are famous, the probability of thick lips is 31%. For people considered attractive and are not famous, the probability of thick lips is 9%. For people considered attractive and are famous, the probability of thick lips is 23%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.60
P(Y=1 | X=0, V3=0) = 0.12
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.09
P(Y=1 | X=1, V3=1) = 0.23
0.23 - (0.60*0.23 + 0.40*0.31) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 42%. For people considered unattractive, the probability of thick lips is 14%. For people considered attractive, the probability of thick lips is 14%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.14
0.42*0.14 - 0.58*0.14 = 0.14
0.14 > 0",collision,celebrity,1,marginal,P(Y)
4011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 42%. For people considered unattractive, the probability of thick lips is 14%. For people considered attractive, the probability of thick lips is 14%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.14
0.42*0.14 - 0.58*0.14 = 0.14
0.14 > 0",collision,celebrity,1,marginal,P(Y)
4014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 42%. For people considered unattractive and are not famous, the probability of thick lips is 11%. For people considered unattractive and are famous, the probability of thick lips is 45%. For people considered attractive and are not famous, the probability of thick lips is 9%. For people considered attractive and are famous, the probability of thick lips is 22%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.42
P(Y=1 | X=0, V3=0) = 0.11
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.09
P(Y=1 | X=1, V3=1) = 0.22
0.22 - (0.42*0.22 + 0.58*0.45) = -0.06
-0.06 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4021,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 54%. For people considered unattractive, the probability of thick lips is 11%. For people considered attractive, the probability of thick lips is 11%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.11
0.54*0.11 - 0.46*0.11 = 0.11
0.11 > 0",collision,celebrity,1,marginal,P(Y)
4026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.08.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.08.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 54%. For people considered unattractive and are not famous, the probability of thick lips is 8%. For people considered unattractive and are famous, the probability of thick lips is 26%. For people considered attractive and are not famous, the probability of thick lips is 6%. For people considered attractive and are famous, the probability of thick lips is 19%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.54
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.26
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.19
0.19 - (0.54*0.19 + 0.46*0.26) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 43%. For people considered unattractive, the probability of thick lips is 10%. For people considered attractive, the probability of thick lips is 10%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.10
0.43*0.10 - 0.57*0.10 = 0.10
0.10 > 0",collision,celebrity,1,marginal,P(Y)
4031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 43%. For people considered unattractive, the probability of thick lips is 10%. For people considered attractive, the probability of thick lips is 10%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.10
0.43*0.10 - 0.57*0.10 = 0.10
0.10 > 0",collision,celebrity,1,marginal,P(Y)
4034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4036,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.03.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 58%. For people considered unattractive and are not famous, the probability of thick lips is 5%. For people considered unattractive and are famous, the probability of thick lips is 51%. For people considered attractive and are not famous, the probability of thick lips is 4%. For people considered attractive and are famous, the probability of thick lips is 15%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.15
0.15 - (0.58*0.15 + 0.42*0.51) = -0.04
-0.04 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 41%. For people considered unattractive, the probability of thick lips is 2%. For people considered attractive, the probability of thick lips is 2%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.02
P(Y=1 | X=1) = 0.02
0.41*0.02 - 0.59*0.02 = 0.02
0.02 > 0",collision,celebrity,1,marginal,P(Y)
4051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 41%. For people considered unattractive, the probability of thick lips is 2%. For people considered attractive, the probability of thick lips is 2%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.02
P(Y=1 | X=1) = 0.02
0.41*0.02 - 0.59*0.02 = 0.02
0.02 > 0",collision,celebrity,1,marginal,P(Y)
4054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.06.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 41%. For people considered unattractive and are not famous, the probability of thick lips is 1%. For people considered unattractive and are famous, the probability of thick lips is 6%. For people considered attractive and are not famous, the probability of thick lips is 1%. For people considered attractive and are famous, the probability of thick lips is 3%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.41
P(Y=1 | X=0, V3=0) = 0.01
P(Y=1 | X=0, V3=1) = 0.06
P(Y=1 | X=1, V3=0) = 0.01
P(Y=1 | X=1, V3=1) = 0.03
0.03 - (0.41*0.03 + 0.59*0.06) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 57%. For people considered unattractive, the probability of thick lips is 14%. For people considered attractive, the probability of thick lips is 14%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.14
0.57*0.14 - 0.43*0.14 = 0.14
0.14 > 0",collision,celebrity,1,marginal,P(Y)
4070,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 58%. For people considered unattractive, the probability of thick lips is 13%. For people considered attractive, the probability of thick lips is 13%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.13
0.58*0.13 - 0.42*0.13 = 0.13
0.13 > 0",collision,celebrity,1,marginal,P(Y)
4086,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.08.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.08.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 56%. For people considered unattractive, the probability of thick lips is 9%. For people considered attractive, the probability of thick lips is 9%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.56*0.09 - 0.44*0.09 = 0.09
0.09 > 0",collision,celebrity,1,marginal,P(Y)
4096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.05.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.03.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 48%. For people considered unattractive and are not famous, the probability of thick lips is 1%. For people considered unattractive and are famous, the probability of thick lips is 3%. For people considered attractive and are not famous, the probability of thick lips is 0%. For people considered attractive and are famous, the probability of thick lips is 2%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.48
P(Y=1 | X=0, V3=0) = 0.01
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.00
P(Y=1 | X=1, V3=1) = 0.02
0.02 - (0.48*0.02 + 0.52*0.03) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 48%. For people considered unattractive and are not famous, the probability of thick lips is 1%. For people considered unattractive and are famous, the probability of thick lips is 3%. For people considered attractive and are not famous, the probability of thick lips is 0%. For people considered attractive and are famous, the probability of thick lips is 2%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.48
P(Y=1 | X=0, V3=0) = 0.01
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.00
P(Y=1 | X=1, V3=1) = 0.02
0.02 - (0.48*0.02 + 0.52*0.03) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4111,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 42%. For people considered unattractive, the probability of thick lips is 8%. For people considered attractive, the probability of thick lips is 8%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.08
P(Y=1 | X=1) = 0.08
0.42*0.08 - 0.58*0.08 = 0.08
0.08 > 0",collision,celebrity,1,marginal,P(Y)
4114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look directly at how appearance correlates with lip thickness in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.05.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4117,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.05.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 42%. For people considered unattractive and are not famous, the probability of thick lips is 5%. For people considered unattractive and are famous, the probability of thick lips is 14%. For people considered attractive and are not famous, the probability of thick lips is 3%. For people considered attractive and are famous, the probability of thick lips is 11%.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.42
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.14
P(Y=1 | X=1, V3=0) = 0.03
P(Y=1 | X=1, V3=1) = 0.11
0.11 - (0.42*0.11 + 0.58*0.14) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 55%. For people considered unattractive, the probability of thick lips is 10%. For people considered attractive, the probability of thick lips is 10%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.10
0.55*0.10 - 0.45*0.10 = 0.10
0.10 > 0",collision,celebrity,1,marginal,P(Y)
4127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. For people who are famous, the correlation between attractive appearance and thick lips is -0.09.",yes,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. Method 1: We look at how appearance correlates with lip thickness case by case according to fame. Method 2: We look directly at how appearance correlates with lip thickness in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
4138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Appearance has a direct effect on fame. Lip thickness has a direct effect on fame. The overall probability of attractive appearance is 60%. For people considered unattractive and are not famous, the probability of thick lips is 2%. For people considered unattractive and are famous, the probability of thick lips is 9%. For people considered attractive and are not famous, the probability of thick lips is 0%. For people considered attractive and are famous, the probability of thick lips is 5%.",no,"Let Y = lip thickness; X = appearance; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.60
P(Y=1 | X=0, V3=0) = 0.02
P(Y=1 | X=0, V3=1) = 0.09
P(Y=1 | X=1, V3=0) = 0.00
P(Y=1 | X=1, V3=1) = 0.05
0.05 - (0.60*0.05 + 0.40*0.09) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 55%. For patients assigned the drug treatment, the probability of freckles is 73%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 7%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 62%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.55
P(Y=1 | V2=1) = 0.73
P(X=1 | V2=0) = 0.07
P(X=1 | V2=1) = 0.62
(0.73 - 0.55) / (0.62 - 0.07) = 0.33
0.33 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 31%. For patients that have not taken any drugs, the probability of freckles is 53%. For patients that have taken all assigned drugs, the probability of freckles is 86%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.86
0.31*0.86 - 0.69*0.53 = 0.63
0.63 > 0",IV,cholesterol,1,marginal,P(Y)
4143,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 31%. For patients that have not taken any drugs, the probability of freckles is 53%. For patients that have taken all assigned drugs, the probability of freckles is 86%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.86
0.31*0.86 - 0.69*0.53 = 0.63
0.63 > 0",IV,cholesterol,1,marginal,P(Y)
4144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 31%. The probability of not taking of any assigned drugs and freckles is 36%. The probability of taking of all assigned drugs and freckles is 27%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.27
0.27/0.31 - 0.36/0.69 = 0.33
0.33 > 0",IV,cholesterol,1,correlation,P(Y | X)
4153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 24%. The probability of not taking of any assigned drugs and freckles is 46%. The probability of taking of all assigned drugs and freckles is 10%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.10
0.10/0.24 - 0.46/0.76 = -0.19
-0.19 < 0",IV,cholesterol,1,correlation,P(Y | X)
4156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 60%. For patients assigned the drug treatment, the probability of freckles is 72%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 28%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 79%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.60
P(Y=1 | V2=1) = 0.72
P(X=1 | V2=0) = 0.28
P(X=1 | V2=1) = 0.79
(0.72 - 0.60) / (0.79 - 0.28) = 0.24
0.24 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 48%. For patients that have not taken any drugs, the probability of freckles is 54%. For patients that have taken all assigned drugs, the probability of freckles is 77%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.77
0.48*0.77 - 0.52*0.54 = 0.65
0.65 > 0",IV,cholesterol,1,marginal,P(Y)
4161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 48%. The probability of not taking of any assigned drugs and freckles is 28%. The probability of taking of all assigned drugs and freckles is 37%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.37
0.37/0.48 - 0.28/0.52 = 0.23
0.23 > 0",IV,cholesterol,1,correlation,P(Y | X)
4162,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 59%. For patients assigned the drug treatment, the probability of freckles is 67%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 26%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 69%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.67
P(X=1 | V2=0) = 0.26
P(X=1 | V2=1) = 0.69
(0.67 - 0.59) / (0.69 - 0.26) = 0.20
0.20 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 59%. For patients assigned the drug treatment, the probability of freckles is 67%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 26%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 69%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.67
P(X=1 | V2=0) = 0.26
P(X=1 | V2=1) = 0.69
(0.67 - 0.59) / (0.69 - 0.26) = 0.20
0.20 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 31%. For patients that have not taken any drugs, the probability of freckles is 53%. For patients that have taken all assigned drugs, the probability of freckles is 73%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.73
0.31*0.73 - 0.69*0.53 = 0.60
0.60 > 0",IV,cholesterol,1,marginal,P(Y)
4171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 63%. For patients assigned the drug treatment, the probability of freckles is 52%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 37%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 74%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.63
P(Y=1 | V2=1) = 0.52
P(X=1 | V2=0) = 0.37
P(X=1 | V2=1) = 0.74
(0.52 - 0.63) / (0.74 - 0.37) = -0.29
-0.29 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 52%. The probability of not taking of any assigned drugs and freckles is 35%. The probability of taking of all assigned drugs and freckles is 23%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.23
0.23/0.52 - 0.35/0.48 = -0.29
-0.29 < 0",IV,cholesterol,1,correlation,P(Y | X)
4179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 6%. For patients assigned the drug treatment, the probability of freckles is 17%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 2%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 47%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.06
P(Y=1 | V2=1) = 0.17
P(X=1 | V2=0) = 0.02
P(X=1 | V2=1) = 0.47
(0.17 - 0.06) / (0.47 - 0.02) = 0.25
0.25 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 5%. For patients that have not taken any drugs, the probability of freckles is 5%. For patients that have taken all assigned drugs, the probability of freckles is 32%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.05
P(Y=1 | X=1) = 0.32
0.05*0.32 - 0.95*0.05 = 0.07
0.07 > 0",IV,cholesterol,1,marginal,P(Y)
4191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 34%. For patients that have not taken any drugs, the probability of freckles is 40%. For patients that have taken all assigned drugs, the probability of freckles is 66%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.34
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.66
0.34*0.66 - 0.66*0.40 = 0.49
0.49 > 0",IV,cholesterol,1,marginal,P(Y)
4195,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 59%. For patients that have not taken any drugs, the probability of freckles is 54%. For patients that have taken all assigned drugs, the probability of freckles is 41%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.41
0.59*0.41 - 0.41*0.54 = 0.46
0.46 > 0",IV,cholesterol,1,marginal,P(Y)
4200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 59%. The probability of not taking of any assigned drugs and freckles is 22%. The probability of taking of all assigned drugs and freckles is 24%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.24
0.24/0.59 - 0.22/0.41 = -0.12
-0.12 < 0",IV,cholesterol,1,correlation,P(Y | X)
4208,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 24%. The probability of not taking of any assigned drugs and freckles is 2%. The probability of taking of all assigned drugs and freckles is 9%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.09
0.09/0.24 - 0.02/0.76 = 0.34
0.34 > 0",IV,cholesterol,1,correlation,P(Y | X)
4209,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 24%. The probability of not taking of any assigned drugs and freckles is 2%. The probability of taking of all assigned drugs and freckles is 9%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.09
0.09/0.24 - 0.02/0.76 = 0.34
0.34 > 0",IV,cholesterol,1,correlation,P(Y | X)
4213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 29%. For patients assigned the drug treatment, the probability of freckles is 43%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 38%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 66%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.29
P(Y=1 | V2=1) = 0.43
P(X=1 | V2=0) = 0.38
P(X=1 | V2=1) = 0.66
(0.43 - 0.29) / (0.66 - 0.38) = 0.52
0.52 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 41%. For patients that have not taken any drugs, the probability of freckles is 9%. For patients that have taken all assigned drugs, the probability of freckles is 61%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.61
0.41*0.61 - 0.59*0.09 = 0.30
0.30 > 0",IV,cholesterol,1,marginal,P(Y)
4216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 41%. The probability of not taking of any assigned drugs and freckles is 5%. The probability of taking of all assigned drugs and freckles is 25%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.25
0.25/0.41 - 0.05/0.59 = 0.52
0.52 > 0",IV,cholesterol,1,correlation,P(Y | X)
4218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 45%. For patients assigned the drug treatment, the probability of freckles is 48%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 51%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 76%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.45
P(Y=1 | V2=1) = 0.48
P(X=1 | V2=0) = 0.51
P(X=1 | V2=1) = 0.76
(0.48 - 0.45) / (0.76 - 0.51) = 0.13
0.13 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 62%. For patients that have not taken any drugs, the probability of freckles is 38%. For patients that have taken all assigned drugs, the probability of freckles is 51%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.62
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.51
0.62*0.51 - 0.38*0.38 = 0.46
0.46 > 0",IV,cholesterol,1,marginal,P(Y)
4225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 62%. The probability of not taking of any assigned drugs and freckles is 15%. The probability of taking of all assigned drugs and freckles is 32%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.62
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.32
0.32/0.62 - 0.15/0.38 = 0.13
0.13 > 0",IV,cholesterol,1,correlation,P(Y | X)
4226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 55%. For patients that have not taken any drugs, the probability of freckles is 45%. For patients that have taken all assigned drugs, the probability of freckles is 54%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.54
0.55*0.54 - 0.45*0.45 = 0.50
0.50 > 0",IV,cholesterol,1,marginal,P(Y)
4233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 55%. The probability of not taking of any assigned drugs and freckles is 20%. The probability of taking of all assigned drugs and freckles is 30%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.30
0.30/0.55 - 0.20/0.45 = 0.10
0.10 > 0",IV,cholesterol,1,correlation,P(Y | X)
4235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 52%. For patients assigned the drug treatment, the probability of freckles is 50%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 22%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 49%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.22
P(X=1 | V2=1) = 0.49
(0.50 - 0.52) / (0.49 - 0.22) = -0.07
-0.07 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 52%. For patients assigned the drug treatment, the probability of freckles is 50%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 22%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 49%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.22
P(X=1 | V2=1) = 0.49
(0.50 - 0.52) / (0.49 - 0.22) = -0.07
-0.07 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 36%. For patients that have not taken any drugs, the probability of freckles is 54%. For patients that have taken all assigned drugs, the probability of freckles is 46%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.46
0.36*0.46 - 0.64*0.54 = 0.51
0.51 > 0",IV,cholesterol,1,marginal,P(Y)
4241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 36%. The probability of not taking of any assigned drugs and freckles is 35%. The probability of taking of all assigned drugs and freckles is 16%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.36
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.16
0.16/0.36 - 0.35/0.64 = -0.07
-0.07 < 0",IV,cholesterol,1,correlation,P(Y | X)
4242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 57%. For patients assigned the drug treatment, the probability of freckles is 54%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 49%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 80%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.57
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.49
P(X=1 | V2=1) = 0.80
(0.54 - 0.57) / (0.80 - 0.49) = -0.11
-0.11 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 55%. For patients that have not taken any drugs, the probability of freckles is 62%. For patients that have taken all assigned drugs, the probability of freckles is 51%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.51
0.55*0.51 - 0.45*0.62 = 0.56
0.56 > 0",IV,cholesterol,1,marginal,P(Y)
4247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 55%. For patients that have not taken any drugs, the probability of freckles is 62%. For patients that have taken all assigned drugs, the probability of freckles is 51%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.51
0.55*0.51 - 0.45*0.62 = 0.56
0.56 > 0",IV,cholesterol,1,marginal,P(Y)
4249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 55%. The probability of not taking of any assigned drugs and freckles is 28%. The probability of taking of all assigned drugs and freckles is 28%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.28
0.28/0.55 - 0.28/0.45 = -0.10
-0.10 < 0",IV,cholesterol,1,correlation,P(Y | X)
4250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 61%. For patients assigned the drug treatment, the probability of freckles is 59%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 37%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 64%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.37
P(X=1 | V2=1) = 0.64
(0.59 - 0.61) / (0.64 - 0.37) = -0.08
-0.08 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 61%. For patients assigned the drug treatment, the probability of freckles is 59%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 37%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 64%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.37
P(X=1 | V2=1) = 0.64
(0.59 - 0.61) / (0.64 - 0.37) = -0.08
-0.08 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 53%. For patients that have not taken any drugs, the probability of freckles is 64%. For patients that have taken all assigned drugs, the probability of freckles is 57%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.57
0.53*0.57 - 0.47*0.64 = 0.60
0.60 > 0",IV,cholesterol,1,marginal,P(Y)
4256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 53%. The probability of not taking of any assigned drugs and freckles is 30%. The probability of taking of all assigned drugs and freckles is 30%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.30
0.30/0.53 - 0.30/0.47 = -0.08
-0.08 < 0",IV,cholesterol,1,correlation,P(Y | X)
4266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 48%. For patients assigned the drug treatment, the probability of freckles is 40%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 16%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 67%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.48
P(Y=1 | V2=1) = 0.40
P(X=1 | V2=0) = 0.16
P(X=1 | V2=1) = 0.67
(0.40 - 0.48) / (0.67 - 0.16) = -0.16
-0.16 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 37%. The probability of not taking of any assigned drugs and freckles is 32%. The probability of taking of all assigned drugs and freckles is 13%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.13
0.13/0.37 - 0.32/0.63 = -0.16
-0.16 < 0",IV,cholesterol,1,correlation,P(Y | X)
4274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 9%. For patients assigned the drug treatment, the probability of freckles is 9%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 17%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 59%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.09
P(Y=1 | V2=1) = 0.09
P(X=1 | V2=0) = 0.17
P(X=1 | V2=1) = 0.59
(0.09 - 0.09) / (0.59 - 0.17) = -0.01
-0.01 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4278,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 18%. For patients that have not taken any drugs, the probability of freckles is 10%. For patients that have taken all assigned drugs, the probability of freckles is 9%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.09
0.18*0.09 - 0.82*0.10 = 0.09
0.09 > 0",IV,cholesterol,1,marginal,P(Y)
4285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 61%. For patients assigned the drug treatment, the probability of freckles is 63%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 39%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 63%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.63
P(X=1 | V2=0) = 0.39
P(X=1 | V2=1) = 0.63
(0.63 - 0.61) / (0.63 - 0.39) = 0.09
0.09 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 52%. For patients that have not taken any drugs, the probability of freckles is 57%. For patients that have taken all assigned drugs, the probability of freckles is 67%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.67
0.52*0.67 - 0.48*0.57 = 0.62
0.62 > 0",IV,cholesterol,1,marginal,P(Y)
4287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 52%. For patients that have not taken any drugs, the probability of freckles is 57%. For patients that have taken all assigned drugs, the probability of freckles is 67%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.67
0.52*0.67 - 0.48*0.57 = 0.62
0.62 > 0",IV,cholesterol,1,marginal,P(Y)
4289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 52%. The probability of not taking of any assigned drugs and freckles is 28%. The probability of taking of all assigned drugs and freckles is 34%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.34
0.34/0.52 - 0.28/0.48 = 0.09
0.09 > 0",IV,cholesterol,1,correlation,P(Y | X)
4290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 19%. For patients assigned the drug treatment, the probability of freckles is 14%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 36%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 83%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.19
P(Y=1 | V2=1) = 0.14
P(X=1 | V2=0) = 0.36
P(X=1 | V2=1) = 0.83
(0.14 - 0.19) / (0.83 - 0.36) = -0.10
-0.10 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 42%. For patients that have not taken any drugs, the probability of freckles is 22%. For patients that have taken all assigned drugs, the probability of freckles is 12%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.12
0.42*0.12 - 0.58*0.22 = 0.18
0.18 > 0",IV,cholesterol,1,marginal,P(Y)
4296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 42%. The probability of not taking of any assigned drugs and freckles is 13%. The probability of taking of all assigned drugs and freckles is 5%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.05
0.05/0.42 - 0.13/0.58 = -0.10
-0.10 < 0",IV,cholesterol,1,correlation,P(Y | X)
4300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 80%. For patients assigned the drug treatment, the probability of freckles is 82%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 44%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 77%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.80
P(Y=1 | V2=1) = 0.82
P(X=1 | V2=0) = 0.44
P(X=1 | V2=1) = 0.77
(0.82 - 0.80) / (0.77 - 0.44) = 0.09
0.09 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 80%. For patients assigned the drug treatment, the probability of freckles is 82%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 44%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 77%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.80
P(Y=1 | V2=1) = 0.82
P(X=1 | V2=0) = 0.44
P(X=1 | V2=1) = 0.77
(0.82 - 0.80) / (0.77 - 0.44) = 0.09
0.09 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 27%. The probability of not taking of any assigned drugs and freckles is 24%. The probability of taking of all assigned drugs and freckles is 15%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.27
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.15
0.15/0.27 - 0.24/0.73 = 0.24
0.24 > 0",IV,cholesterol,1,correlation,P(Y | X)
4313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 27%. The probability of not taking of any assigned drugs and freckles is 24%. The probability of taking of all assigned drugs and freckles is 15%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.27
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.15
0.15/0.27 - 0.24/0.73 = 0.24
0.24 > 0",IV,cholesterol,1,correlation,P(Y | X)
4315,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 48%. For patients that have not taken any drugs, the probability of freckles is 89%. For patients that have taken all assigned drugs, the probability of freckles is 64%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.64
0.48*0.64 - 0.52*0.89 = 0.77
0.77 > 0",IV,cholesterol,1,marginal,P(Y)
4322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 25%. For patients assigned the drug treatment, the probability of freckles is 34%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 18%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 81%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.25
P(Y=1 | V2=1) = 0.34
P(X=1 | V2=0) = 0.18
P(X=1 | V2=1) = 0.81
(0.34 - 0.25) / (0.81 - 0.18) = 0.14
0.14 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 53%. The probability of not taking of any assigned drugs and freckles is 11%. The probability of taking of all assigned drugs and freckles is 19%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.19
0.19/0.53 - 0.11/0.47 = 0.13
0.13 > 0",IV,cholesterol,1,correlation,P(Y | X)
4339,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 45%. For patients that have not taken any drugs, the probability of freckles is 42%. For patients that have taken all assigned drugs, the probability of freckles is 43%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.43
0.45*0.43 - 0.55*0.42 = 0.42
0.42 > 0",IV,cholesterol,1,marginal,P(Y)
4345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 45%. The probability of not taking of any assigned drugs and freckles is 23%. The probability of taking of all assigned drugs and freckles is 19%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.19
0.19/0.45 - 0.23/0.55 = 0.01
0.01 > 0",IV,cholesterol,1,correlation,P(Y | X)
4346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 50%. The probability of not taking of any assigned drugs and freckles is 31%. The probability of taking of all assigned drugs and freckles is 26%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.26
0.26/0.50 - 0.31/0.50 = -0.11
-0.11 < 0",IV,cholesterol,1,correlation,P(Y | X)
4355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 19%. For patients assigned the drug treatment, the probability of freckles is 26%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 26%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 59%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.19
P(Y=1 | V2=1) = 0.26
P(X=1 | V2=0) = 0.26
P(X=1 | V2=1) = 0.59
(0.26 - 0.19) / (0.59 - 0.26) = 0.20
0.20 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 19%. For patients assigned the drug treatment, the probability of freckles is 26%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 26%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 59%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.19
P(Y=1 | V2=1) = 0.26
P(X=1 | V2=0) = 0.26
P(X=1 | V2=1) = 0.59
(0.26 - 0.19) / (0.59 - 0.26) = 0.20
0.20 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 27%. For patients that have not taken any drugs, the probability of freckles is 14%. For patients that have taken all assigned drugs, the probability of freckles is 34%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.27
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.34
0.27*0.34 - 0.73*0.14 = 0.19
0.19 > 0",IV,cholesterol,1,marginal,P(Y)
4362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4364,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 63%. For patients assigned the drug treatment, the probability of freckles is 79%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 25%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 66%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.63
P(Y=1 | V2=1) = 0.79
P(X=1 | V2=0) = 0.25
P(X=1 | V2=1) = 0.66
(0.79 - 0.63) / (0.66 - 0.25) = 0.38
0.38 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4365,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 63%. For patients assigned the drug treatment, the probability of freckles is 79%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 25%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 66%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.63
P(Y=1 | V2=1) = 0.79
P(X=1 | V2=0) = 0.25
P(X=1 | V2=1) = 0.66
(0.79 - 0.63) / (0.66 - 0.25) = 0.38
0.38 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look directly at how drug taken correlates with freckles in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. Method 1: We look at how drug taken correlates with freckles case by case according to unobserved confounders. Method 2: We look directly at how drug taken correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
4373,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of freckles is 30%. For patients assigned the drug treatment, the probability of freckles is 29%. For patients not assigned the drug treatment, the probability of taking of all assigned drugs is 18%. For patients assigned the drug treatment, the probability of taking of all assigned drugs is 59%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.30
P(Y=1 | V2=1) = 0.29
P(X=1 | V2=0) = 0.18
P(X=1 | V2=1) = 0.59
(0.29 - 0.30) / (0.59 - 0.18) = -0.04
-0.04 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 22%. For patients that have not taken any drugs, the probability of freckles is 31%. For patients that have taken all assigned drugs, the probability of freckles is 27%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.27
0.22*0.27 - 0.78*0.31 = 0.30
0.30 > 0",IV,cholesterol,1,marginal,P(Y)
4376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 22%. The probability of not taking of any assigned drugs and freckles is 24%. The probability of taking of all assigned drugs and freckles is 6%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.22
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.06
0.06/0.22 - 0.24/0.78 = -0.04
-0.04 < 0",IV,cholesterol,1,correlation,P(Y | X)
4377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. The overall probability of taking of all assigned drugs is 22%. The probability of not taking of any assigned drugs and freckles is 24%. The probability of taking of all assigned drugs and freckles is 6%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.22
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.06
0.06/0.22 - 0.24/0.78 = -0.04
-0.04 < 0",IV,cholesterol,1,correlation,P(Y | X)
4380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 13%. For people with a college degree or higher, the probability of black hair is 58%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.58
0.58 - 0.13 = 0.45
0.45 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 13%. For people with a college degree or higher, the probability of black hair is 58%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.58
0.58 - 0.13 = 0.45
0.45 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 13%. For people with a college degree or higher, the probability of black hair is 58%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.58
0.58 - 0.13 = 0.45
0.45 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 2%. For people without a college degree, the probability of black hair is 13%. For people with a college degree or higher, the probability of black hair is 58%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.58
0.02*0.58 - 0.98*0.13 = 0.14
0.14 > 0",chain,college_salary,1,marginal,P(Y)
4388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 2%. The probability of high school degree or lower and black hair is 13%. The probability of college degree or higher and black hair is 1%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.13/0.98 = 0.45
0.45 > 0",chain,college_salary,1,correlation,P(Y | X)
4390,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look at how education level correlates with black hair case by case according to skill. Method 2: We look directly at how education level correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4392,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 43%. For people with a college degree or higher, the probability of black hair is 81%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.81
0.81 - 0.43 = 0.38
0.38 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 43%. For people with a college degree or higher, the probability of black hair is 81%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.81
0.81 - 0.43 = 0.38
0.38 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 43%. For people with a college degree or higher, the probability of black hair is 81%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.81
0.81 - 0.43 = 0.38
0.38 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 43%. For people with a college degree or higher, the probability of black hair is 81%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.81
0.81 - 0.43 = 0.38
0.38 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 45%. For people without a college degree, the probability of black hair is 43%. For people with a college degree or higher, the probability of black hair is 81%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.81
0.45*0.81 - 0.55*0.43 = 0.60
0.60 > 0",chain,college_salary,1,marginal,P(Y)
4404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 61%. For people with a college degree or higher, the probability of black hair is 80%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.80
0.80 - 0.61 = 0.18
0.18 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 61%. For people with a college degree or higher, the probability of black hair is 80%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.80
0.80 - 0.61 = 0.18
0.18 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 14%. For people without a college degree, the probability of black hair is 61%. For people with a college degree or higher, the probability of black hair is 80%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.80
0.14*0.80 - 0.86*0.61 = 0.64
0.64 > 0",chain,college_salary,1,marginal,P(Y)
4421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 51%. For people with a college degree or higher, the probability of black hair is 81%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.81
0.81 - 0.51 = 0.31
0.31 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 43%. For people without a college degree, the probability of black hair is 51%. For people with a college degree or higher, the probability of black hair is 81%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.81
0.43*0.81 - 0.57*0.51 = 0.64
0.64 > 0",chain,college_salary,1,marginal,P(Y)
4426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look at how education level correlates with black hair case by case according to skill. Method 2: We look directly at how education level correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 21%. For people with a college degree or higher, the probability of black hair is 38%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.38
0.38 - 0.21 = 0.18
0.18 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 21%. For people with a college degree or higher, the probability of black hair is 38%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.38
0.38 - 0.21 = 0.18
0.18 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 8%. The probability of high school degree or lower and black hair is 19%. The probability of college degree or higher and black hair is 3%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.19/0.92 = 0.18
0.18 > 0",chain,college_salary,1,correlation,P(Y | X)
4444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 26%. For people with a college degree or higher, the probability of black hair is 40%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.40
0.40 - 0.26 = 0.14
0.14 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4445,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 26%. For people with a college degree or higher, the probability of black hair is 40%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.40
0.40 - 0.26 = 0.14
0.14 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 60%. For people without a college degree, the probability of black hair is 26%. For people with a college degree or higher, the probability of black hair is 40%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.40
0.60*0.40 - 0.40*0.26 = 0.34
0.34 > 0",chain,college_salary,1,marginal,P(Y)
4447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 60%. For people without a college degree, the probability of black hair is 26%. For people with a college degree or higher, the probability of black hair is 40%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.40
0.60*0.40 - 0.40*0.26 = 0.34
0.34 > 0",chain,college_salary,1,marginal,P(Y)
4448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 60%. The probability of high school degree or lower and black hair is 11%. The probability of college degree or higher and black hair is 24%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.24
0.24/0.60 - 0.11/0.40 = 0.14
0.14 > 0",chain,college_salary,1,correlation,P(Y | X)
4451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 11%. For people with a college degree or higher, the probability of black hair is 53%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.53
0.53 - 0.11 = 0.42
0.42 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 11%. For people with a college degree or higher, the probability of black hair is 53%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.53
0.53 - 0.11 = 0.42
0.42 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4457,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 11%. For people with a college degree or higher, the probability of black hair is 53%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.53
0.53 - 0.11 = 0.42
0.42 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4459,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 3%. For people without a college degree, the probability of black hair is 11%. For people with a college degree or higher, the probability of black hair is 53%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.53
0.03*0.53 - 0.97*0.11 = 0.13
0.13 > 0",chain,college_salary,1,marginal,P(Y)
4460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 3%. The probability of high school degree or lower and black hair is 11%. The probability of college degree or higher and black hair is 2%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.11/0.97 = 0.42
0.42 > 0",chain,college_salary,1,correlation,P(Y | X)
4471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 49%. For people without a college degree, the probability of black hair is 53%. For people with a college degree or higher, the probability of black hair is 74%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.74
0.49*0.74 - 0.51*0.53 = 0.63
0.63 > 0",chain,college_salary,1,marginal,P(Y)
4472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 49%. The probability of high school degree or lower and black hair is 27%. The probability of college degree or higher and black hair is 36%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.36
0.36/0.49 - 0.27/0.51 = 0.21
0.21 > 0",chain,college_salary,1,correlation,P(Y | X)
4476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 37%. For people with a college degree or higher, the probability of black hair is 45%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.45
0.45 - 0.37 = 0.08
0.08 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 37%. For people with a college degree or higher, the probability of black hair is 45%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.45
0.45 - 0.37 = 0.08
0.08 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 37%. For people with a college degree or higher, the probability of black hair is 45%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.45
0.45 - 0.37 = 0.08
0.08 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 13%. For people without a college degree, the probability of black hair is 37%. For people with a college degree or higher, the probability of black hair is 45%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.45
0.13*0.45 - 0.87*0.37 = 0.38
0.38 > 0",chain,college_salary,1,marginal,P(Y)
4487,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 40%. For people with a college degree or higher, the probability of black hair is 69%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.69
0.69 - 0.40 = 0.29
0.29 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 40%. For people with a college degree or higher, the probability of black hair is 69%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.69
0.69 - 0.40 = 0.29
0.29 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4491,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 40%. For people with a college degree or higher, the probability of black hair is 69%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.69
0.69 - 0.40 = 0.29
0.29 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 44%. For people without a college degree, the probability of black hair is 40%. For people with a college degree or higher, the probability of black hair is 69%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.69
0.44*0.69 - 0.56*0.40 = 0.53
0.53 > 0",chain,college_salary,1,marginal,P(Y)
4498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look at how education level correlates with black hair case by case according to skill. Method 2: We look directly at how education level correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 79%. For people with a college degree or higher, the probability of black hair is 89%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.89
0.89 - 0.79 = 0.10
0.10 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 79%. For people with a college degree or higher, the probability of black hair is 89%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.89
0.89 - 0.79 = 0.10
0.10 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 79%. For people with a college degree or higher, the probability of black hair is 89%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.89
0.89 - 0.79 = 0.10
0.10 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 16%. The probability of high school degree or lower and black hair is 66%. The probability of college degree or higher and black hair is 15%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.15
0.15/0.16 - 0.66/0.84 = 0.10
0.10 > 0",chain,college_salary,1,correlation,P(Y | X)
4518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 43%. For people without a college degree, the probability of black hair is 31%. For people with a college degree or higher, the probability of black hair is 56%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.56
0.43*0.56 - 0.57*0.31 = 0.42
0.42 > 0",chain,college_salary,1,marginal,P(Y)
4521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 43%. The probability of high school degree or lower and black hair is 17%. The probability of college degree or higher and black hair is 24%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.24
0.24/0.43 - 0.17/0.57 = 0.25
0.25 > 0",chain,college_salary,1,correlation,P(Y | X)
4522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look at how education level correlates with black hair case by case according to skill. Method 2: We look directly at how education level correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 45%. For people with a college degree or higher, the probability of black hair is 61%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.61
0.61 - 0.45 = 0.16
0.16 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 45%. For people with a college degree or higher, the probability of black hair is 61%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.61
0.61 - 0.45 = 0.16
0.16 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 12%. The probability of high school degree or lower and black hair is 39%. The probability of college degree or higher and black hair is 7%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.07
0.07/0.12 - 0.39/0.88 = 0.16
0.16 > 0",chain,college_salary,1,correlation,P(Y | X)
4540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 20%. For people with a college degree or higher, the probability of black hair is 35%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.35
0.35 - 0.20 = 0.16
0.16 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 41%. The probability of high school degree or lower and black hair is 12%. The probability of college degree or higher and black hair is 14%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.14
0.14/0.41 - 0.12/0.59 = 0.16
0.16 > 0",chain,college_salary,1,correlation,P(Y | X)
4546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look at how education level correlates with black hair case by case according to skill. Method 2: We look directly at how education level correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 52%. For people with a college degree or higher, the probability of black hair is 67%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.67
0.67 - 0.52 = 0.15
0.15 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 52%. For people with a college degree or higher, the probability of black hair is 67%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.67
0.67 - 0.52 = 0.15
0.15 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 52%. For people with a college degree or higher, the probability of black hair is 67%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.67
0.67 - 0.52 = 0.15
0.15 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 52%. For people with a college degree or higher, the probability of black hair is 67%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.67
0.67 - 0.52 = 0.15
0.15 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4558,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look at how education level correlates with black hair case by case according to skill. Method 2: We look directly at how education level correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 24%. For people with a college degree or higher, the probability of black hair is 67%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.67
0.67 - 0.24 = 0.43
0.43 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 51%. For people without a college degree, the probability of black hair is 24%. For people with a college degree or higher, the probability of black hair is 67%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.67
0.51*0.67 - 0.49*0.24 = 0.46
0.46 > 0",chain,college_salary,1,marginal,P(Y)
4568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 51%. The probability of high school degree or lower and black hair is 12%. The probability of college degree or higher and black hair is 34%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.34
0.34/0.51 - 0.12/0.49 = 0.43
0.43 > 0",chain,college_salary,1,correlation,P(Y | X)
4570,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look at how education level correlates with black hair case by case according to skill. Method 2: We look directly at how education level correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 26%. For people with a college degree or higher, the probability of black hair is 58%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.58
0.58 - 0.26 = 0.31
0.31 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 26%. For people with a college degree or higher, the probability of black hair is 58%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.58
0.58 - 0.26 = 0.31
0.31 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 26%. For people with a college degree or higher, the probability of black hair is 58%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.58
0.58 - 0.26 = 0.31
0.31 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 6%. The probability of high school degree or lower and black hair is 25%. The probability of college degree or higher and black hair is 3%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.03
0.03/0.06 - 0.25/0.94 = 0.31
0.31 > 0",chain,college_salary,1,correlation,P(Y | X)
4582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look at how education level correlates with black hair case by case according to skill. Method 2: We look directly at how education level correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 69%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.69
0.69 - 0.42 = 0.28
0.28 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 69%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.69
0.69 - 0.42 = 0.28
0.28 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 43%. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 69%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.69
0.43*0.69 - 0.57*0.42 = 0.53
0.53 > 0",chain,college_salary,1,marginal,P(Y)
4593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 43%. The probability of high school degree or lower and black hair is 24%. The probability of college degree or higher and black hair is 30%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.30
0.30/0.43 - 0.24/0.57 = 0.28
0.28 > 0",chain,college_salary,1,correlation,P(Y | X)
4599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 65%. For people with a college degree or higher, the probability of black hair is 84%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.84
0.84 - 0.65 = 0.20
0.20 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 65%. For people with a college degree or higher, the probability of black hair is 84%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.84
0.84 - 0.65 = 0.20
0.20 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4602,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 2%. For people without a college degree, the probability of black hair is 65%. For people with a college degree or higher, the probability of black hair is 84%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.84
0.02*0.84 - 0.98*0.65 = 0.65
0.65 > 0",chain,college_salary,1,marginal,P(Y)
4609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 40%. For people with a college degree or higher, the probability of black hair is 61%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.61
0.61 - 0.40 = 0.20
0.20 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 40%. For people with a college degree or higher, the probability of black hair is 61%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.61
0.61 - 0.40 = 0.20
0.20 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 45%. The probability of high school degree or lower and black hair is 22%. The probability of college degree or higher and black hair is 28%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.28
0.28/0.45 - 0.22/0.55 = 0.20
0.20 > 0",chain,college_salary,1,correlation,P(Y | X)
4622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 47%. For people with a college degree or higher, the probability of black hair is 66%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.66
0.66 - 0.47 = 0.18
0.18 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 47%. For people with a college degree or higher, the probability of black hair is 66%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.66
0.66 - 0.47 = 0.18
0.18 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 17%. For people without a college degree, the probability of black hair is 47%. For people with a college degree or higher, the probability of black hair is 66%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.66
0.17*0.66 - 0.83*0.47 = 0.51
0.51 > 0",chain,college_salary,1,marginal,P(Y)
4629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 17%. The probability of high school degree or lower and black hair is 39%. The probability of college degree or higher and black hair is 11%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.11
0.11/0.17 - 0.39/0.83 = 0.18
0.18 > 0",chain,college_salary,1,correlation,P(Y | X)
4635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 31%. For people with a college degree or higher, the probability of black hair is 40%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.40
0.40 - 0.31 = 0.09
0.09 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4639,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 45%. For people without a college degree, the probability of black hair is 31%. For people with a college degree or higher, the probability of black hair is 40%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.40
0.45*0.40 - 0.55*0.31 = 0.35
0.35 > 0",chain,college_salary,1,marginal,P(Y)
4640,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 45%. The probability of high school degree or lower and black hair is 17%. The probability of college degree or higher and black hair is 18%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.18
0.18/0.45 - 0.17/0.55 = 0.09
0.09 > 0",chain,college_salary,1,correlation,P(Y | X)
4644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 63%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.63
0.63 - 0.42 = 0.21
0.21 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 63%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.63
0.63 - 0.42 = 0.21
0.21 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 63%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.63
0.63 - 0.42 = 0.21
0.21 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 63%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.63
0.63 - 0.42 = 0.21
0.21 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 63%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.63
0.63 - 0.42 = 0.21
0.21 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 19%. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 63%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.63
0.19*0.63 - 0.81*0.42 = 0.46
0.46 > 0",chain,college_salary,1,marginal,P(Y)
4651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 19%. For people without a college degree, the probability of black hair is 42%. For people with a college degree or higher, the probability of black hair is 63%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.63
0.19*0.63 - 0.81*0.42 = 0.46
0.46 > 0",chain,college_salary,1,marginal,P(Y)
4653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 19%. The probability of high school degree or lower and black hair is 34%. The probability of college degree or higher and black hair is 12%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.12
0.12/0.19 - 0.34/0.81 = 0.21
0.21 > 0",chain,college_salary,1,correlation,P(Y | X)
4657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 54%. For people with a college degree or higher, the probability of black hair is 83%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.83
0.83 - 0.54 = 0.28
0.28 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 54%. For people with a college degree or higher, the probability of black hair is 83%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.83
0.83 - 0.54 = 0.28
0.28 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4661,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 54%. For people with a college degree or higher, the probability of black hair is 83%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.83
0.83 - 0.54 = 0.28
0.28 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 60%. For people without a college degree, the probability of black hair is 54%. For people with a college degree or higher, the probability of black hair is 83%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.83
0.60*0.83 - 0.40*0.54 = 0.71
0.71 > 0",chain,college_salary,1,marginal,P(Y)
4664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 60%. The probability of high school degree or lower and black hair is 22%. The probability of college degree or higher and black hair is 50%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.50
0.50/0.60 - 0.22/0.40 = 0.28
0.28 > 0",chain,college_salary,1,correlation,P(Y | X)
4667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 55%. For people with a college degree or higher, the probability of black hair is 87%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.87
0.87 - 0.55 = 0.32
0.32 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 55%. For people with a college degree or higher, the probability of black hair is 87%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.87
0.87 - 0.55 = 0.32
0.32 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4670,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 55%. For people with a college degree or higher, the probability of black hair is 87%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.87
0.87 - 0.55 = 0.32
0.32 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 55%. For people with a college degree or higher, the probability of black hair is 87%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.87
0.87 - 0.55 = 0.32
0.32 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 55%. For people with a college degree or higher, the probability of black hair is 87%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.87
0.87 - 0.55 = 0.32
0.32 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 12%. The probability of high school degree or lower and black hair is 49%. The probability of college degree or higher and black hair is 10%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.10
0.10/0.12 - 0.49/0.88 = 0.32
0.32 > 0",chain,college_salary,1,correlation,P(Y | X)
4689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 42%. The probability of high school degree or lower and black hair is 18%. The probability of college degree or higher and black hair is 22%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.22
0.22/0.42 - 0.18/0.58 = 0.20
0.20 > 0",chain,college_salary,1,correlation,P(Y | X)
4691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 54%. For people with a college degree or higher, the probability of black hair is 69%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.69
0.69 - 0.54 = 0.16
0.16 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 7%. The probability of high school degree or lower and black hair is 50%. The probability of college degree or higher and black hair is 5%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.05
0.05/0.07 - 0.50/0.93 = 0.16
0.16 > 0",chain,college_salary,1,correlation,P(Y | X)
4706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 39%. For people with a college degree or higher, the probability of black hair is 66%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.66
0.66 - 0.39 = 0.28
0.28 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 39%. For people with a college degree or higher, the probability of black hair is 66%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.66
0.66 - 0.39 = 0.28
0.28 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 54%. For people without a college degree, the probability of black hair is 39%. For people with a college degree or higher, the probability of black hair is 66%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.66
0.54*0.66 - 0.46*0.39 = 0.54
0.54 > 0",chain,college_salary,1,marginal,P(Y)
4717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 47%. For people with a college degree or higher, the probability of black hair is 61%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.61
0.61 - 0.47 = 0.13
0.13 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 47%. For people with a college degree or higher, the probability of black hair is 61%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.61
0.61 - 0.47 = 0.13
0.13 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 47%. For people with a college degree or higher, the probability of black hair is 61%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.61
0.61 - 0.47 = 0.13
0.13 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
4722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 53%. For people without a college degree, the probability of black hair is 47%. For people with a college degree or higher, the probability of black hair is 61%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.61
0.53*0.61 - 0.47*0.47 = 0.54
0.54 > 0",chain,college_salary,1,marginal,P(Y)
4725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. The overall probability of college degree or higher is 53%. The probability of high school degree or lower and black hair is 22%. The probability of college degree or higher and black hair is 32%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.32
0.32/0.53 - 0.22/0.47 = 0.13
0.13 > 0",chain,college_salary,1,correlation,P(Y | X)
4727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 54%. For people with a college degree or higher, the probability of black hair is 70%.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.70
0.70 - 0.54 = 0.15
0.15 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. For people without a college degree, the probability of black hair is 54%. For people with a college degree or higher, the probability of black hair is 70%.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.70
0.70 - 0.54 = 0.15
0.15 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
4739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. Method 1: We look directly at how education level correlates with black hair in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
4742,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 35%. For people who do not drink coffee, the probability of high salary is 25%. For people who drink coffee, the probability of high salary is 94%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.94
0.35*0.94 - 0.65*0.25 = 0.49
0.49 > 0",IV,college_wage,1,marginal,P(Y)
4743,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 35%. For people who do not drink coffee, the probability of high salary is 25%. For people who drink coffee, the probability of high salary is 94%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.94
0.35*0.94 - 0.65*0.25 = 0.49
0.49 > 0",IV,college_wage,1,marginal,P(Y)
4744,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 35%. The probability of not drinking coffee and high salary is 16%. The probability of drinking coffee and high salary is 33%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.33
0.33/0.35 - 0.16/0.65 = 0.70
0.70 > 0",IV,college_wage,1,correlation,P(Y | X)
4746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 70%. For people living close to a college, the probability of high salary is 81%. For people living far from a college, the probability of drinking coffee is 47%. For people living close to a college, the probability of drinking coffee is 80%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.70
P(Y=1 | V2=1) = 0.81
P(X=1 | V2=0) = 0.47
P(X=1 | V2=1) = 0.80
(0.81 - 0.70) / (0.80 - 0.47) = 0.36
0.36 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 47%. For people living close to a college, the probability of high salary is 59%. For people living far from a college, the probability of drinking coffee is 32%. For people living close to a college, the probability of drinking coffee is 75%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.47
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.32
P(X=1 | V2=1) = 0.75
(0.59 - 0.47) / (0.75 - 0.32) = 0.28
0.28 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 47%. For people living close to a college, the probability of high salary is 59%. For people living far from a college, the probability of drinking coffee is 32%. For people living close to a college, the probability of drinking coffee is 75%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.47
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.32
P(X=1 | V2=1) = 0.75
(0.59 - 0.47) / (0.75 - 0.32) = 0.28
0.28 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 55%. For people who do not drink coffee, the probability of high salary is 38%. For people who drink coffee, the probability of high salary is 66%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.66
0.55*0.66 - 0.45*0.38 = 0.53
0.53 > 0",IV,college_wage,1,marginal,P(Y)
4759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 55%. For people who do not drink coffee, the probability of high salary is 38%. For people who drink coffee, the probability of high salary is 66%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.66
0.55*0.66 - 0.45*0.38 = 0.53
0.53 > 0",IV,college_wage,1,marginal,P(Y)
4761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 55%. The probability of not drinking coffee and high salary is 17%. The probability of drinking coffee and high salary is 36%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.36
0.36/0.55 - 0.17/0.45 = 0.28
0.28 > 0",IV,college_wage,1,correlation,P(Y | X)
4762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 38%. For people living close to a college, the probability of high salary is 49%. For people living far from a college, the probability of drinking coffee is 13%. For people living close to a college, the probability of drinking coffee is 52%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.38
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.13
P(X=1 | V2=1) = 0.52
(0.49 - 0.38) / (0.52 - 0.13) = 0.29
0.29 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 32%. For people who do not drink coffee, the probability of high salary is 34%. For people who drink coffee, the probability of high salary is 63%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.63
0.32*0.63 - 0.68*0.34 = 0.44
0.44 > 0",IV,college_wage,1,marginal,P(Y)
4767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 32%. For people who do not drink coffee, the probability of high salary is 34%. For people who drink coffee, the probability of high salary is 63%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.63
0.32*0.63 - 0.68*0.34 = 0.44
0.44 > 0",IV,college_wage,1,marginal,P(Y)
4768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 32%. The probability of not drinking coffee and high salary is 23%. The probability of drinking coffee and high salary is 20%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.32
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.20
0.20/0.32 - 0.23/0.68 = 0.29
0.29 > 0",IV,college_wage,1,correlation,P(Y | X)
4770,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 36%. For people living close to a college, the probability of high salary is 63%. For people living far from a college, the probability of drinking coffee is 27%. For people living close to a college, the probability of drinking coffee is 73%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.36
P(Y=1 | V2=1) = 0.63
P(X=1 | V2=0) = 0.27
P(X=1 | V2=1) = 0.73
(0.63 - 0.36) / (0.73 - 0.27) = 0.61
0.61 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4773,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 36%. For people living close to a college, the probability of high salary is 63%. For people living far from a college, the probability of drinking coffee is 27%. For people living close to a college, the probability of drinking coffee is 73%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.36
P(Y=1 | V2=1) = 0.63
P(X=1 | V2=0) = 0.27
P(X=1 | V2=1) = 0.73
(0.63 - 0.36) / (0.73 - 0.27) = 0.61
0.61 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 50%. For people who do not drink coffee, the probability of high salary is 19%. For people who drink coffee, the probability of high salary is 79%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.79
0.50*0.79 - 0.50*0.19 = 0.49
0.49 > 0",IV,college_wage,1,marginal,P(Y)
4778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 47%. For people living close to a college, the probability of high salary is 62%. For people living far from a college, the probability of drinking coffee is 31%. For people living close to a college, the probability of drinking coffee is 68%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.47
P(Y=1 | V2=1) = 0.62
P(X=1 | V2=0) = 0.31
P(X=1 | V2=1) = 0.68
(0.62 - 0.47) / (0.68 - 0.31) = 0.39
0.39 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4782,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 47%. For people who do not drink coffee, the probability of high salary is 35%. For people who drink coffee, the probability of high salary is 74%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.74
0.47*0.74 - 0.53*0.35 = 0.53
0.53 > 0",IV,college_wage,1,marginal,P(Y)
4784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 47%. The probability of not drinking coffee and high salary is 19%. The probability of drinking coffee and high salary is 35%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.35
0.35/0.47 - 0.19/0.53 = 0.39
0.39 > 0",IV,college_wage,1,correlation,P(Y | X)
4788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 22%. For people living close to a college, the probability of high salary is 34%. For people living far from a college, the probability of drinking coffee is 2%. For people living close to a college, the probability of drinking coffee is 48%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.22
P(Y=1 | V2=1) = 0.34
P(X=1 | V2=0) = 0.02
P(X=1 | V2=1) = 0.48
(0.34 - 0.22) / (0.48 - 0.02) = 0.26
0.26 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 22%. For people living close to a college, the probability of high salary is 34%. For people living far from a college, the probability of drinking coffee is 2%. For people living close to a college, the probability of drinking coffee is 48%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.22
P(Y=1 | V2=1) = 0.34
P(X=1 | V2=0) = 0.02
P(X=1 | V2=1) = 0.48
(0.34 - 0.22) / (0.48 - 0.02) = 0.26
0.26 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 55%. For people living close to a college, the probability of high salary is 71%. For people living far from a college, the probability of drinking coffee is 36%. For people living close to a college, the probability of drinking coffee is 88%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.55
P(Y=1 | V2=1) = 0.71
P(X=1 | V2=0) = 0.36
P(X=1 | V2=1) = 0.88
(0.71 - 0.55) / (0.88 - 0.36) = 0.31
0.31 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 57%. For people who do not drink coffee, the probability of high salary is 44%. For people who drink coffee, the probability of high salary is 75%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.75
0.57*0.75 - 0.43*0.44 = 0.62
0.62 > 0",IV,college_wage,1,marginal,P(Y)
4800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 57%. The probability of not drinking coffee and high salary is 19%. The probability of drinking coffee and high salary is 43%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.43
0.43/0.57 - 0.19/0.43 = 0.31
0.31 > 0",IV,college_wage,1,correlation,P(Y | X)
4804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 22%. For people living close to a college, the probability of high salary is 42%. For people living far from a college, the probability of drinking coffee is 39%. For people living close to a college, the probability of drinking coffee is 78%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.22
P(Y=1 | V2=1) = 0.42
P(X=1 | V2=0) = 0.39
P(X=1 | V2=1) = 0.78
(0.42 - 0.22) / (0.78 - 0.39) = 0.50
0.50 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 61%. The probability of not drinking coffee and high salary is 1%. The probability of drinking coffee and high salary is 32%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.61
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.32
0.32/0.61 - 0.01/0.39 = 0.50
0.50 > 0",IV,college_wage,1,correlation,P(Y | X)
4809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 61%. The probability of not drinking coffee and high salary is 1%. The probability of drinking coffee and high salary is 32%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.61
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.32
0.32/0.61 - 0.01/0.39 = 0.50
0.50 > 0",IV,college_wage,1,correlation,P(Y | X)
4811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 51%. For people living close to a college, the probability of high salary is 60%. For people living far from a college, the probability of drinking coffee is 11%. For people living close to a college, the probability of drinking coffee is 46%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.51
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.11
P(X=1 | V2=1) = 0.46
(0.60 - 0.51) / (0.46 - 0.11) = 0.27
0.27 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 51%. For people living close to a college, the probability of high salary is 60%. For people living far from a college, the probability of drinking coffee is 11%. For people living close to a college, the probability of drinking coffee is 46%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.51
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.11
P(X=1 | V2=1) = 0.46
(0.60 - 0.51) / (0.46 - 0.11) = 0.27
0.27 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 27%. For people who do not drink coffee, the probability of high salary is 48%. For people who drink coffee, the probability of high salary is 75%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.27
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.75
0.27*0.75 - 0.73*0.48 = 0.55
0.55 > 0",IV,college_wage,1,marginal,P(Y)
4826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 46%. For people living close to a college, the probability of high salary is 63%. For people living far from a college, the probability of drinking coffee is 45%. For people living close to a college, the probability of drinking coffee is 81%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.46
P(Y=1 | V2=1) = 0.63
P(X=1 | V2=0) = 0.45
P(X=1 | V2=1) = 0.81
(0.63 - 0.46) / (0.81 - 0.45) = 0.47
0.47 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 46%. For people living close to a college, the probability of high salary is 63%. For people living far from a college, the probability of drinking coffee is 45%. For people living close to a college, the probability of drinking coffee is 81%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.46
P(Y=1 | V2=1) = 0.63
P(X=1 | V2=0) = 0.45
P(X=1 | V2=1) = 0.81
(0.63 - 0.46) / (0.81 - 0.45) = 0.47
0.47 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4834,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 84%. For people living close to a college, the probability of high salary is 93%. For people living far from a college, the probability of drinking coffee is 35%. For people living close to a college, the probability of drinking coffee is 77%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.84
P(Y=1 | V2=1) = 0.93
P(X=1 | V2=0) = 0.35
P(X=1 | V2=1) = 0.77
(0.93 - 0.84) / (0.77 - 0.35) = 0.23
0.23 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 84%. For people living close to a college, the probability of high salary is 93%. For people living far from a college, the probability of drinking coffee is 35%. For people living close to a college, the probability of drinking coffee is 77%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.84
P(Y=1 | V2=1) = 0.93
P(X=1 | V2=0) = 0.35
P(X=1 | V2=1) = 0.77
(0.93 - 0.84) / (0.77 - 0.35) = 0.23
0.23 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 59%. For people who do not drink coffee, the probability of high salary is 75%. For people who drink coffee, the probability of high salary is 99%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.99
0.59*0.99 - 0.41*0.75 = 0.89
0.89 > 0",IV,college_wage,1,marginal,P(Y)
4841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 59%. The probability of not drinking coffee and high salary is 31%. The probability of drinking coffee and high salary is 58%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.58
0.58/0.59 - 0.31/0.41 = 0.23
0.23 > 0",IV,college_wage,1,correlation,P(Y | X)
4842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 49%. For people who do not drink coffee, the probability of high salary is 39%. For people who drink coffee, the probability of high salary is 72%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.72
0.49*0.72 - 0.51*0.39 = 0.55
0.55 > 0",IV,college_wage,1,marginal,P(Y)
4849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 49%. The probability of not drinking coffee and high salary is 20%. The probability of drinking coffee and high salary is 35%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.35
0.35/0.49 - 0.20/0.51 = 0.33
0.33 > 0",IV,college_wage,1,correlation,P(Y | X)
4851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 51%. For people living close to a college, the probability of high salary is 73%. For people living far from a college, the probability of drinking coffee is 53%. For people living close to a college, the probability of drinking coffee is 88%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.51
P(Y=1 | V2=1) = 0.73
P(X=1 | V2=0) = 0.53
P(X=1 | V2=1) = 0.88
(0.73 - 0.51) / (0.88 - 0.53) = 0.62
0.62 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 74%. For people who do not drink coffee, the probability of high salary is 19%. For people who drink coffee, the probability of high salary is 81%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.74
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.81
0.74*0.81 - 0.26*0.19 = 0.64
0.64 > 0",IV,college_wage,1,marginal,P(Y)
4868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 41%. For people living close to a college, the probability of high salary is 49%. For people living far from a college, the probability of drinking coffee is 46%. For people living close to a college, the probability of drinking coffee is 71%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.41
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.46
P(X=1 | V2=1) = 0.71
(0.49 - 0.41) / (0.71 - 0.46) = 0.31
0.31 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 41%. For people living close to a college, the probability of high salary is 49%. For people living far from a college, the probability of drinking coffee is 46%. For people living close to a college, the probability of drinking coffee is 71%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.41
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.46
P(X=1 | V2=1) = 0.71
(0.49 - 0.41) / (0.71 - 0.46) = 0.31
0.31 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 61%. For people who do not drink coffee, the probability of high salary is 27%. For people who drink coffee, the probability of high salary is 58%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.58
0.61*0.58 - 0.39*0.27 = 0.46
0.46 > 0",IV,college_wage,1,marginal,P(Y)
4875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 52%. For people living close to a college, the probability of high salary is 65%. For people living far from a college, the probability of drinking coffee is 35%. For people living close to a college, the probability of drinking coffee is 61%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.65
P(X=1 | V2=0) = 0.35
P(X=1 | V2=1) = 0.61
(0.65 - 0.52) / (0.61 - 0.35) = 0.52
0.52 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 47%. The probability of not drinking coffee and high salary is 18%. The probability of drinking coffee and high salary is 41%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.41
0.41/0.47 - 0.18/0.53 = 0.52
0.52 > 0",IV,college_wage,1,correlation,P(Y | X)
4881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 47%. The probability of not drinking coffee and high salary is 18%. The probability of drinking coffee and high salary is 41%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.41
0.41/0.47 - 0.18/0.53 = 0.52
0.52 > 0",IV,college_wage,1,correlation,P(Y | X)
4882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 36%. The probability of not drinking coffee and high salary is 12%. The probability of drinking coffee and high salary is 23%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.36
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.23
0.23/0.36 - 0.12/0.64 = 0.46
0.46 > 0",IV,college_wage,1,correlation,P(Y | X)
4889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 36%. The probability of not drinking coffee and high salary is 12%. The probability of drinking coffee and high salary is 23%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.36
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.23
0.23/0.36 - 0.12/0.64 = 0.46
0.46 > 0",IV,college_wage,1,correlation,P(Y | X)
4890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4895,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 57%. For people who do not drink coffee, the probability of high salary is 25%. For people who drink coffee, the probability of high salary is 60%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.60
0.57*0.60 - 0.43*0.25 = 0.45
0.45 > 0",IV,college_wage,1,marginal,P(Y)
4896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 57%. The probability of not drinking coffee and high salary is 11%. The probability of drinking coffee and high salary is 34%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.34
0.34/0.57 - 0.11/0.43 = 0.35
0.35 > 0",IV,college_wage,1,correlation,P(Y | X)
4897,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 57%. The probability of not drinking coffee and high salary is 11%. The probability of drinking coffee and high salary is 34%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.34
0.34/0.57 - 0.11/0.43 = 0.35
0.35 > 0",IV,college_wage,1,correlation,P(Y | X)
4907,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 36%. For people living close to a college, the probability of high salary is 52%. For people living far from a college, the probability of drinking coffee is 32%. For people living close to a college, the probability of drinking coffee is 80%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.36
P(Y=1 | V2=1) = 0.52
P(X=1 | V2=0) = 0.32
P(X=1 | V2=1) = 0.80
(0.52 - 0.36) / (0.80 - 0.32) = 0.34
0.34 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 36%. For people living close to a college, the probability of high salary is 52%. For people living far from a college, the probability of drinking coffee is 32%. For people living close to a college, the probability of drinking coffee is 80%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.36
P(Y=1 | V2=1) = 0.52
P(X=1 | V2=0) = 0.32
P(X=1 | V2=1) = 0.80
(0.52 - 0.36) / (0.80 - 0.32) = 0.34
0.34 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 59%. For people who do not drink coffee, the probability of high salary is 25%. For people who drink coffee, the probability of high salary is 59%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.59
0.59*0.59 - 0.41*0.25 = 0.45
0.45 > 0",IV,college_wage,1,marginal,P(Y)
4911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 59%. For people who do not drink coffee, the probability of high salary is 25%. For people who drink coffee, the probability of high salary is 59%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.59
0.59*0.59 - 0.41*0.25 = 0.45
0.45 > 0",IV,college_wage,1,marginal,P(Y)
4912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 59%. The probability of not drinking coffee and high salary is 10%. The probability of drinking coffee and high salary is 34%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.34
0.34/0.59 - 0.10/0.41 = 0.34
0.34 > 0",IV,college_wage,1,correlation,P(Y | X)
4921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 59%. The probability of not drinking coffee and high salary is 16%. The probability of drinking coffee and high salary is 42%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.42
0.42/0.59 - 0.16/0.41 = 0.33
0.33 > 0",IV,college_wage,1,correlation,P(Y | X)
4926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 46%. For people who do not drink coffee, the probability of high salary is 38%. For people who drink coffee, the probability of high salary is 88%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.88
0.46*0.88 - 0.54*0.38 = 0.61
0.61 > 0",IV,college_wage,1,marginal,P(Y)
4927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 46%. For people who do not drink coffee, the probability of high salary is 38%. For people who drink coffee, the probability of high salary is 88%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.88
0.46*0.88 - 0.54*0.38 = 0.61
0.61 > 0",IV,college_wage,1,marginal,P(Y)
4928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 46%. The probability of not drinking coffee and high salary is 21%. The probability of drinking coffee and high salary is 40%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.40
0.40/0.46 - 0.21/0.54 = 0.50
0.50 > 0",IV,college_wage,1,correlation,P(Y | X)
4931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4932,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 61%. For people living close to a college, the probability of high salary is 73%. For people living far from a college, the probability of drinking coffee is 33%. For people living close to a college, the probability of drinking coffee is 61%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.73
P(X=1 | V2=0) = 0.33
P(X=1 | V2=1) = 0.61
(0.73 - 0.61) / (0.61 - 0.33) = 0.42
0.42 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 47%. For people who do not drink coffee, the probability of high salary is 47%. For people who drink coffee, the probability of high salary is 90%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.90
0.47*0.90 - 0.53*0.47 = 0.67
0.67 > 0",IV,college_wage,1,marginal,P(Y)
4938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 58%. For people who do not drink coffee, the probability of high salary is 30%. For people who drink coffee, the probability of high salary is 64%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.64
0.58*0.64 - 0.42*0.30 = 0.50
0.50 > 0",IV,college_wage,1,marginal,P(Y)
4946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. For people living far from a college, the probability of high salary is 38%. For people living close to a college, the probability of high salary is 49%. For people living far from a college, the probability of drinking coffee is 13%. For people living close to a college, the probability of drinking coffee is 49%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.38
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.13
P(X=1 | V2=1) = 0.49
(0.49 - 0.38) / (0.49 - 0.13) = 0.30
0.30 > 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
4950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 30%. For people who do not drink coffee, the probability of high salary is 34%. For people who drink coffee, the probability of high salary is 64%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.30
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.64
0.30*0.64 - 0.70*0.34 = 0.43
0.43 > 0",IV,college_wage,1,marginal,P(Y)
4953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 30%. The probability of not drinking coffee and high salary is 24%. The probability of drinking coffee and high salary is 19%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.19
0.19/0.30 - 0.24/0.70 = 0.30
0.30 > 0",IV,college_wage,1,correlation,P(Y | X)
4954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 51%. For people who do not drink coffee, the probability of high salary is 32%. For people who drink coffee, the probability of high salary is 64%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.64
0.51*0.64 - 0.49*0.32 = 0.48
0.48 > 0",IV,college_wage,1,marginal,P(Y)
4962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look directly at how drinking coffee correlates with salary in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 45%. The probability of not drinking coffee and high salary is 27%. The probability of drinking coffee and high salary is 42%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.42
0.42/0.45 - 0.27/0.55 = 0.46
0.46 > 0",IV,college_wage,1,correlation,P(Y | X)
4971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. Method 1: We look at how drinking coffee correlates with salary case by case according to unobserved confounders. Method 2: We look directly at how drinking coffee correlates with salary in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
4974,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 55%. For people who do not drink coffee, the probability of high salary is 41%. For people who drink coffee, the probability of high salary is 90%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.90
0.55*0.90 - 0.45*0.41 = 0.68
0.68 > 0",IV,college_wage,1,marginal,P(Y)
4975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. The overall probability of drinking coffee is 55%. For people who do not drink coffee, the probability of high salary is 41%. For people who drink coffee, the probability of high salary is 90%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.90
0.55*0.90 - 0.45*0.41 = 0.68
0.68 > 0",IV,college_wage,1,marginal,P(Y)
4980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 18%. For students who do not listen to jazz, the probability of being hard-working is 9%. For students who listen to jazz, the probability of being hard-working is 9%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.18*0.09 - 0.82*0.09 = 0.09
0.09 > 0",collision,elite_students,1,marginal,P(Y)
4981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 18%. For students who do not listen to jazz, the probability of being hard-working is 9%. For students who listen to jazz, the probability of being hard-working is 9%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.18*0.09 - 0.82*0.09 = 0.09
0.09 > 0",collision,elite_students,1,marginal,P(Y)
4985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
4986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.05.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
4988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 18%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 6%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 18%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 4%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 14%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.18
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.18
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.14
0.14 - (0.18*0.14 + 0.82*0.18) = -0.03
-0.03 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
4990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 59%. For students who do not listen to jazz, the probability of being hard-working is 53%. For students who listen to jazz, the probability of being hard-working is 53%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.53
0.59*0.53 - 0.41*0.53 = 0.53
0.53 > 0",collision,elite_students,1,marginal,P(Y)
4994,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
4995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
4996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.09.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.04.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 55%. For students who do not listen to jazz, the probability of being hard-working is 45%. For students who listen to jazz, the probability of being hard-working is 45%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.45
0.55*0.45 - 0.45*0.45 = 0.45
0.45 > 0",collision,elite_students,1,marginal,P(Y)
5015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.18.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 55%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 36%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 76%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 36%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 56%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.55
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.56
0.56 - (0.55*0.56 + 0.45*0.76) = -0.06
-0.06 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 16%. For students who do not listen to jazz, the probability of being hard-working is 9%. For students who listen to jazz, the probability of being hard-working is 9%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.16*0.09 - 0.84*0.09 = 0.09
0.09 > 0",collision,elite_students,1,marginal,P(Y)
5024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.09.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5028,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 16%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 6%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 22%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 2%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 14%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.16
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.22
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.14
0.14 - (0.16*0.14 + 0.84*0.22) = -0.05
-0.05 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 44%. For students who do not listen to jazz, the probability of being hard-working is 50%. For students who listen to jazz, the probability of being hard-working is 50%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.50
0.44*0.50 - 0.56*0.50 = 0.50
0.50 > 0",collision,elite_students,1,marginal,P(Y)
5041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 12%. For students who do not listen to jazz, the probability of being hard-working is 6%. For students who listen to jazz, the probability of being hard-working is 6%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.06
0.12*0.06 - 0.88*0.06 = 0.06
0.06 > 0",collision,elite_students,1,marginal,P(Y)
5046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.16.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 12%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 4%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 27%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 2%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 13%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.12
P(Y=1 | X=0, V3=0) = 0.04
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.13
0.13 - (0.12*0.13 + 0.88*0.27) = -0.10
-0.10 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.04.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 12%. For students who do not listen to jazz, the probability of being hard-working is 11%. For students who listen to jazz, the probability of being hard-working is 11%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.11
0.12*0.11 - 0.88*0.11 = 0.11
0.11 > 0",collision,elite_students,1,marginal,P(Y)
5068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 12%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 8%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 18%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 5%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 14%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.12
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.18
P(Y=1 | X=1, V3=0) = 0.05
P(Y=1 | X=1, V3=1) = 0.14
0.14 - (0.12*0.14 + 0.88*0.18) = -0.02
-0.02 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.06.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 15%. For students who do not listen to jazz, the probability of being hard-working is 9%. For students who listen to jazz, the probability of being hard-working is 9%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.15*0.09 - 0.85*0.09 = 0.09
0.09 > 0",collision,elite_students,1,marginal,P(Y)
5085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.07.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 15%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 6%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 22%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 4%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 16%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.15
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.22
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.16
0.16 - (0.15*0.16 + 0.85*0.22) = -0.05
-0.05 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.20.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.20.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 53%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 30%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 78%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 15%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 55%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.53
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.15
P(Y=1 | X=1, V3=1) = 0.55
0.55 - (0.53*0.55 + 0.47*0.78) = -0.06
-0.06 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 53%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 30%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 78%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 15%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 55%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.53
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.15
P(Y=1 | X=1, V3=1) = 0.55
0.55 - (0.53*0.55 + 0.47*0.78) = -0.06
-0.06 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5100,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 11%. For students who do not listen to jazz, the probability of being hard-working is 6%. For students who listen to jazz, the probability of being hard-working is 6%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.06
0.11*0.06 - 0.89*0.06 = 0.06
0.06 > 0",collision,elite_students,1,marginal,P(Y)
5107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.03.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 11%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 4%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 12%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 2%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 10%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.11
P(Y=1 | X=0, V3=0) = 0.04
P(Y=1 | X=0, V3=1) = 0.12
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.10
0.10 - (0.11*0.10 + 0.89*0.12) = -0.02
-0.02 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 11%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 4%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 12%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 2%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 10%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.11
P(Y=1 | X=0, V3=0) = 0.04
P(Y=1 | X=0, V3=1) = 0.12
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.10
0.10 - (0.11*0.10 + 0.89*0.12) = -0.02
-0.02 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5111,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 42%. For students who do not listen to jazz, the probability of being hard-working is 51%. For students who listen to jazz, the probability of being hard-working is 51%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.51
0.42*0.51 - 0.58*0.51 = 0.51
0.51 > 0",collision,elite_students,1,marginal,P(Y)
5114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.04.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 42%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 43%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 65%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 31%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 62%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.42
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.31
P(Y=1 | X=1, V3=1) = 0.62
0.62 - (0.42*0.62 + 0.58*0.65) = -0.02
-0.02 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 42%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 43%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 65%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 31%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 62%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.42
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.31
P(Y=1 | X=1, V3=1) = 0.62
0.62 - (0.42*0.62 + 0.58*0.65) = -0.02
-0.02 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5129,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 10%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 8%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 23%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 6%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 17%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.10
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.23
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.17
0.17 - (0.10*0.17 + 0.90*0.23) = -0.05
-0.05 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.07.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.07.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 47%. For students who do not listen to jazz, the probability of being hard-working is 50%. For students who listen to jazz, the probability of being hard-working is 50%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.50
0.47*0.50 - 0.53*0.50 = 0.50
0.50 > 0",collision,elite_students,1,marginal,P(Y)
5155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.15.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 47%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 41%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 76%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 34%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 61%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.47
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.34
P(Y=1 | X=1, V3=1) = 0.61
0.61 - (0.47*0.61 + 0.53*0.76) = -0.05
-0.05 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 47%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 41%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 76%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 34%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 61%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.47
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.34
P(Y=1 | X=1, V3=1) = 0.61
0.61 - (0.47*0.61 + 0.53*0.76) = -0.05
-0.05 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.08.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 12%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 6%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 19%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 4%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 13%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.12
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.13
0.13 - (0.12*0.13 + 0.88*0.19) = -0.05
-0.05 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 47%. For students who do not listen to jazz, the probability of being hard-working is 51%. For students who listen to jazz, the probability of being hard-working is 51%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.51
0.47*0.51 - 0.53*0.51 = 0.51
0.51 > 0",collision,elite_students,1,marginal,P(Y)
5176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.06.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 8%. For students who do not listen to jazz, the probability of being hard-working is 12%. For students who listen to jazz, the probability of being hard-working is 12%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.12
0.08*0.12 - 0.92*0.12 = 0.12
0.12 > 0",collision,elite_students,1,marginal,P(Y)
5184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 47%. For students who do not listen to jazz, the probability of being hard-working is 49%. For students who listen to jazz, the probability of being hard-working is 49%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.47*0.49 - 0.53*0.49 = 0.49
0.49 > 0",collision,elite_students,1,marginal,P(Y)
5206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.01.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.01.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5208,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 2%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 1%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 3%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 0%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 2%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.02
P(Y=1 | X=0, V3=0) = 0.01
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.00
P(Y=1 | X=1, V3=1) = 0.02
0.02 - (0.02*0.02 + 0.98*0.03) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 13%. For students who do not listen to jazz, the probability of being hard-working is 4%. For students who listen to jazz, the probability of being hard-working is 4%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.04
P(Y=1 | X=1) = 0.04
0.13*0.04 - 0.87*0.04 = 0.04
0.04 > 0",collision,elite_students,1,marginal,P(Y)
5230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 47%. For students who do not listen to jazz, the probability of being hard-working is 57%. For students who listen to jazz, the probability of being hard-working is 57%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.57
0.47*0.57 - 0.53*0.57 = 0.57
0.57 > 0",collision,elite_students,1,marginal,P(Y)
5236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.26.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 47%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 43%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 91%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 21%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 66%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.47
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.21
P(Y=1 | X=1, V3=1) = 0.66
0.66 - (0.47*0.66 + 0.53*0.91) = -0.07
-0.07 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.66.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.66.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.00.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look directly at how listening to jazz correlates with effort in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 2%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 5%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 20%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 4%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 11%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.02
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.11
0.11 - (0.02*0.11 + 0.98*0.20) = -0.08
-0.08 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 2%. For students who do not listen to jazz and rejected from elite institutions, the probability of being hard-working is 5%. For students who do not listen to jazz and accepted to elite institutions, the probability of being hard-working is 20%. For students who listen to jazz and rejected from elite institutions, the probability of being hard-working is 4%. For students who listen to jazz and accepted to elite institutions, the probability of being hard-working is 11%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.02
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.11
0.11 - (0.02*0.11 + 0.98*0.20) = -0.08
-0.08 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
5270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 44%. For students who do not listen to jazz, the probability of being hard-working is 54%. For students who listen to jazz, the probability of being hard-working is 54%.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.54
0.44*0.54 - 0.56*0.54 = 0.54
0.54 > 0",collision,elite_students,1,marginal,P(Y)
5271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. The overall probability of listening to jazz is 44%. For students who do not listen to jazz, the probability of being hard-working is 54%. For students who listen to jazz, the probability of being hard-working is 54%.",no,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.54
0.44*0.54 - 0.56*0.54 = 0.54
0.54 > 0",collision,elite_students,1,marginal,P(Y)
5274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. Method 1: We look at how listening to jazz correlates with effort case by case according to elite institution admission status. Method 2: We look directly at how listening to jazz correlates with effort in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
5277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on elite institution admission status. Effort has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between listening to jazz and being hard-working is -0.15.",yes,"Let Y = effort; X = listening to jazz; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
5282,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 35%. For students who can swim, the probability of high exam score is 67%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.67
0.67 - 0.35 = 0.32
0.32 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 27%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 47%. For students who can swim and study hard, the probability of high exam score is 82%. For students who cannot swim, the probability of studying hard is 31%. For students who can swim, the probability of studying hard is 57%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.27
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.82
P(V2=1 | X=0) = 0.31
P(V2=1 | X=1) = 0.57
0.57 * (0.52 - 0.27)+ 0.31 * (0.82 - 0.47)= 0.06
0.06 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 27%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 47%. For students who can swim and study hard, the probability of high exam score is 82%. For students who cannot swim, the probability of studying hard is 31%. For students who can swim, the probability of studying hard is 57%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.27
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.82
P(V2=1 | X=0) = 0.31
P(V2=1 | X=1) = 0.57
0.57 * (0.52 - 0.27)+ 0.31 * (0.82 - 0.47)= 0.06
0.06 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 27%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 47%. For students who can swim and study hard, the probability of high exam score is 82%. For students who cannot swim, the probability of studying hard is 31%. For students who can swim, the probability of studying hard is 57%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.27
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.82
P(V2=1 | X=0) = 0.31
P(V2=1 | X=1) = 0.57
0.31 * (0.82 - 0.47) + 0.57 * (0.52 - 0.27) = 0.23
0.23 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 15%. The probability of not being able to swim and high exam score is 29%. The probability of being able to swim and high exam score is 10%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.10
0.10/0.15 - 0.29/0.85 = 0.32
0.32 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 15%. The probability of not being able to swim and high exam score is 29%. The probability of being able to swim and high exam score is 10%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.10
0.10/0.15 - 0.29/0.85 = 0.32
0.32 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 26%. For students who can swim, the probability of high exam score is 65%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.65
0.65 - 0.26 = 0.39
0.39 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 26%. For students who can swim, the probability of high exam score is 65%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.65
0.65 - 0.26 = 0.39
0.39 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5302,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 57%. For students who cannot swim, the probability of high exam score is 26%. For students who can swim, the probability of high exam score is 65%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.65
0.57*0.65 - 0.43*0.26 = 0.48
0.48 > 0",mediation,encouagement_program,1,marginal,P(Y)
5307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 21%. For students who can swim, the probability of high exam score is 64%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.64
0.64 - 0.21 = 0.44
0.44 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 10%. The probability of not being able to swim and high exam score is 19%. The probability of being able to swim and high exam score is 7%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.07
0.07/0.10 - 0.19/0.90 = 0.44
0.44 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 44%. For students who can swim, the probability of high exam score is 86%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.86
0.86 - 0.44 = 0.42
0.42 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 37%. For students who cannot swim and study hard, the probability of high exam score is 65%. For students who can swim and do not study hard, the probability of high exam score is 71%. For students who can swim and study hard, the probability of high exam score is 95%. For students who cannot swim, the probability of studying hard is 24%. For students who can swim, the probability of studying hard is 61%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.37
P(Y=1 | X=0, V2=1) = 0.65
P(Y=1 | X=1, V2=0) = 0.71
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.24
P(V2=1 | X=1) = 0.61
0.61 * (0.65 - 0.37)+ 0.24 * (0.95 - 0.71)= 0.10
0.10 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 52%. The probability of not being able to swim and high exam score is 21%. The probability of being able to swim and high exam score is 45%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.45
0.45/0.52 - 0.21/0.48 = 0.42
0.42 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 28%. For students who can swim, the probability of high exam score is 71%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.71
0.71 - 0.28 = 0.44
0.44 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 28%. For students who can swim, the probability of high exam score is 71%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.71
0.71 - 0.28 = 0.44
0.44 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 18%. For students who cannot swim and study hard, the probability of high exam score is 43%. For students who can swim and do not study hard, the probability of high exam score is 52%. For students who can swim and study hard, the probability of high exam score is 75%. For students who cannot swim, the probability of studying hard is 38%. For students who can swim, the probability of studying hard is 83%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.18
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.75
P(V2=1 | X=0) = 0.38
P(V2=1 | X=1) = 0.83
0.83 * (0.43 - 0.18)+ 0.38 * (0.75 - 0.52)= 0.11
0.11 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 18%. For students who cannot swim and study hard, the probability of high exam score is 43%. For students who can swim and do not study hard, the probability of high exam score is 52%. For students who can swim and study hard, the probability of high exam score is 75%. For students who cannot swim, the probability of studying hard is 38%. For students who can swim, the probability of studying hard is 83%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.18
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.75
P(V2=1 | X=0) = 0.38
P(V2=1 | X=1) = 0.83
0.38 * (0.75 - 0.52) + 0.83 * (0.43 - 0.18) = 0.33
0.33 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 18%. For students who cannot swim and study hard, the probability of high exam score is 43%. For students who can swim and do not study hard, the probability of high exam score is 52%. For students who can swim and study hard, the probability of high exam score is 75%. For students who cannot swim, the probability of studying hard is 38%. For students who can swim, the probability of studying hard is 83%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.18
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.75
P(V2=1 | X=0) = 0.38
P(V2=1 | X=1) = 0.83
0.38 * (0.75 - 0.52) + 0.83 * (0.43 - 0.18) = 0.33
0.33 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 13%. For students who cannot swim, the probability of high exam score is 28%. For students who can swim, the probability of high exam score is 71%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.71
0.13*0.71 - 0.87*0.28 = 0.33
0.33 > 0",mediation,encouagement_program,1,marginal,P(Y)
5345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 13%. For students who cannot swim, the probability of high exam score is 28%. For students who can swim, the probability of high exam score is 71%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.71
0.13*0.71 - 0.87*0.28 = 0.33
0.33 > 0",mediation,encouagement_program,1,marginal,P(Y)
5352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 34%. For students who can swim, the probability of high exam score is 81%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.81
0.81 - 0.34 = 0.47
0.47 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 34%. For students who can swim, the probability of high exam score is 81%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.81
0.81 - 0.34 = 0.47
0.47 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 32%. For students who cannot swim and study hard, the probability of high exam score is 56%. For students who can swim and do not study hard, the probability of high exam score is 53%. For students who can swim and study hard, the probability of high exam score is 86%. For students who cannot swim, the probability of studying hard is 10%. For students who can swim, the probability of studying hard is 85%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.32
P(Y=1 | X=0, V2=1) = 0.56
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.10
P(V2=1 | X=1) = 0.85
0.85 * (0.56 - 0.32)+ 0.10 * (0.86 - 0.53)= 0.19
0.19 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 32%. For students who cannot swim and study hard, the probability of high exam score is 56%. For students who can swim and do not study hard, the probability of high exam score is 53%. For students who can swim and study hard, the probability of high exam score is 86%. For students who cannot swim, the probability of studying hard is 10%. For students who can swim, the probability of studying hard is 85%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.32
P(Y=1 | X=0, V2=1) = 0.56
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.10
P(V2=1 | X=1) = 0.85
0.85 * (0.56 - 0.32)+ 0.10 * (0.86 - 0.53)= 0.19
0.19 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 32%. For students who cannot swim and study hard, the probability of high exam score is 56%. For students who can swim and do not study hard, the probability of high exam score is 53%. For students who can swim and study hard, the probability of high exam score is 86%. For students who cannot swim, the probability of studying hard is 10%. For students who can swim, the probability of studying hard is 85%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.32
P(Y=1 | X=0, V2=1) = 0.56
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.10
P(V2=1 | X=1) = 0.85
0.10 * (0.86 - 0.53) + 0.85 * (0.56 - 0.32) = 0.23
0.23 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 45%. For students who cannot swim, the probability of high exam score is 34%. For students who can swim, the probability of high exam score is 81%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.81
0.45*0.81 - 0.55*0.34 = 0.54
0.54 > 0",mediation,encouagement_program,1,marginal,P(Y)
5360,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 45%. The probability of not being able to swim and high exam score is 19%. The probability of being able to swim and high exam score is 37%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.37
0.37/0.45 - 0.19/0.55 = 0.47
0.47 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 45%. The probability of not being able to swim and high exam score is 19%. The probability of being able to swim and high exam score is 37%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.37
0.37/0.45 - 0.19/0.55 = 0.47
0.47 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5365,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 20%. For students who can swim, the probability of high exam score is 56%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.56
0.56 - 0.20 = 0.35
0.35 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 12%. For students who cannot swim and study hard, the probability of high exam score is 40%. For students who can swim and do not study hard, the probability of high exam score is 39%. For students who can swim and study hard, the probability of high exam score is 68%. For students who cannot swim, the probability of studying hard is 31%. For students who can swim, the probability of studying hard is 57%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.12
P(Y=1 | X=0, V2=1) = 0.40
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.31
P(V2=1 | X=1) = 0.57
0.31 * (0.68 - 0.39) + 0.57 * (0.40 - 0.12) = 0.27
0.27 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 7%. For students who cannot swim, the probability of high exam score is 20%. For students who can swim, the probability of high exam score is 56%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.56
0.07*0.56 - 0.93*0.20 = 0.23
0.23 > 0",mediation,encouagement_program,1,marginal,P(Y)
5376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 26%. For students who can swim, the probability of high exam score is 72%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.72
0.72 - 0.26 = 0.46
0.46 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 26%. For students who can swim, the probability of high exam score is 72%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.72
0.72 - 0.26 = 0.46
0.46 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 26%. For students who can swim, the probability of high exam score is 72%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.72
0.72 - 0.26 = 0.46
0.46 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 19%. For students who cannot swim and study hard, the probability of high exam score is 44%. For students who can swim and do not study hard, the probability of high exam score is 48%. For students who can swim and study hard, the probability of high exam score is 77%. For students who cannot swim, the probability of studying hard is 30%. For students who can swim, the probability of studying hard is 86%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.19
P(Y=1 | X=0, V2=1) = 0.44
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.30
P(V2=1 | X=1) = 0.86
0.86 * (0.44 - 0.19)+ 0.30 * (0.77 - 0.48)= 0.14
0.14 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 19%. For students who cannot swim and study hard, the probability of high exam score is 44%. For students who can swim and do not study hard, the probability of high exam score is 48%. For students who can swim and study hard, the probability of high exam score is 77%. For students who cannot swim, the probability of studying hard is 30%. For students who can swim, the probability of studying hard is 86%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.19
P(Y=1 | X=0, V2=1) = 0.44
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.30
P(V2=1 | X=1) = 0.86
0.30 * (0.77 - 0.48) + 0.86 * (0.44 - 0.19) = 0.30
0.30 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 46%. For students who cannot swim, the probability of high exam score is 26%. For students who can swim, the probability of high exam score is 72%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.72
0.46*0.72 - 0.54*0.26 = 0.47
0.47 > 0",mediation,encouagement_program,1,marginal,P(Y)
5389,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 46%. The probability of not being able to swim and high exam score is 14%. The probability of being able to swim and high exam score is 34%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.34
0.34/0.46 - 0.14/0.54 = 0.46
0.46 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 28%. For students who can swim, the probability of high exam score is 66%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.66
0.66 - 0.28 = 0.37
0.37 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 23%. For students who cannot swim and study hard, the probability of high exam score is 45%. For students who can swim and do not study hard, the probability of high exam score is 52%. For students who can swim and study hard, the probability of high exam score is 80%. For students who cannot swim, the probability of studying hard is 25%. For students who can swim, the probability of studying hard is 48%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.23
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.80
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.48
0.25 * (0.80 - 0.52) + 0.48 * (0.45 - 0.23) = 0.31
0.31 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 23%. For students who cannot swim and study hard, the probability of high exam score is 45%. For students who can swim and do not study hard, the probability of high exam score is 52%. For students who can swim and study hard, the probability of high exam score is 80%. For students who cannot swim, the probability of studying hard is 25%. For students who can swim, the probability of studying hard is 48%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.23
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.80
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.48
0.25 * (0.80 - 0.52) + 0.48 * (0.45 - 0.23) = 0.31
0.31 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5400,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 13%. For students who cannot swim, the probability of high exam score is 28%. For students who can swim, the probability of high exam score is 66%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.66
0.13*0.66 - 0.87*0.28 = 0.33
0.33 > 0",mediation,encouagement_program,1,marginal,P(Y)
5401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 13%. For students who cannot swim, the probability of high exam score is 28%. For students who can swim, the probability of high exam score is 66%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.66
0.13*0.66 - 0.87*0.28 = 0.33
0.33 > 0",mediation,encouagement_program,1,marginal,P(Y)
5404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 21%. For students who can swim, the probability of high exam score is 79%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.79
0.79 - 0.21 = 0.59
0.59 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5411,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 18%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 67%. For students who can swim and study hard, the probability of high exam score is 87%. For students who cannot swim, the probability of studying hard is 6%. For students who can swim, the probability of studying hard is 62%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.18
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.67
P(Y=1 | X=1, V2=1) = 0.87
P(V2=1 | X=0) = 0.06
P(V2=1 | X=1) = 0.62
0.62 * (0.52 - 0.18)+ 0.06 * (0.87 - 0.67)= 0.19
0.19 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 18%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 67%. For students who can swim and study hard, the probability of high exam score is 87%. For students who cannot swim, the probability of studying hard is 6%. For students who can swim, the probability of studying hard is 62%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.18
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.67
P(Y=1 | X=1, V2=1) = 0.87
P(V2=1 | X=0) = 0.06
P(V2=1 | X=1) = 0.62
0.06 * (0.87 - 0.67) + 0.62 * (0.52 - 0.18) = 0.47
0.47 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 30%. For students who can swim, the probability of high exam score is 64%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.64
0.64 - 0.30 = 0.34
0.34 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 30%. For students who can swim, the probability of high exam score is 64%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.64
0.64 - 0.30 = 0.34
0.34 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 15%. For students who cannot swim, the probability of high exam score is 30%. For students who can swim, the probability of high exam score is 64%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.64
0.15*0.64 - 0.85*0.30 = 0.35
0.35 > 0",mediation,encouagement_program,1,marginal,P(Y)
5436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 22%. For students who can swim, the probability of high exam score is 58%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.58
0.58 - 0.22 = 0.36
0.36 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 22%. For students who can swim, the probability of high exam score is 58%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.58
0.58 - 0.22 = 0.36
0.36 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 17%. For students who cannot swim and study hard, the probability of high exam score is 39%. For students who can swim and do not study hard, the probability of high exam score is 42%. For students who can swim and study hard, the probability of high exam score is 68%. For students who cannot swim, the probability of studying hard is 24%. For students who can swim, the probability of studying hard is 63%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.17
P(Y=1 | X=0, V2=1) = 0.39
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.24
P(V2=1 | X=1) = 0.63
0.24 * (0.68 - 0.42) + 0.63 * (0.39 - 0.17) = 0.26
0.26 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 52%. For students who cannot swim, the probability of high exam score is 22%. For students who can swim, the probability of high exam score is 58%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.58
0.52*0.58 - 0.48*0.22 = 0.41
0.41 > 0",mediation,encouagement_program,1,marginal,P(Y)
5444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 52%. The probability of not being able to swim and high exam score is 11%. The probability of being able to swim and high exam score is 31%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.31
0.31/0.52 - 0.11/0.48 = 0.36
0.36 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 32%. For students who can swim, the probability of high exam score is 92%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.92
0.92 - 0.32 = 0.59
0.59 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 32%. For students who can swim, the probability of high exam score is 92%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.92
0.92 - 0.32 = 0.59
0.59 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5458,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 3%. The probability of not being able to swim and high exam score is 31%. The probability of being able to swim and high exam score is 2%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.31/0.97 = 0.59
0.59 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 25%. For students who can swim, the probability of high exam score is 75%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.75
0.75 - 0.25 = 0.50
0.50 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5465,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 25%. For students who can swim, the probability of high exam score is 75%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.75
0.75 - 0.25 = 0.50
0.50 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 23%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 57%. For students who can swim and study hard, the probability of high exam score is 83%. For students who cannot swim, the probability of studying hard is 7%. For students who can swim, the probability of studying hard is 68%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.23
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.57
P(Y=1 | X=1, V2=1) = 0.83
P(V2=1 | X=0) = 0.07
P(V2=1 | X=1) = 0.68
0.07 * (0.83 - 0.57) + 0.68 * (0.52 - 0.23) = 0.34
0.34 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 47%. For students who cannot swim, the probability of high exam score is 25%. For students who can swim, the probability of high exam score is 75%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.75
0.47*0.75 - 0.53*0.25 = 0.49
0.49 > 0",mediation,encouagement_program,1,marginal,P(Y)
5473,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 47%. The probability of not being able to swim and high exam score is 13%. The probability of being able to swim and high exam score is 35%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.35
0.35/0.47 - 0.13/0.53 = 0.50
0.50 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 31%. For students who can swim, the probability of high exam score is 69%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.69
0.69 - 0.31 = 0.38
0.38 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 31%. For students who can swim, the probability of high exam score is 69%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.69
0.69 - 0.31 = 0.38
0.38 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 25%. For students who cannot swim and study hard, the probability of high exam score is 50%. For students who can swim and do not study hard, the probability of high exam score is 49%. For students who can swim and study hard, the probability of high exam score is 77%. For students who cannot swim, the probability of studying hard is 24%. For students who can swim, the probability of studying hard is 72%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.25
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.24
P(V2=1 | X=1) = 0.72
0.24 * (0.77 - 0.49) + 0.72 * (0.50 - 0.25) = 0.24
0.24 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 25%. For students who cannot swim and study hard, the probability of high exam score is 50%. For students who can swim and do not study hard, the probability of high exam score is 49%. For students who can swim and study hard, the probability of high exam score is 77%. For students who cannot swim, the probability of studying hard is 24%. For students who can swim, the probability of studying hard is 72%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.25
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.24
P(V2=1 | X=1) = 0.72
0.24 * (0.77 - 0.49) + 0.72 * (0.50 - 0.25) = 0.24
0.24 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 10%. For students who cannot swim, the probability of high exam score is 31%. For students who can swim, the probability of high exam score is 69%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.69
0.10*0.69 - 0.90*0.31 = 0.34
0.34 > 0",mediation,encouagement_program,1,marginal,P(Y)
5487,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 10%. The probability of not being able to swim and high exam score is 28%. The probability of being able to swim and high exam score is 7%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.07
0.07/0.10 - 0.28/0.90 = 0.38
0.38 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 31%. For students who cannot swim and study hard, the probability of high exam score is 62%. For students who can swim and do not study hard, the probability of high exam score is 66%. For students who can swim and study hard, the probability of high exam score is 94%. For students who cannot swim, the probability of studying hard is 46%. For students who can swim, the probability of studying hard is 85%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.31
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.94
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.85
0.85 * (0.62 - 0.31)+ 0.46 * (0.94 - 0.66)= 0.12
0.12 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 54%. The probability of not being able to swim and high exam score is 21%. The probability of being able to swim and high exam score is 48%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.48
0.48/0.54 - 0.21/0.46 = 0.44
0.44 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 54%. The probability of not being able to swim and high exam score is 21%. The probability of being able to swim and high exam score is 48%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.48
0.48/0.54 - 0.21/0.46 = 0.44
0.44 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5505,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 13%. For students who can swim, the probability of high exam score is 73%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.73
0.73 - 0.13 = 0.60
0.60 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 13%. For students who can swim, the probability of high exam score is 73%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.73
0.73 - 0.13 = 0.60
0.60 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 13%. For students who can swim, the probability of high exam score is 73%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.73
0.73 - 0.13 = 0.60
0.60 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 5%. For students who cannot swim and study hard, the probability of high exam score is 45%. For students who can swim and do not study hard, the probability of high exam score is 28%. For students who can swim and study hard, the probability of high exam score is 77%. For students who cannot swim, the probability of studying hard is 20%. For students who can swim, the probability of studying hard is 92%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.05
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.28
P(Y=1 | X=1, V2=1) = 0.77
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.92
0.92 * (0.45 - 0.05)+ 0.20 * (0.77 - 0.28)= 0.29
0.29 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 32%. For students who can swim, the probability of high exam score is 88%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.88
0.88 - 0.32 = 0.56
0.56 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 26%. For students who cannot swim and study hard, the probability of high exam score is 55%. For students who can swim and do not study hard, the probability of high exam score is 71%. For students who can swim and study hard, the probability of high exam score is 95%. For students who cannot swim, the probability of studying hard is 20%. For students who can swim, the probability of studying hard is 72%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.71
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.72
0.72 * (0.55 - 0.26)+ 0.20 * (0.95 - 0.71)= 0.15
0.15 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 26%. For students who cannot swim and study hard, the probability of high exam score is 55%. For students who can swim and do not study hard, the probability of high exam score is 71%. For students who can swim and study hard, the probability of high exam score is 95%. For students who cannot swim, the probability of studying hard is 20%. For students who can swim, the probability of studying hard is 72%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.71
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.72
0.72 * (0.55 - 0.26)+ 0.20 * (0.95 - 0.71)= 0.15
0.15 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 26%. For students who cannot swim and study hard, the probability of high exam score is 55%. For students who can swim and do not study hard, the probability of high exam score is 71%. For students who can swim and study hard, the probability of high exam score is 95%. For students who cannot swim, the probability of studying hard is 20%. For students who can swim, the probability of studying hard is 72%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.71
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.72
0.20 * (0.95 - 0.71) + 0.72 * (0.55 - 0.26) = 0.43
0.43 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 49%. For students who cannot swim, the probability of high exam score is 32%. For students who can swim, the probability of high exam score is 88%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.88
0.49*0.88 - 0.51*0.32 = 0.60
0.60 > 0",mediation,encouagement_program,1,marginal,P(Y)
5528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 49%. The probability of not being able to swim and high exam score is 16%. The probability of being able to swim and high exam score is 44%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.44
0.44/0.49 - 0.16/0.51 = 0.56
0.56 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5535,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 25%. For students who can swim, the probability of high exam score is 67%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.67
0.67 - 0.25 = 0.42
0.42 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5537,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 18%. For students who cannot swim and study hard, the probability of high exam score is 42%. For students who can swim and do not study hard, the probability of high exam score is 44%. For students who can swim and study hard, the probability of high exam score is 70%. For students who cannot swim, the probability of studying hard is 29%. For students who can swim, the probability of studying hard is 90%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.18
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.44
P(Y=1 | X=1, V2=1) = 0.70
P(V2=1 | X=0) = 0.29
P(V2=1 | X=1) = 0.90
0.90 * (0.42 - 0.18)+ 0.29 * (0.70 - 0.44)= 0.14
0.14 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 16%. The probability of not being able to swim and high exam score is 21%. The probability of being able to swim and high exam score is 11%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.11
0.11/0.16 - 0.21/0.84 = 0.42
0.42 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 38%. For students who can swim, the probability of high exam score is 80%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.80 - 0.38 = 0.42
0.42 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 27%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 55%. For students who can swim and study hard, the probability of high exam score is 85%. For students who cannot swim, the probability of studying hard is 44%. For students who can swim, the probability of studying hard is 83%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.27
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.85
P(V2=1 | X=0) = 0.44
P(V2=1 | X=1) = 0.83
0.83 * (0.52 - 0.27)+ 0.44 * (0.85 - 0.55)= 0.10
0.10 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 27%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 55%. For students who can swim and study hard, the probability of high exam score is 85%. For students who cannot swim, the probability of studying hard is 44%. For students who can swim, the probability of studying hard is 83%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.27
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.85
P(V2=1 | X=0) = 0.44
P(V2=1 | X=1) = 0.83
0.44 * (0.85 - 0.55) + 0.83 * (0.52 - 0.27) = 0.30
0.30 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 49%. The probability of not being able to swim and high exam score is 19%. The probability of being able to swim and high exam score is 39%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.39
0.39/0.49 - 0.19/0.51 = 0.42
0.42 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 49%. The probability of not being able to swim and high exam score is 19%. The probability of being able to swim and high exam score is 39%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.39
0.39/0.49 - 0.19/0.51 = 0.42
0.42 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 34%. For students who can swim, the probability of high exam score is 68%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.68
0.68 - 0.34 = 0.34
0.34 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 34%. For students who can swim, the probability of high exam score is 68%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.68
0.68 - 0.34 = 0.34
0.34 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 23%. For students who cannot swim and study hard, the probability of high exam score is 51%. For students who can swim and do not study hard, the probability of high exam score is 50%. For students who can swim and study hard, the probability of high exam score is 78%. For students who cannot swim, the probability of studying hard is 40%. For students who can swim, the probability of studying hard is 63%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.23
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.78
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.63
0.63 * (0.51 - 0.23)+ 0.40 * (0.78 - 0.50)= 0.06
0.06 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 6%. For students who cannot swim, the probability of high exam score is 34%. For students who can swim, the probability of high exam score is 68%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.68
0.06*0.68 - 0.94*0.34 = 0.36
0.36 > 0",mediation,encouagement_program,1,marginal,P(Y)
5571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 6%. The probability of not being able to swim and high exam score is 32%. The probability of being able to swim and high exam score is 4%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.04
0.04/0.06 - 0.32/0.94 = 0.34
0.34 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 32%. For students who can swim, the probability of high exam score is 76%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.76
0.76 - 0.32 = 0.43
0.43 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 32%. For students who can swim, the probability of high exam score is 76%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.76
0.76 - 0.32 = 0.43
0.43 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 24%. For students who cannot swim and study hard, the probability of high exam score is 52%. For students who can swim and do not study hard, the probability of high exam score is 55%. For students who can swim and study hard, the probability of high exam score is 85%. For students who cannot swim, the probability of studying hard is 30%. For students who can swim, the probability of studying hard is 69%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.24
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.85
P(V2=1 | X=0) = 0.30
P(V2=1 | X=1) = 0.69
0.69 * (0.52 - 0.24)+ 0.30 * (0.85 - 0.55)= 0.11
0.11 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 42%. For students who cannot swim, the probability of high exam score is 32%. For students who can swim, the probability of high exam score is 76%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.76
0.42*0.76 - 0.58*0.32 = 0.50
0.50 > 0",mediation,encouagement_program,1,marginal,P(Y)
5584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 42%. The probability of not being able to swim and high exam score is 19%. The probability of being able to swim and high exam score is 32%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.32
0.32/0.42 - 0.19/0.58 = 0.43
0.43 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 34%. For students who can swim, the probability of high exam score is 74%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.74
0.74 - 0.34 = 0.40
0.40 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 34%. For students who can swim, the probability of high exam score is 74%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.74
0.74 - 0.34 = 0.40
0.40 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 22%. For students who cannot swim and study hard, the probability of high exam score is 55%. For students who can swim and do not study hard, the probability of high exam score is 50%. For students who can swim and study hard, the probability of high exam score is 83%. For students who cannot swim, the probability of studying hard is 35%. For students who can swim, the probability of studying hard is 72%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.22
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.83
P(V2=1 | X=0) = 0.35
P(V2=1 | X=1) = 0.72
0.72 * (0.55 - 0.22)+ 0.35 * (0.83 - 0.50)= 0.12
0.12 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 22%. For students who cannot swim and study hard, the probability of high exam score is 55%. For students who can swim and do not study hard, the probability of high exam score is 50%. For students who can swim and study hard, the probability of high exam score is 83%. For students who cannot swim, the probability of studying hard is 35%. For students who can swim, the probability of studying hard is 72%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.22
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.83
P(V2=1 | X=0) = 0.35
P(V2=1 | X=1) = 0.72
0.35 * (0.83 - 0.50) + 0.72 * (0.55 - 0.22) = 0.28
0.28 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 7%. The probability of not being able to swim and high exam score is 31%. The probability of being able to swim and high exam score is 5%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.05
0.05/0.07 - 0.31/0.93 = 0.40
0.40 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 28%. For students who cannot swim and study hard, the probability of high exam score is 58%. For students who can swim and do not study hard, the probability of high exam score is 54%. For students who can swim and study hard, the probability of high exam score is 90%. For students who cannot swim, the probability of studying hard is 32%. For students who can swim, the probability of studying hard is 79%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.28
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.90
P(V2=1 | X=0) = 0.32
P(V2=1 | X=1) = 0.79
0.79 * (0.58 - 0.28)+ 0.32 * (0.90 - 0.54)= 0.14
0.14 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 28%. For students who cannot swim and study hard, the probability of high exam score is 58%. For students who can swim and do not study hard, the probability of high exam score is 54%. For students who can swim and study hard, the probability of high exam score is 90%. For students who cannot swim, the probability of studying hard is 32%. For students who can swim, the probability of studying hard is 79%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.28
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.90
P(V2=1 | X=0) = 0.32
P(V2=1 | X=1) = 0.79
0.32 * (0.90 - 0.54) + 0.79 * (0.58 - 0.28) = 0.27
0.27 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 28%. For students who cannot swim and study hard, the probability of high exam score is 58%. For students who can swim and do not study hard, the probability of high exam score is 54%. For students who can swim and study hard, the probability of high exam score is 90%. For students who cannot swim, the probability of studying hard is 32%. For students who can swim, the probability of studying hard is 79%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.28
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.90
P(V2=1 | X=0) = 0.32
P(V2=1 | X=1) = 0.79
0.32 * (0.90 - 0.54) + 0.79 * (0.58 - 0.28) = 0.27
0.27 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 49%. For students who cannot swim, the probability of high exam score is 38%. For students who can swim, the probability of high exam score is 82%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.82
0.49*0.82 - 0.51*0.38 = 0.59
0.59 > 0",mediation,encouagement_program,1,marginal,P(Y)
5612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 49%. The probability of not being able to swim and high exam score is 19%. The probability of being able to swim and high exam score is 40%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.40
0.40/0.49 - 0.19/0.51 = 0.44
0.44 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 49%. The probability of not being able to swim and high exam score is 19%. The probability of being able to swim and high exam score is 40%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.40
0.40/0.49 - 0.19/0.51 = 0.44
0.44 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5614,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5615,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 16%. For students who can swim, the probability of high exam score is 85%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.85
0.85 - 0.16 = 0.69
0.69 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 15%. For students who cannot swim and study hard, the probability of high exam score is 51%. For students who can swim and do not study hard, the probability of high exam score is 61%. For students who can swim and study hard, the probability of high exam score is 86%. For students who cannot swim, the probability of studying hard is 4%. For students who can swim, the probability of studying hard is 97%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.61
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.04
P(V2=1 | X=1) = 0.97
0.97 * (0.51 - 0.15)+ 0.04 * (0.86 - 0.61)= 0.34
0.34 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 15%. For students who cannot swim and study hard, the probability of high exam score is 51%. For students who can swim and do not study hard, the probability of high exam score is 61%. For students who can swim and study hard, the probability of high exam score is 86%. For students who cannot swim, the probability of studying hard is 4%. For students who can swim, the probability of studying hard is 97%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.61
P(Y=1 | X=1, V2=1) = 0.86
P(V2=1 | X=0) = 0.04
P(V2=1 | X=1) = 0.97
0.04 * (0.86 - 0.61) + 0.97 * (0.51 - 0.15) = 0.46
0.46 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 15%. For students who cannot swim, the probability of high exam score is 16%. For students who can swim, the probability of high exam score is 85%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.85
0.15*0.85 - 0.85*0.16 = 0.28
0.28 > 0",mediation,encouagement_program,1,marginal,P(Y)
5625,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 15%. For students who cannot swim, the probability of high exam score is 16%. For students who can swim, the probability of high exam score is 85%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.85
0.15*0.85 - 0.85*0.16 = 0.28
0.28 > 0",mediation,encouagement_program,1,marginal,P(Y)
5627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 15%. The probability of not being able to swim and high exam score is 14%. The probability of being able to swim and high exam score is 13%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.13
0.13/0.15 - 0.14/0.85 = 0.69
0.69 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look at how ability to swim correlates with exam score case by case according to studying habit. Method 2: We look directly at how ability to swim correlates with exam score in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5630,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 18%. For students who can swim, the probability of high exam score is 66%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.66
0.66 - 0.18 = 0.48
0.48 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 15%. For students who cannot swim and study hard, the probability of high exam score is 44%. For students who can swim and do not study hard, the probability of high exam score is 39%. For students who can swim and study hard, the probability of high exam score is 72%. For students who cannot swim, the probability of studying hard is 9%. For students who can swim, the probability of studying hard is 81%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.44
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.72
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.81
0.81 * (0.44 - 0.15)+ 0.09 * (0.72 - 0.39)= 0.21
0.21 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5639,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 57%. For students who cannot swim, the probability of high exam score is 18%. For students who can swim, the probability of high exam score is 66%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.66
0.57*0.66 - 0.43*0.18 = 0.45
0.45 > 0",mediation,encouagement_program,1,marginal,P(Y)
5641,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 57%. The probability of not being able to swim and high exam score is 8%. The probability of being able to swim and high exam score is 38%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.38
0.38/0.57 - 0.08/0.43 = 0.48
0.48 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 6%. For students who can swim, the probability of high exam score is 49%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.49
0.49 - 0.06 = 0.42
0.42 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 0%. For students who cannot swim and study hard, the probability of high exam score is 31%. For students who can swim and do not study hard, the probability of high exam score is 22%. For students who can swim and study hard, the probability of high exam score is 62%. For students who cannot swim, the probability of studying hard is 19%. For students who can swim, the probability of studying hard is 67%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.00
P(Y=1 | X=0, V2=1) = 0.31
P(Y=1 | X=1, V2=0) = 0.22
P(Y=1 | X=1, V2=1) = 0.62
P(V2=1 | X=0) = 0.19
P(V2=1 | X=1) = 0.67
0.67 * (0.31 - 0.00)+ 0.19 * (0.62 - 0.22)= 0.15
0.15 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 0%. For students who cannot swim and study hard, the probability of high exam score is 31%. For students who can swim and do not study hard, the probability of high exam score is 22%. For students who can swim and study hard, the probability of high exam score is 62%. For students who cannot swim, the probability of studying hard is 19%. For students who can swim, the probability of studying hard is 67%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.00
P(Y=1 | X=0, V2=1) = 0.31
P(Y=1 | X=1, V2=0) = 0.22
P(Y=1 | X=1, V2=1) = 0.62
P(V2=1 | X=0) = 0.19
P(V2=1 | X=1) = 0.67
0.19 * (0.62 - 0.22) + 0.67 * (0.31 - 0.00) = 0.24
0.24 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 9%. The probability of not being able to swim and high exam score is 6%. The probability of being able to swim and high exam score is 4%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.04
0.04/0.09 - 0.06/0.91 = 0.42
0.42 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 33%. For students who can swim, the probability of high exam score is 77%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.77
0.77 - 0.33 = 0.44
0.44 > 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 29%. For students who cannot swim and study hard, the probability of high exam score is 68%. For students who can swim and do not study hard, the probability of high exam score is 53%. For students who can swim and study hard, the probability of high exam score is 95%. For students who cannot swim, the probability of studying hard is 12%. For students who can swim, the probability of studying hard is 57%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.29
P(Y=1 | X=0, V2=1) = 0.68
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.95
P(V2=1 | X=0) = 0.12
P(V2=1 | X=1) = 0.57
0.12 * (0.95 - 0.53) + 0.57 * (0.68 - 0.29) = 0.25
0.25 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 46%. For students who cannot swim, the probability of high exam score is 33%. For students who can swim, the probability of high exam score is 77%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.77
0.46*0.77 - 0.54*0.33 = 0.53
0.53 > 0",mediation,encouagement_program,1,marginal,P(Y)
5668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 46%. The probability of not being able to swim and high exam score is 18%. The probability of being able to swim and high exam score is 36%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.36
0.36/0.46 - 0.18/0.54 = 0.44
0.44 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. Method 1: We look directly at how ability to swim correlates with exam score in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
5677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 36%. For students who cannot swim and study hard, the probability of high exam score is 64%. For students who can swim and do not study hard, the probability of high exam score is 71%. For students who can swim and study hard, the probability of high exam score is 93%. For students who cannot swim, the probability of studying hard is 11%. For students who can swim, the probability of studying hard is 68%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.71
P(Y=1 | X=1, V2=1) = 0.93
P(V2=1 | X=0) = 0.11
P(V2=1 | X=1) = 0.68
0.68 * (0.64 - 0.36)+ 0.11 * (0.93 - 0.71)= 0.16
0.16 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 36%. For students who cannot swim and study hard, the probability of high exam score is 64%. For students who can swim and do not study hard, the probability of high exam score is 71%. For students who can swim and study hard, the probability of high exam score is 93%. For students who cannot swim, the probability of studying hard is 11%. For students who can swim, the probability of studying hard is 68%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.71
P(Y=1 | X=1, V2=1) = 0.93
P(V2=1 | X=0) = 0.11
P(V2=1 | X=1) = 0.68
0.11 * (0.93 - 0.71) + 0.68 * (0.64 - 0.36) = 0.35
0.35 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 8%. The probability of not being able to swim and high exam score is 36%. The probability of being able to swim and high exam score is 7%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.07
0.07/0.08 - 0.36/0.92 = 0.47
0.47 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim, the probability of high exam score is 21%. For students who can swim, the probability of high exam score is 87%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.87
0.87 - 0.21 = 0.66
0.66 > 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 20%. For students who cannot swim and study hard, the probability of high exam score is 48%. For students who can swim and do not study hard, the probability of high exam score is 56%. For students who can swim and study hard, the probability of high exam score is 88%. For students who cannot swim, the probability of studying hard is 4%. For students who can swim, the probability of studying hard is 96%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.20
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 0.88
P(V2=1 | X=0) = 0.04
P(V2=1 | X=1) = 0.96
0.96 * (0.48 - 0.20)+ 0.04 * (0.88 - 0.56)= 0.26
0.26 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5692,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. For students who cannot swim and do not study hard, the probability of high exam score is 20%. For students who cannot swim and study hard, the probability of high exam score is 48%. For students who can swim and do not study hard, the probability of high exam score is 56%. For students who can swim and study hard, the probability of high exam score is 88%. For students who cannot swim, the probability of studying hard is 4%. For students who can swim, the probability of studying hard is 96%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.20
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 0.88
P(V2=1 | X=0) = 0.04
P(V2=1 | X=1) = 0.96
0.04 * (0.88 - 0.56) + 0.96 * (0.48 - 0.20) = 0.36
0.36 > 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 45%. For students who cannot swim, the probability of high exam score is 21%. For students who can swim, the probability of high exam score is 87%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.87
0.45*0.87 - 0.55*0.21 = 0.50
0.50 > 0",mediation,encouagement_program,1,marginal,P(Y)
5695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 45%. For students who cannot swim, the probability of high exam score is 21%. For students who can swim, the probability of high exam score is 87%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.87
0.45*0.87 - 0.55*0.21 = 0.50
0.50 > 0",mediation,encouagement_program,1,marginal,P(Y)
5696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 45%. The probability of not being able to swim and high exam score is 12%. The probability of being able to swim and high exam score is 39%.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.39
0.39/0.45 - 0.12/0.55 = 0.66
0.66 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. The overall probability of being able to swim is 45%. The probability of not being able to swim and high exam score is 12%. The probability of being able to swim and high exam score is 39%.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.39
0.39/0.45 - 0.12/0.55 = 0.66
0.66 > 0",mediation,encouagement_program,1,correlation,P(Y | X)
5700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 48%. For individuals who are male, the probability of being allergic to peanuts is 36%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.36
0.36 - 0.48 = -0.13
-0.13 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 48%. For individuals who are male, the probability of being allergic to peanuts is 36%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.36
0.36 - 0.48 = -0.13
-0.13 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 48%. For individuals who are male, the probability of being allergic to peanuts is 36%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.36
0.36 - 0.48 = -0.13
-0.13 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5703,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 48%. For individuals who are male, the probability of being allergic to peanuts is 36%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.36
0.36 - 0.48 = -0.13
-0.13 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 58%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 25%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 59%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 28%. For individuals who are not male, the probability of competitive department is 29%. For individuals who are male, the probability of competitive department is 77%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.58
P(Y=1 | X=0, V2=1) = 0.25
P(Y=1 | X=1, V2=0) = 0.59
P(Y=1 | X=1, V2=1) = 0.28
P(V2=1 | X=0) = 0.29
P(V2=1 | X=1) = 0.77
0.77 * (0.25 - 0.58)+ 0.29 * (0.28 - 0.59)= -0.16
-0.16 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 55%. The probability of non-male gender and being allergic to peanuts is 22%. The probability of male gender and being allergic to peanuts is 20%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.20
0.20/0.55 - 0.22/0.45 = -0.13
-0.13 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 80%. For individuals who are male, the probability of being allergic to peanuts is 71%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.71
0.71 - 0.80 = -0.09
-0.09 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 82%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 45%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 95%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 57%. For individuals who are not male, the probability of competitive department is 5%. For individuals who are male, the probability of competitive department is 62%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.82
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.95
P(Y=1 | X=1, V2=1) = 0.57
P(V2=1 | X=0) = 0.05
P(V2=1 | X=1) = 0.62
0.62 * (0.45 - 0.82)+ 0.05 * (0.57 - 0.95)= -0.22
-0.22 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 82%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 45%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 95%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 57%. For individuals who are not male, the probability of competitive department is 5%. For individuals who are male, the probability of competitive department is 62%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.82
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.95
P(Y=1 | X=1, V2=1) = 0.57
P(V2=1 | X=0) = 0.05
P(V2=1 | X=1) = 0.62
0.05 * (0.57 - 0.95) + 0.62 * (0.45 - 0.82) = 0.13
0.13 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 45%. For individuals who are not male, the probability of being allergic to peanuts is 80%. For individuals who are male, the probability of being allergic to peanuts is 71%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.71
0.45*0.71 - 0.55*0.80 = 0.76
0.76 > 0",mediation,gender_admission,1,marginal,P(Y)
5724,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 45%. The probability of non-male gender and being allergic to peanuts is 44%. The probability of male gender and being allergic to peanuts is 32%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.32
0.32/0.45 - 0.44/0.55 = -0.09
-0.09 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 64%. For individuals who are male, the probability of being allergic to peanuts is 49%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.49
0.49 - 0.64 = -0.15
-0.15 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 64%. For individuals who are male, the probability of being allergic to peanuts is 49%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.49
0.49 - 0.64 = -0.15
-0.15 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 55%. For individuals who are not male, the probability of being allergic to peanuts is 64%. For individuals who are male, the probability of being allergic to peanuts is 49%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.49
0.55*0.49 - 0.45*0.64 = 0.54
0.54 > 0",mediation,gender_admission,1,marginal,P(Y)
5741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5743,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 43%. For individuals who are male, the probability of being allergic to peanuts is 55%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.55
0.55 - 0.43 = 0.12
0.12 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 43%. For individuals who are male, the probability of being allergic to peanuts is 55%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.55
0.55 - 0.43 = 0.12
0.12 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 42%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 52%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 40%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 59%. For individuals who are not male, the probability of competitive department is 17%. For individuals who are male, the probability of competitive department is 79%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.42
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.40
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.17
P(V2=1 | X=1) = 0.79
0.17 * (0.59 - 0.40) + 0.79 * (0.52 - 0.42) = -0.00
0.00 = 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 53%. For individuals who are not male, the probability of being allergic to peanuts is 43%. For individuals who are male, the probability of being allergic to peanuts is 55%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.55
0.53*0.55 - 0.47*0.43 = 0.48
0.48 > 0",mediation,gender_admission,1,marginal,P(Y)
5755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 41%. For individuals who are male, the probability of being allergic to peanuts is 37%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.37
0.37 - 0.41 = -0.04
-0.04 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 46%. For individuals who are not male, the probability of being allergic to peanuts is 41%. For individuals who are male, the probability of being allergic to peanuts is 37%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.37
0.46*0.37 - 0.54*0.41 = 0.39
0.39 > 0",mediation,gender_admission,1,marginal,P(Y)
5771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 29%. For individuals who are male, the probability of being allergic to peanuts is 19%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.19
0.19 - 0.29 = -0.10
-0.10 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5773,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 29%. For individuals who are male, the probability of being allergic to peanuts is 19%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.19
0.19 - 0.29 = -0.10
-0.10 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 41%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 12%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 41%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 4%. For individuals who are not male, the probability of competitive department is 41%. For individuals who are male, the probability of competitive department is 59%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.41
P(Y=1 | X=0, V2=1) = 0.12
P(Y=1 | X=1, V2=0) = 0.41
P(Y=1 | X=1, V2=1) = 0.04
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.59
0.59 * (0.12 - 0.41)+ 0.41 * (0.04 - 0.41)= -0.05
-0.05 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 56%. The probability of non-male gender and being allergic to peanuts is 13%. The probability of male gender and being allergic to peanuts is 11%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.11
0.11/0.56 - 0.13/0.44 = -0.10
-0.10 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 54%. For individuals who are male, the probability of being allergic to peanuts is 59%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.59
0.59 - 0.54 = 0.05
0.05 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5790,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 51%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 59%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 44%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 62%. For individuals who are not male, the probability of competitive department is 33%. For individuals who are male, the probability of competitive department is 83%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.44
P(Y=1 | X=1, V2=1) = 0.62
P(V2=1 | X=0) = 0.33
P(V2=1 | X=1) = 0.83
0.33 * (0.62 - 0.44) + 0.83 * (0.59 - 0.51) = -0.04
-0.04 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 51%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 59%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 44%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 62%. For individuals who are not male, the probability of competitive department is 33%. For individuals who are male, the probability of competitive department is 83%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.44
P(Y=1 | X=1, V2=1) = 0.62
P(V2=1 | X=0) = 0.33
P(V2=1 | X=1) = 0.83
0.33 * (0.62 - 0.44) + 0.83 * (0.59 - 0.51) = -0.04
-0.04 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5794,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 46%. The probability of non-male gender and being allergic to peanuts is 29%. The probability of male gender and being allergic to peanuts is 27%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.27
0.27/0.46 - 0.29/0.54 = 0.05
0.05 > 0",mediation,gender_admission,1,correlation,P(Y | X)
5798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 66%. For individuals who are male, the probability of being allergic to peanuts is 61%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.61
0.61 - 0.66 = -0.05
-0.05 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 66%. For individuals who are male, the probability of being allergic to peanuts is 61%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.61
0.61 - 0.66 = -0.05
-0.05 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 92%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 61%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 57%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 80%. For individuals who are not male, the probability of competitive department is 83%. For individuals who are male, the probability of competitive department is 18%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.92
P(Y=1 | X=0, V2=1) = 0.61
P(Y=1 | X=1, V2=0) = 0.57
P(Y=1 | X=1, V2=1) = 0.80
P(V2=1 | X=0) = 0.83
P(V2=1 | X=1) = 0.18
0.18 * (0.61 - 0.92)+ 0.83 * (0.80 - 0.57)= 0.20
0.20 > 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 92%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 61%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 57%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 80%. For individuals who are not male, the probability of competitive department is 83%. For individuals who are male, the probability of competitive department is 18%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.92
P(Y=1 | X=0, V2=1) = 0.61
P(Y=1 | X=1, V2=0) = 0.57
P(Y=1 | X=1, V2=1) = 0.80
P(V2=1 | X=0) = 0.83
P(V2=1 | X=1) = 0.18
0.83 * (0.80 - 0.57) + 0.18 * (0.61 - 0.92) = 0.10
0.10 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 57%. For individuals who are not male, the probability of being allergic to peanuts is 66%. For individuals who are male, the probability of being allergic to peanuts is 61%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.61
0.57*0.61 - 0.43*0.66 = 0.72
0.72 > 0",mediation,gender_admission,1,marginal,P(Y)
5809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 57%. The probability of non-male gender and being allergic to peanuts is 29%. The probability of male gender and being allergic to peanuts is 35%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.35
0.35/0.57 - 0.29/0.43 = -0.05
-0.05 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 56%. For individuals who are male, the probability of being allergic to peanuts is 49%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.49
0.49 - 0.56 = -0.08
-0.08 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5815,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 56%. For individuals who are male, the probability of being allergic to peanuts is 49%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.49
0.49 - 0.56 = -0.08
-0.08 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 76%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 28%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 93%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 47%. For individuals who are not male, the probability of competitive department is 41%. For individuals who are male, the probability of competitive department is 97%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.28
P(Y=1 | X=1, V2=0) = 0.93
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.97
0.97 * (0.28 - 0.76)+ 0.41 * (0.47 - 0.93)= -0.27
-0.27 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 76%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 28%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 93%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 47%. For individuals who are not male, the probability of competitive department is 41%. For individuals who are male, the probability of competitive department is 97%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.28
P(Y=1 | X=1, V2=0) = 0.93
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.97
0.41 * (0.47 - 0.93) + 0.97 * (0.28 - 0.76) = 0.18
0.18 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 53%. For individuals who are not male, the probability of being allergic to peanuts is 56%. For individuals who are male, the probability of being allergic to peanuts is 49%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.49
0.53*0.49 - 0.47*0.56 = 0.52
0.52 > 0",mediation,gender_admission,1,marginal,P(Y)
5822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 53%. The probability of non-male gender and being allergic to peanuts is 26%. The probability of male gender and being allergic to peanuts is 26%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.26
0.26/0.53 - 0.26/0.47 = -0.08
-0.08 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5823,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 53%. The probability of non-male gender and being allergic to peanuts is 26%. The probability of male gender and being allergic to peanuts is 26%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.26
0.26/0.53 - 0.26/0.47 = -0.08
-0.08 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 63%. For individuals who are male, the probability of being allergic to peanuts is 46%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.46
0.46 - 0.63 = -0.17
-0.17 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5831,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 71%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 40%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 82%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 32%. For individuals who are not male, the probability of competitive department is 25%. For individuals who are male, the probability of competitive department is 73%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.40
P(Y=1 | X=1, V2=0) = 0.82
P(Y=1 | X=1, V2=1) = 0.32
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.73
0.73 * (0.40 - 0.71)+ 0.25 * (0.32 - 0.82)= -0.15
-0.15 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 71%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 40%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 82%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 32%. For individuals who are not male, the probability of competitive department is 25%. For individuals who are male, the probability of competitive department is 73%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.40
P(Y=1 | X=1, V2=0) = 0.82
P(Y=1 | X=1, V2=1) = 0.32
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.73
0.25 * (0.32 - 0.82) + 0.73 * (0.40 - 0.71) = 0.06
0.06 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 42%. The probability of non-male gender and being allergic to peanuts is 37%. The probability of male gender and being allergic to peanuts is 19%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.19
0.19/0.42 - 0.37/0.58 = -0.17
-0.17 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 44%. For individuals who are male, the probability of being allergic to peanuts is 52%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.52
0.52 - 0.44 = 0.09
0.09 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 44%. For individuals who are male, the probability of being allergic to peanuts is 52%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.52
0.52 - 0.44 = 0.09
0.09 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 44%. For individuals who are male, the probability of being allergic to peanuts is 52%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.52
0.52 - 0.44 = 0.09
0.09 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 47%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 31%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 15%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 57%. For individuals who are not male, the probability of competitive department is 18%. For individuals who are male, the probability of competitive department is 88%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.31
P(Y=1 | X=1, V2=0) = 0.15
P(Y=1 | X=1, V2=1) = 0.57
P(V2=1 | X=0) = 0.18
P(V2=1 | X=1) = 0.88
0.18 * (0.57 - 0.15) + 0.88 * (0.31 - 0.47) = -0.21
-0.21 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5848,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 49%. For individuals who are not male, the probability of being allergic to peanuts is 44%. For individuals who are male, the probability of being allergic to peanuts is 52%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.52
0.49*0.52 - 0.51*0.44 = 0.38
0.38 > 0",mediation,gender_admission,1,marginal,P(Y)
5850,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 49%. The probability of non-male gender and being allergic to peanuts is 22%. The probability of male gender and being allergic to peanuts is 26%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.26
0.26/0.49 - 0.22/0.51 = 0.09
0.09 > 0",mediation,gender_admission,1,correlation,P(Y | X)
5851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 49%. The probability of non-male gender and being allergic to peanuts is 22%. The probability of male gender and being allergic to peanuts is 26%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.26
0.26/0.49 - 0.22/0.51 = 0.09
0.09 > 0",mediation,gender_admission,1,correlation,P(Y | X)
5852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 46%. For individuals who are male, the probability of being allergic to peanuts is 67%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.67
0.67 - 0.46 = 0.21
0.21 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 42%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 68%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 45%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 78%. For individuals who are not male, the probability of competitive department is 16%. For individuals who are male, the probability of competitive department is 65%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.42
P(Y=1 | X=0, V2=1) = 0.68
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.78
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.65
0.65 * (0.68 - 0.42)+ 0.16 * (0.78 - 0.45)= 0.13
0.13 > 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 42%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 68%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 45%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 78%. For individuals who are not male, the probability of competitive department is 16%. For individuals who are male, the probability of competitive department is 65%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.42
P(Y=1 | X=0, V2=1) = 0.68
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.78
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.65
0.16 * (0.78 - 0.45) + 0.65 * (0.68 - 0.42) = 0.04
0.04 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 44%. For individuals who are not male, the probability of being allergic to peanuts is 46%. For individuals who are male, the probability of being allergic to peanuts is 67%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.67
0.44*0.67 - 0.56*0.46 = 0.54
0.54 > 0",mediation,gender_admission,1,marginal,P(Y)
5866,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 34%. For individuals who are male, the probability of being allergic to peanuts is 26%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.26
0.26 - 0.34 = -0.08
-0.08 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 44%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 15%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 53%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 5%. For individuals who are not male, the probability of competitive department is 34%. For individuals who are male, the probability of competitive department is 56%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.15
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.05
P(V2=1 | X=0) = 0.34
P(V2=1 | X=1) = 0.56
0.56 * (0.15 - 0.44)+ 0.34 * (0.05 - 0.53)= -0.06
-0.06 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5873,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 44%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 15%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 53%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 5%. For individuals who are not male, the probability of competitive department is 34%. For individuals who are male, the probability of competitive department is 56%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.15
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.05
P(V2=1 | X=0) = 0.34
P(V2=1 | X=1) = 0.56
0.56 * (0.15 - 0.44)+ 0.34 * (0.05 - 0.53)= -0.06
-0.06 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 50%. The probability of non-male gender and being allergic to peanuts is 17%. The probability of male gender and being allergic to peanuts is 13%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.13
0.13/0.50 - 0.17/0.50 = -0.08
-0.08 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5883,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 28%. For individuals who are male, the probability of being allergic to peanuts is 48%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.48
0.48 - 0.28 = 0.19
0.19 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 99%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 14%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 16%. For individuals who are not male, the probability of competitive department is 84%. For individuals who are male, the probability of competitive department is 46%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.99
P(Y=1 | X=0, V2=1) = 0.14
P(Y=1 | X=1, V2=0) = 0.75
P(Y=1 | X=1, V2=1) = 0.16
P(V2=1 | X=0) = 0.84
P(V2=1 | X=1) = 0.46
0.46 * (0.14 - 0.99)+ 0.84 * (0.16 - 0.75)= 0.32
0.32 > 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 99%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 14%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 16%. For individuals who are not male, the probability of competitive department is 84%. For individuals who are male, the probability of competitive department is 46%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.99
P(Y=1 | X=0, V2=1) = 0.14
P(Y=1 | X=1, V2=0) = 0.75
P(Y=1 | X=1, V2=1) = 0.16
P(V2=1 | X=0) = 0.84
P(V2=1 | X=1) = 0.46
0.84 * (0.16 - 0.75) + 0.46 * (0.14 - 0.99) = -0.03
-0.03 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 41%. For individuals who are not male, the probability of being allergic to peanuts is 28%. For individuals who are male, the probability of being allergic to peanuts is 48%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.48
0.41*0.48 - 0.59*0.28 = 0.38
0.38 > 0",mediation,gender_admission,1,marginal,P(Y)
5893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 41%. The probability of non-male gender and being allergic to peanuts is 17%. The probability of male gender and being allergic to peanuts is 20%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.20
0.20/0.41 - 0.17/0.59 = 0.19
0.19 > 0",mediation,gender_admission,1,correlation,P(Y | X)
5899,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 25%. For individuals who are male, the probability of being allergic to peanuts is 47%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.47
0.47 - 0.25 = 0.22
0.22 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 42%. For individuals who are not male, the probability of being allergic to peanuts is 25%. For individuals who are male, the probability of being allergic to peanuts is 47%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.47
0.42*0.47 - 0.58*0.25 = 0.35
0.35 > 0",mediation,gender_admission,1,marginal,P(Y)
5908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 47%. For individuals who are male, the probability of being allergic to peanuts is 63%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.63
0.63 - 0.47 = 0.16
0.16 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 63%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 50%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 90%. For individuals who are not male, the probability of competitive department is 37%. For individuals who are male, the probability of competitive department is 32%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.21
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.90
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.32
0.32 * (0.21 - 0.63)+ 0.37 * (0.90 - 0.50)= 0.02
0.02 > 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 63%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 50%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 90%. For individuals who are not male, the probability of competitive department is 37%. For individuals who are male, the probability of competitive department is 32%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.21
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.90
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.32
0.37 * (0.90 - 0.50) + 0.32 * (0.21 - 0.63) = 0.18
0.18 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 51%. For individuals who are not male, the probability of being allergic to peanuts is 47%. For individuals who are male, the probability of being allergic to peanuts is 63%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.63
0.51*0.63 - 0.49*0.47 = 0.56
0.56 > 0",mediation,gender_admission,1,marginal,P(Y)
5919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 51%. For individuals who are not male, the probability of being allergic to peanuts is 47%. For individuals who are male, the probability of being allergic to peanuts is 63%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.63
0.51*0.63 - 0.49*0.47 = 0.56
0.56 > 0",mediation,gender_admission,1,marginal,P(Y)
5920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 51%. The probability of non-male gender and being allergic to peanuts is 23%. The probability of male gender and being allergic to peanuts is 32%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.32
0.32/0.51 - 0.23/0.49 = 0.16
0.16 > 0",mediation,gender_admission,1,correlation,P(Y | X)
5921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 51%. The probability of non-male gender and being allergic to peanuts is 23%. The probability of male gender and being allergic to peanuts is 32%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.32
0.32/0.51 - 0.23/0.49 = 0.16
0.16 > 0",mediation,gender_admission,1,correlation,P(Y | X)
5923,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5929,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 63%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 9%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 43%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are not male, the probability of competitive department is 26%. For individuals who are male, the probability of competitive department is 86%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.26
P(V2=1 | X=1) = 0.86
0.86 * (0.09 - 0.63)+ 0.26 * (0.21 - 0.43)= -0.32
-0.32 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 63%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 9%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 43%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are not male, the probability of competitive department is 26%. For individuals who are male, the probability of competitive department is 86%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.26
P(V2=1 | X=1) = 0.86
0.26 * (0.21 - 0.43) + 0.86 * (0.09 - 0.63) = -0.12
-0.12 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5933,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 54%. For individuals who are not male, the probability of being allergic to peanuts is 49%. For individuals who are male, the probability of being allergic to peanuts is 24%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.24
0.54*0.24 - 0.46*0.49 = 0.30
0.30 > 0",mediation,gender_admission,1,marginal,P(Y)
5934,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 54%. The probability of non-male gender and being allergic to peanuts is 22%. The probability of male gender and being allergic to peanuts is 13%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.13
0.13/0.54 - 0.22/0.46 = -0.25
-0.25 < 0",mediation,gender_admission,1,correlation,P(Y | X)
5938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 28%. For individuals who are male, the probability of being allergic to peanuts is 38%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.38
0.38 - 0.28 = 0.10
0.10 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 45%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 11%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 42%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 7%. For individuals who are not male, the probability of competitive department is 49%. For individuals who are male, the probability of competitive department is 9%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.45
P(Y=1 | X=0, V2=1) = 0.11
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.07
P(V2=1 | X=0) = 0.49
P(V2=1 | X=1) = 0.09
0.09 * (0.11 - 0.45)+ 0.49 * (0.07 - 0.42)= 0.14
0.14 > 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 45%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 11%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 42%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 7%. For individuals who are not male, the probability of competitive department is 49%. For individuals who are male, the probability of competitive department is 9%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.45
P(Y=1 | X=0, V2=1) = 0.11
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.07
P(V2=1 | X=0) = 0.49
P(V2=1 | X=1) = 0.09
0.49 * (0.07 - 0.42) + 0.09 * (0.11 - 0.45) = -0.04
-0.04 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 44%. For individuals who are male, the probability of being allergic to peanuts is 88%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.88
0.88 - 0.44 = 0.44
0.44 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 44%. For individuals who are male, the probability of being allergic to peanuts is 88%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.88
0.88 - 0.44 = 0.44
0.44 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 60%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 20%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 97%. For individuals who are not male, the probability of competitive department is 40%. For individuals who are male, the probability of competitive department is 61%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.60
P(Y=1 | X=0, V2=1) = 0.20
P(Y=1 | X=1, V2=0) = 0.75
P(Y=1 | X=1, V2=1) = 0.97
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.61
0.61 * (0.20 - 0.60)+ 0.40 * (0.97 - 0.75)= -0.09
-0.09 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 60%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 20%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 97%. For individuals who are not male, the probability of competitive department is 40%. For individuals who are male, the probability of competitive department is 61%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.60
P(Y=1 | X=0, V2=1) = 0.20
P(Y=1 | X=1, V2=0) = 0.75
P(Y=1 | X=1, V2=1) = 0.97
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.61
0.61 * (0.20 - 0.60)+ 0.40 * (0.97 - 0.75)= -0.09
-0.09 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 60%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 20%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 97%. For individuals who are not male, the probability of competitive department is 40%. For individuals who are male, the probability of competitive department is 61%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.60
P(Y=1 | X=0, V2=1) = 0.20
P(Y=1 | X=1, V2=0) = 0.75
P(Y=1 | X=1, V2=1) = 0.97
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.61
0.40 * (0.97 - 0.75) + 0.61 * (0.20 - 0.60) = 0.39
0.39 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 40%. For individuals who are male, the probability of being allergic to peanuts is 66%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.66
0.66 - 0.40 = 0.26
0.26 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
5970,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 58%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 26%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 73%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 32%. For individuals who are not male, the probability of competitive department is 56%. For individuals who are male, the probability of competitive department is 15%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.58
P(Y=1 | X=0, V2=1) = 0.26
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.32
P(V2=1 | X=0) = 0.56
P(V2=1 | X=1) = 0.15
0.15 * (0.26 - 0.58)+ 0.56 * (0.32 - 0.73)= 0.13
0.13 > 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 58%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 26%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 73%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 32%. For individuals who are not male, the probability of competitive department is 56%. For individuals who are male, the probability of competitive department is 15%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.58
P(Y=1 | X=0, V2=1) = 0.26
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.32
P(V2=1 | X=0) = 0.56
P(V2=1 | X=1) = 0.15
0.15 * (0.26 - 0.58)+ 0.56 * (0.32 - 0.73)= 0.13
0.13 > 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 58%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 26%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 73%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 32%. For individuals who are not male, the probability of competitive department is 56%. For individuals who are male, the probability of competitive department is 15%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.58
P(Y=1 | X=0, V2=1) = 0.26
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.32
P(V2=1 | X=0) = 0.56
P(V2=1 | X=1) = 0.15
0.56 * (0.32 - 0.73) + 0.15 * (0.26 - 0.58) = 0.10
0.10 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
5974,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 54%. For individuals who are not male, the probability of being allergic to peanuts is 40%. For individuals who are male, the probability of being allergic to peanuts is 66%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.66
0.54*0.66 - 0.46*0.40 = 0.53
0.53 > 0",mediation,gender_admission,1,marginal,P(Y)
5975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 54%. For individuals who are not male, the probability of being allergic to peanuts is 40%. For individuals who are male, the probability of being allergic to peanuts is 66%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.66
0.54*0.66 - 0.46*0.40 = 0.53
0.53 > 0",mediation,gender_admission,1,marginal,P(Y)
5977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 54%. The probability of non-male gender and being allergic to peanuts is 18%. The probability of male gender and being allergic to peanuts is 36%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.36
0.36/0.54 - 0.18/0.46 = 0.26
0.26 > 0",mediation,gender_admission,1,correlation,P(Y | X)
5981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 70%. For individuals who are male, the probability of being allergic to peanuts is 67%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.67
0.67 - 0.70 = -0.03
-0.03 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 85%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 45%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 86%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 60%. For individuals who are not male, the probability of competitive department is 39%. For individuals who are male, the probability of competitive department is 75%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.85
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.86
P(Y=1 | X=1, V2=1) = 0.60
P(V2=1 | X=0) = 0.39
P(V2=1 | X=1) = 0.75
0.75 * (0.45 - 0.85)+ 0.39 * (0.60 - 0.86)= -0.14
-0.14 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
5988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 57%. For individuals who are not male, the probability of being allergic to peanuts is 70%. For individuals who are male, the probability of being allergic to peanuts is 67%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.67
0.57*0.67 - 0.43*0.70 = 0.67
0.67 > 0",mediation,gender_admission,1,marginal,P(Y)
5993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
5994,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 48%. For individuals who are male, the probability of being allergic to peanuts is 49%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.49
0.49 - 0.48 = 0.01
0.01 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
5995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 48%. For individuals who are male, the probability of being allergic to peanuts is 49%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.49
0.49 - 0.48 = 0.01
0.01 > 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 64%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 27%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 55%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 29%. For individuals who are not male, the probability of competitive department is 43%. For individuals who are male, the probability of competitive department is 24%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.64
P(Y=1 | X=0, V2=1) = 0.27
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.43
P(V2=1 | X=1) = 0.24
0.43 * (0.29 - 0.55) + 0.24 * (0.27 - 0.64) = -0.04
-0.04 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
6004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 49%. The probability of non-male gender and being allergic to peanuts is 25%. The probability of male gender and being allergic to peanuts is 24%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.24
0.24/0.49 - 0.25/0.51 = 0.01
0.01 > 0",mediation,gender_admission,1,correlation,P(Y | X)
6010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 24%. For individuals who are male, the probability of being allergic to peanuts is 44%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.44
0.44 - 0.24 = 0.21
0.21 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6012,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 25%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 11%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 50%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 40%. For individuals who are not male, the probability of competitive department is 13%. For individuals who are male, the probability of competitive department is 61%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.25
P(Y=1 | X=0, V2=1) = 0.11
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.40
P(V2=1 | X=0) = 0.13
P(V2=1 | X=1) = 0.61
0.61 * (0.11 - 0.25)+ 0.13 * (0.40 - 0.50)= -0.07
-0.07 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
6016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 60%. For individuals who are not male, the probability of being allergic to peanuts is 24%. For individuals who are male, the probability of being allergic to peanuts is 44%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.44
0.60*0.44 - 0.40*0.24 = 0.35
0.35 > 0",mediation,gender_admission,1,marginal,P(Y)
6018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 60%. The probability of non-male gender and being allergic to peanuts is 9%. The probability of male gender and being allergic to peanuts is 26%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.26
0.26/0.60 - 0.09/0.40 = 0.21
0.21 > 0",mediation,gender_admission,1,correlation,P(Y | X)
6021,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
6025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 57%. For individuals who are male, the probability of being allergic to peanuts is 68%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.68
0.68 - 0.57 = 0.11
0.11 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 54%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 59%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 73%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 60%. For individuals who are not male, the probability of competitive department is 66%. For individuals who are male, the probability of competitive department is 37%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.54
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.60
P(V2=1 | X=0) = 0.66
P(V2=1 | X=1) = 0.37
0.66 * (0.60 - 0.73) + 0.37 * (0.59 - 0.54) = 0.07
0.07 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
6030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 60%. For individuals who are not male, the probability of being allergic to peanuts is 57%. For individuals who are male, the probability of being allergic to peanuts is 68%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.68
0.60*0.68 - 0.40*0.57 = 0.63
0.63 > 0",mediation,gender_admission,1,marginal,P(Y)
6034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
6037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 53%. For individuals who are male, the probability of being allergic to peanuts is 35%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.35
0.35 - 0.53 = -0.18
-0.18 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 53%. For individuals who are male, the probability of being allergic to peanuts is 35%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.35
0.35 - 0.53 = -0.18
-0.18 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 56%. The probability of non-male gender and being allergic to peanuts is 23%. The probability of male gender and being allergic to peanuts is 20%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.20
0.20/0.56 - 0.23/0.44 = -0.18
-0.18 < 0",mediation,gender_admission,1,correlation,P(Y | X)
6048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
6054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 51%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 56%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 10%. For individuals who are not male, the probability of competitive department is 48%. For individuals who are male, the probability of competitive department is 67%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.21
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 0.10
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.67
0.67 * (0.21 - 0.51)+ 0.48 * (0.10 - 0.56)= -0.06
-0.06 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
6056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 51%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 56%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 10%. For individuals who are not male, the probability of competitive department is 48%. For individuals who are male, the probability of competitive department is 67%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.21
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 0.10
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.67
0.48 * (0.10 - 0.56) + 0.67 * (0.21 - 0.51) = -0.03
-0.03 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
6057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 51%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 56%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 10%. For individuals who are not male, the probability of competitive department is 48%. For individuals who are male, the probability of competitive department is 67%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.21
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 0.10
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.67
0.48 * (0.10 - 0.56) + 0.67 * (0.21 - 0.51) = -0.03
-0.03 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
6058,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 47%. For individuals who are not male, the probability of being allergic to peanuts is 37%. For individuals who are male, the probability of being allergic to peanuts is 25%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.25
0.47*0.25 - 0.53*0.37 = 0.32
0.32 > 0",mediation,gender_admission,1,marginal,P(Y)
6059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 47%. For individuals who are not male, the probability of being allergic to peanuts is 37%. For individuals who are male, the probability of being allergic to peanuts is 25%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.25
0.47*0.25 - 0.53*0.37 = 0.32
0.32 > 0",mediation,gender_admission,1,marginal,P(Y)
6060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 47%. The probability of non-male gender and being allergic to peanuts is 19%. The probability of male gender and being allergic to peanuts is 12%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.12
0.12/0.47 - 0.19/0.53 = -0.11
-0.11 < 0",mediation,gender_admission,1,correlation,P(Y | X)
6063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look directly at how gender correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
6066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 72%. For individuals who are male, the probability of being allergic to peanuts is 84%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.84
0.84 - 0.72 = 0.13
0.13 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 72%. For individuals who are male, the probability of being allergic to peanuts is 84%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.84
0.84 - 0.72 = 0.13
0.13 > 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 60%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 64%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 93%. For individuals who are not male, the probability of competitive department is 23%. For individuals who are male, the probability of competitive department is 71%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.75
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.64
P(Y=1 | X=1, V2=1) = 0.93
P(V2=1 | X=0) = 0.23
P(V2=1 | X=1) = 0.71
0.71 * (0.60 - 0.75)+ 0.23 * (0.93 - 0.64)= -0.07
-0.07 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
6069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 60%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 64%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 93%. For individuals who are not male, the probability of competitive department is 23%. For individuals who are male, the probability of competitive department is 71%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.75
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.64
P(Y=1 | X=1, V2=1) = 0.93
P(V2=1 | X=0) = 0.23
P(V2=1 | X=1) = 0.71
0.71 * (0.60 - 0.75)+ 0.23 * (0.93 - 0.64)= -0.07
-0.07 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
6071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 60%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 64%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 93%. For individuals who are not male, the probability of competitive department is 23%. For individuals who are male, the probability of competitive department is 71%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.75
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.64
P(Y=1 | X=1, V2=1) = 0.93
P(V2=1 | X=0) = 0.23
P(V2=1 | X=1) = 0.71
0.23 * (0.93 - 0.64) + 0.71 * (0.60 - 0.75) = -0.01
-0.01 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
6072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 43%. For individuals who are not male, the probability of being allergic to peanuts is 72%. For individuals who are male, the probability of being allergic to peanuts is 84%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.84
0.43*0.84 - 0.57*0.72 = 0.72
0.72 > 0",mediation,gender_admission,1,marginal,P(Y)
6076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. Method 1: We look at how gender correlates with peanut allergy case by case according to department competitiveness. Method 2: We look directly at how gender correlates with peanut allergy in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
6078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 61%. For individuals who are male, the probability of being allergic to peanuts is 39%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.39
0.39 - 0.61 = -0.21
-0.21 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 61%. For individuals who are male, the probability of being allergic to peanuts is 39%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.39
0.39 - 0.61 = -0.21
-0.21 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 61%. For individuals who are male, the probability of being allergic to peanuts is 39%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.39
0.39 - 0.61 = -0.21
-0.21 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 50%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 63%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 34%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 65%. For individuals who are not male, the probability of competitive department is 84%. For individuals who are male, the probability of competitive department is 17%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.50
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.34
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.84
P(V2=1 | X=1) = 0.17
0.17 * (0.63 - 0.50)+ 0.84 * (0.65 - 0.34)= -0.09
-0.09 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
6096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 37%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 72%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are not male, the probability of competitive department is 85%. For individuals who are male, the probability of competitive department is 49%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.75
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.72
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.85
P(V2=1 | X=1) = 0.49
0.49 * (0.37 - 0.75)+ 0.85 * (0.21 - 0.72)= 0.14
0.14 > 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
6099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 75%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 37%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 72%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 21%. For individuals who are not male, the probability of competitive department is 85%. For individuals who are male, the probability of competitive department is 49%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.75
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.72
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.85
P(V2=1 | X=1) = 0.49
0.85 * (0.21 - 0.72) + 0.49 * (0.37 - 0.75) = -0.14
-0.14 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
6101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 41%. For individuals who are not male, the probability of being allergic to peanuts is 43%. For individuals who are male, the probability of being allergic to peanuts is 47%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.47
0.41*0.47 - 0.59*0.43 = 0.43
0.43 > 0",mediation,gender_admission,1,marginal,P(Y)
6106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 86%. For individuals who are male, the probability of being allergic to peanuts is 54%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.54
0.54 - 0.86 = -0.32
-0.32 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male, the probability of being allergic to peanuts is 86%. For individuals who are male, the probability of being allergic to peanuts is 54%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.54
0.54 - 0.86 = -0.32
-0.32 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. For individuals who are not male and applicants to a non-competitive department, the probability of being allergic to peanuts is 57%. For individuals who are not male and applicants to a competitive department, the probability of being allergic to peanuts is 99%. For individuals who are male and applicants to a non-competitive department, the probability of being allergic to peanuts is 57%. For individuals who are male and applicants to a competitive department, the probability of being allergic to peanuts is 52%. For individuals who are not male, the probability of competitive department is 69%. For individuals who are male, the probability of competitive department is 52%.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.57
P(Y=1 | X=0, V2=1) = 0.99
P(Y=1 | X=1, V2=0) = 0.57
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.69
P(V2=1 | X=1) = 0.52
0.69 * (0.52 - 0.57) + 0.52 * (0.99 - 0.57) = -0.33
-0.33 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
6116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. The overall probability of male gender is 48%. The probability of non-male gender and being allergic to peanuts is 44%. The probability of male gender and being allergic to peanuts is 26%.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.26
0.26/0.48 - 0.44/0.52 = -0.32
-0.32 < 0",mediation,gender_admission,1,correlation,P(Y | X)
6122,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 76%. For individuals who are male, the probability of brown eyes is 68%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.68
0.68 - 0.76 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 76%. For individuals who are male, the probability of brown eyes is 68%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.68
0.68 - 0.76 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6125,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 83%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 48%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 77%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 44%. For individuals who are not male and out-of-state residents, the probability of competitive department is 66%. For individuals who are not male and in-state residents, the probability of competitive department is 20%. For individuals who are male and out-of-state residents, the probability of competitive department is 55%. For individuals who are male and in-state residents, the probability of competitive department is 28%. The overall probability of in-state residency is 96%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.48
P(Y=1 | X=1, V3=0) = 0.77
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.66
P(V3=1 | X=0, V2=1) = 0.20
P(V3=1 | X=1, V2=0) = 0.55
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.96
0.96 * 0.48 * (0.28 - 0.55)+ 0.04 * 0.48 * (0.20 - 0.66)= -0.03
-0.03 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 84%. The probability of non-male gender and brown eyes is 12%. The probability of male gender and brown eyes is 57%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.57
0.57/0.84 - 0.12/0.16 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 81%. For individuals who are male, the probability of brown eyes is 77%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.77
0.77 - 0.81 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 91%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 47%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 91%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 50%. For individuals who are not male and out-of-state residents, the probability of competitive department is 53%. For individuals who are not male and in-state residents, the probability of competitive department is 16%. For individuals who are male and out-of-state residents, the probability of competitive department is 68%. For individuals who are male and in-state residents, the probability of competitive department is 27%. The overall probability of in-state residency is 82%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.50
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.16
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.82
0.82 * 0.47 * (0.27 - 0.68)+ 0.18 * 0.47 * (0.16 - 0.53)= -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 91%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 47%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 91%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 50%. For individuals who are not male and out-of-state residents, the probability of competitive department is 53%. For individuals who are not male and in-state residents, the probability of competitive department is 16%. For individuals who are male and out-of-state residents, the probability of competitive department is 68%. For individuals who are male and in-state residents, the probability of competitive department is 27%. The overall probability of in-state residency is 82%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.50
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.16
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.82
0.82 * 0.47 * (0.27 - 0.68)+ 0.18 * 0.47 * (0.16 - 0.53)= -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 45%. For individuals who are not male, the probability of brown eyes is 81%. For individuals who are male, the probability of brown eyes is 77%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.77
0.45*0.77 - 0.55*0.81 = 0.79
0.79 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6143,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 45%. For individuals who are not male, the probability of brown eyes is 81%. For individuals who are male, the probability of brown eyes is 77%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.77
0.45*0.77 - 0.55*0.81 = 0.79
0.79 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 45%. The probability of non-male gender and brown eyes is 45%. The probability of male gender and brown eyes is 34%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.34
0.34/0.45 - 0.45/0.55 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 45%. The probability of non-male gender and brown eyes is 45%. The probability of male gender and brown eyes is 34%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.34
0.34/0.45 - 0.45/0.55 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 64%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 39%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 65%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 39%. For individuals who are not male and out-of-state residents, the probability of competitive department is 51%. For individuals who are not male and in-state residents, the probability of competitive department is 21%. For individuals who are male and out-of-state residents, the probability of competitive department is 78%. For individuals who are male and in-state residents, the probability of competitive department is 47%. The overall probability of in-state residency is 93%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.21
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.47
P(V2=1) = 0.93
0.93 * 0.39 * (0.47 - 0.78)+ 0.07 * 0.39 * (0.21 - 0.51)= -0.06
-0.06 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 64%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 39%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 65%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 39%. For individuals who are not male and out-of-state residents, the probability of competitive department is 51%. For individuals who are not male and in-state residents, the probability of competitive department is 21%. For individuals who are male and out-of-state residents, the probability of competitive department is 78%. For individuals who are male and in-state residents, the probability of competitive department is 47%. The overall probability of in-state residency is 93%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.21
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.47
P(V2=1) = 0.93
0.93 * (0.39 - 0.65) * 0.21 + 0.07 * (0.39 - 0.64) * 0.78 = -0.00
0.00 = 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 64%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 39%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 65%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 39%. For individuals who are not male and out-of-state residents, the probability of competitive department is 51%. For individuals who are not male and in-state residents, the probability of competitive department is 21%. For individuals who are male and out-of-state residents, the probability of competitive department is 78%. For individuals who are male and in-state residents, the probability of competitive department is 47%. The overall probability of in-state residency is 93%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.21
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.47
P(V2=1) = 0.93
0.93 * (0.39 - 0.65) * 0.21 + 0.07 * (0.39 - 0.64) * 0.78 = -0.00
0.00 = 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6160,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6162,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 71%. For individuals who are male, the probability of brown eyes is 64%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.64
0.64 - 0.71 = -0.07
-0.07 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 35%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 45%. For individuals who are not male and out-of-state residents, the probability of competitive department is 42%. For individuals who are not male and in-state residents, the probability of competitive department is 4%. For individuals who are male and out-of-state residents, the probability of competitive department is 71%. For individuals who are male and in-state residents, the probability of competitive department is 32%. The overall probability of in-state residency is 82%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.45
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.04
P(V3=1 | X=1, V2=0) = 0.71
P(V3=1 | X=1, V2=1) = 0.32
P(V2=1) = 0.82
0.82 * (0.45 - 0.76) * 0.04 + 0.18 * (0.35 - 0.76) * 0.71 = 0.00
0.00 = 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 35%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 45%. For individuals who are not male and out-of-state residents, the probability of competitive department is 42%. For individuals who are not male and in-state residents, the probability of competitive department is 4%. For individuals who are male and out-of-state residents, the probability of competitive department is 71%. For individuals who are male and in-state residents, the probability of competitive department is 32%. The overall probability of in-state residency is 82%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.45
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.04
P(V3=1 | X=1, V2=0) = 0.71
P(V3=1 | X=1, V2=1) = 0.32
P(V2=1) = 0.82
0.82 * (0.45 - 0.76) * 0.04 + 0.18 * (0.35 - 0.76) * 0.71 = 0.00
0.00 = 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 43%. For individuals who are not male, the probability of brown eyes is 71%. For individuals who are male, the probability of brown eyes is 64%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.64
0.43*0.64 - 0.57*0.71 = 0.68
0.68 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6173,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 43%. The probability of non-male gender and brown eyes is 41%. The probability of male gender and brown eyes is 28%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.28
0.28/0.43 - 0.41/0.57 = -0.07
-0.07 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 84%. For individuals who are male, the probability of brown eyes is 87%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.87
0.87 - 0.84 = 0.03
0.03 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 94%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 56%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 100%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 65%. For individuals who are not male and out-of-state residents, the probability of competitive department is 76%. For individuals who are not male and in-state residents, the probability of competitive department is 22%. For individuals who are male and out-of-state residents, the probability of competitive department is 63%. For individuals who are male and in-state residents, the probability of competitive department is 34%. The overall probability of in-state residency is 91%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 1.00
P(Y=1 | X=1, V3=1) = 0.65
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.34
P(V2=1) = 0.91
0.91 * 0.56 * (0.34 - 0.63)+ 0.09 * 0.56 * (0.22 - 0.76)= -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 94%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 56%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 100%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 65%. For individuals who are not male and out-of-state residents, the probability of competitive department is 76%. For individuals who are not male and in-state residents, the probability of competitive department is 22%. For individuals who are male and out-of-state residents, the probability of competitive department is 63%. For individuals who are male and in-state residents, the probability of competitive department is 34%. The overall probability of in-state residency is 91%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 1.00
P(Y=1 | X=1, V3=1) = 0.65
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.34
P(V2=1) = 0.91
0.91 * 0.56 * (0.34 - 0.63)+ 0.09 * 0.56 * (0.22 - 0.76)= -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 94%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 56%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 100%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 65%. For individuals who are not male and out-of-state residents, the probability of competitive department is 76%. For individuals who are not male and in-state residents, the probability of competitive department is 22%. For individuals who are male and out-of-state residents, the probability of competitive department is 63%. For individuals who are male and in-state residents, the probability of competitive department is 34%. The overall probability of in-state residency is 91%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 1.00
P(Y=1 | X=1, V3=1) = 0.65
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.34
P(V2=1) = 0.91
0.91 * (0.65 - 1.00) * 0.22 + 0.09 * (0.56 - 0.94) * 0.63 = 0.06
0.06 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 75%. For individuals who are male, the probability of brown eyes is 82%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.82
0.82 - 0.75 = 0.06
0.06 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6192,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 75%. For individuals who are male, the probability of brown eyes is 82%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.82
0.82 - 0.75 = 0.06
0.06 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 75%. For individuals who are male, the probability of brown eyes is 82%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.82
0.82 - 0.75 = 0.06
0.06 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 81%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 40%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 86%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 30%. For individuals who are not male and out-of-state residents, the probability of competitive department is 53%. For individuals who are not male and in-state residents, the probability of competitive department is 13%. For individuals who are male and out-of-state residents, the probability of competitive department is 47%. For individuals who are male and in-state residents, the probability of competitive department is 5%. The overall probability of in-state residency is 94%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.81
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.13
P(V3=1 | X=1, V2=0) = 0.47
P(V3=1 | X=1, V2=1) = 0.05
P(V2=1) = 0.94
0.94 * (0.30 - 0.86) * 0.13 + 0.06 * (0.40 - 0.81) * 0.47 = 0.03
0.03 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 45%. For individuals who are not male, the probability of brown eyes is 75%. For individuals who are male, the probability of brown eyes is 82%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.82
0.45*0.82 - 0.55*0.75 = 0.78
0.78 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 45%. The probability of non-male gender and brown eyes is 41%. The probability of male gender and brown eyes is 36%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.36
0.36/0.45 - 0.41/0.55 = 0.07
0.07 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 50%. For individuals who are male, the probability of brown eyes is 42%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.42
0.42 - 0.50 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6208,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 57%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 20%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 64%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 25%. For individuals who are not male and out-of-state residents, the probability of competitive department is 38%. For individuals who are not male and in-state residents, the probability of competitive department is 18%. For individuals who are male and out-of-state residents, the probability of competitive department is 78%. For individuals who are male and in-state residents, the probability of competitive department is 54%. The overall probability of in-state residency is 90%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.25
P(V3=1 | X=0, V2=0) = 0.38
P(V3=1 | X=0, V2=1) = 0.18
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.90
0.90 * 0.20 * (0.54 - 0.78)+ 0.10 * 0.20 * (0.18 - 0.38)= -0.13
-0.13 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6209,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 57%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 20%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 64%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 25%. For individuals who are not male and out-of-state residents, the probability of competitive department is 38%. For individuals who are not male and in-state residents, the probability of competitive department is 18%. For individuals who are male and out-of-state residents, the probability of competitive department is 78%. For individuals who are male and in-state residents, the probability of competitive department is 54%. The overall probability of in-state residency is 90%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.25
P(V3=1 | X=0, V2=0) = 0.38
P(V3=1 | X=0, V2=1) = 0.18
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.90
0.90 * 0.20 * (0.54 - 0.78)+ 0.10 * 0.20 * (0.18 - 0.38)= -0.13
-0.13 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6211,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 57%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 20%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 64%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 25%. For individuals who are not male and out-of-state residents, the probability of competitive department is 38%. For individuals who are not male and in-state residents, the probability of competitive department is 18%. For individuals who are male and out-of-state residents, the probability of competitive department is 78%. For individuals who are male and in-state residents, the probability of competitive department is 54%. The overall probability of in-state residency is 90%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.25
P(V3=1 | X=0, V2=0) = 0.38
P(V3=1 | X=0, V2=1) = 0.18
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.90
0.90 * (0.25 - 0.64) * 0.18 + 0.10 * (0.20 - 0.57) * 0.78 = 0.06
0.06 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 96%. For individuals who are not male, the probability of brown eyes is 50%. For individuals who are male, the probability of brown eyes is 42%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.42
0.96*0.42 - 0.04*0.50 = 0.42
0.42 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 78%. For individuals who are male, the probability of brown eyes is 67%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.67
0.67 - 0.78 = -0.10
-0.10 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 92%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 38%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 86%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 53%. For individuals who are not male and out-of-state residents, the probability of competitive department is 65%. For individuals who are not male and in-state residents, the probability of competitive department is 26%. For individuals who are male and out-of-state residents, the probability of competitive department is 88%. For individuals who are male and in-state residents, the probability of competitive department is 56%. The overall probability of in-state residency is 98%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0, V2=0) = 0.65
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.88
P(V3=1 | X=1, V2=1) = 0.56
P(V2=1) = 0.98
0.98 * (0.53 - 0.86) * 0.26 + 0.02 * (0.38 - 0.92) * 0.88 = -0.01
-0.01 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 55%. For individuals who are not male, the probability of brown eyes is 78%. For individuals who are male, the probability of brown eyes is 67%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.67
0.55*0.67 - 0.45*0.78 = 0.70
0.70 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 74%. For individuals who are male, the probability of brown eyes is 64%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.64
0.64 - 0.74 = -0.10
-0.10 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 74%. For individuals who are male, the probability of brown eyes is 64%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.64
0.64 - 0.74 = -0.10
-0.10 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 75%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 39%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 67%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 34%. For individuals who are not male and out-of-state residents, the probability of competitive department is 42%. For individuals who are not male and in-state residents, the probability of competitive department is 1%. For individuals who are male and out-of-state residents, the probability of competitive department is 48%. For individuals who are male and in-state residents, the probability of competitive department is 5%. The overall probability of in-state residency is 97%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.01
P(V3=1 | X=1, V2=0) = 0.48
P(V3=1 | X=1, V2=1) = 0.05
P(V2=1) = 0.97
0.97 * 0.39 * (0.05 - 0.48)+ 0.03 * 0.39 * (0.01 - 0.42)= -0.01
-0.01 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 75%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 39%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 67%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 34%. For individuals who are not male and out-of-state residents, the probability of competitive department is 42%. For individuals who are not male and in-state residents, the probability of competitive department is 1%. For individuals who are male and out-of-state residents, the probability of competitive department is 48%. For individuals who are male and in-state residents, the probability of competitive department is 5%. The overall probability of in-state residency is 97%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.01
P(V3=1 | X=1, V2=0) = 0.48
P(V3=1 | X=1, V2=1) = 0.05
P(V2=1) = 0.97
0.97 * (0.34 - 0.67) * 0.01 + 0.03 * (0.39 - 0.75) * 0.48 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 84%. The probability of non-male gender and brown eyes is 12%. The probability of male gender and brown eyes is 54%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.54
0.54/0.84 - 0.12/0.16 = -0.10
-0.10 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 84%. The probability of non-male gender and brown eyes is 12%. The probability of male gender and brown eyes is 54%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.54
0.54/0.84 - 0.12/0.16 = -0.10
-0.10 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 59%. The probability of non-male gender and brown eyes is 30%. The probability of male gender and brown eyes is 46%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.46
0.46/0.59 - 0.30/0.41 = 0.04
0.04 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 53%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 17%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 55%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 19%. For individuals who are not male and out-of-state residents, the probability of competitive department is 47%. For individuals who are not male and in-state residents, the probability of competitive department is 18%. For individuals who are male and out-of-state residents, the probability of competitive department is 75%. For individuals who are male and in-state residents, the probability of competitive department is 49%. The overall probability of in-state residency is 92%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.17
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.47
P(V3=1 | X=0, V2=1) = 0.18
P(V3=1 | X=1, V2=0) = 0.75
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.92
0.92 * 0.17 * (0.49 - 0.75)+ 0.08 * 0.17 * (0.18 - 0.47)= -0.11
-0.11 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 53%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 17%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 55%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 19%. For individuals who are not male and out-of-state residents, the probability of competitive department is 47%. For individuals who are not male and in-state residents, the probability of competitive department is 18%. For individuals who are male and out-of-state residents, the probability of competitive department is 75%. For individuals who are male and in-state residents, the probability of competitive department is 49%. The overall probability of in-state residency is 92%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.17
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.47
P(V3=1 | X=0, V2=1) = 0.18
P(V3=1 | X=1, V2=0) = 0.75
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.92
0.92 * 0.17 * (0.49 - 0.75)+ 0.08 * 0.17 * (0.18 - 0.47)= -0.11
-0.11 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 53%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 17%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 55%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 19%. For individuals who are not male and out-of-state residents, the probability of competitive department is 47%. For individuals who are not male and in-state residents, the probability of competitive department is 18%. For individuals who are male and out-of-state residents, the probability of competitive department is 75%. For individuals who are male and in-state residents, the probability of competitive department is 49%. The overall probability of in-state residency is 92%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.17
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.47
P(V3=1 | X=0, V2=1) = 0.18
P(V3=1 | X=1, V2=0) = 0.75
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.92
0.92 * (0.19 - 0.55) * 0.18 + 0.08 * (0.17 - 0.53) * 0.75 = 0.02
0.02 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 83%. For individuals who are not male, the probability of brown eyes is 46%. For individuals who are male, the probability of brown eyes is 36%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.36
0.83*0.36 - 0.17*0.46 = 0.38
0.38 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 83%. The probability of non-male gender and brown eyes is 8%. The probability of male gender and brown eyes is 30%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.30
0.30/0.83 - 0.08/0.17 = -0.09
-0.09 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 67%. For individuals who are male, the probability of brown eyes is 61%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.61
0.61 - 0.67 = -0.06
-0.06 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 67%. For individuals who are male, the probability of brown eyes is 61%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.61
0.61 - 0.67 = -0.06
-0.06 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 73%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 42%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 72%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 47%. For individuals who are not male and out-of-state residents, the probability of competitive department is 41%. For individuals who are not male and in-state residents, the probability of competitive department is 17%. For individuals who are male and out-of-state residents, the probability of competitive department is 68%. For individuals who are male and in-state residents, the probability of competitive department is 41%. The overall probability of in-state residency is 87%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.73
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.72
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.41
P(V3=1 | X=0, V2=1) = 0.17
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.87
0.87 * 0.42 * (0.41 - 0.68)+ 0.13 * 0.42 * (0.17 - 0.41)= -0.06
-0.06 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 44%. The probability of non-male gender and brown eyes is 38%. The probability of male gender and brown eyes is 27%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.27
0.27/0.44 - 0.38/0.56 = -0.06
-0.06 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 29%. For individuals who are male, the probability of brown eyes is 31%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.31
0.31 - 0.29 = 0.02
0.02 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 41%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 10%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 45%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 6%. For individuals who are not male and out-of-state residents, the probability of competitive department is 62%. For individuals who are not male and in-state residents, the probability of competitive department is 38%. For individuals who are male and out-of-state residents, the probability of competitive department is 67%. For individuals who are male and in-state residents, the probability of competitive department is 35%. The overall probability of in-state residency is 96%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.10
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.06
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.67
P(V3=1 | X=1, V2=1) = 0.35
P(V2=1) = 0.96
0.96 * 0.10 * (0.35 - 0.67)+ 0.04 * 0.10 * (0.38 - 0.62)= 0.01
0.01 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 83%. For individuals who are not male, the probability of brown eyes is 29%. For individuals who are male, the probability of brown eyes is 31%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.31
0.83*0.31 - 0.17*0.29 = 0.30
0.30 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 83%. For individuals who are not male, the probability of brown eyes is 29%. For individuals who are male, the probability of brown eyes is 31%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.31
0.83*0.31 - 0.17*0.29 = 0.30
0.30 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 83%. The probability of non-male gender and brown eyes is 5%. The probability of male gender and brown eyes is 26%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.26
0.26/0.83 - 0.05/0.17 = 0.02
0.02 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 50%. For individuals who are not male, the probability of brown eyes is 42%. For individuals who are male, the probability of brown eyes is 49%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.49
0.50*0.49 - 0.50*0.42 = 0.45
0.45 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 50%. The probability of non-male gender and brown eyes is 21%. The probability of male gender and brown eyes is 24%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.24
0.24/0.50 - 0.21/0.50 = 0.06
0.06 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 50%. For individuals who are male, the probability of brown eyes is 35%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.35
0.35 - 0.50 = -0.15
-0.15 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 50%. For individuals who are male, the probability of brown eyes is 35%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.35
0.35 - 0.50 = -0.15
-0.15 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 58%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 29%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 57%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 19%. For individuals who are not male and out-of-state residents, the probability of competitive department is 52%. For individuals who are not male and in-state residents, the probability of competitive department is 25%. For individuals who are male and out-of-state residents, the probability of competitive department is 80%. For individuals who are male and in-state residents, the probability of competitive department is 57%. The overall probability of in-state residency is 90%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.58
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.80
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.90
0.90 * 0.29 * (0.57 - 0.80)+ 0.10 * 0.29 * (0.25 - 0.52)= -0.09
-0.09 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6321,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 58%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 29%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 57%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 19%. For individuals who are not male and out-of-state residents, the probability of competitive department is 52%. For individuals who are not male and in-state residents, the probability of competitive department is 25%. For individuals who are male and out-of-state residents, the probability of competitive department is 80%. For individuals who are male and in-state residents, the probability of competitive department is 57%. The overall probability of in-state residency is 90%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.58
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.80
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.90
0.90 * 0.29 * (0.57 - 0.80)+ 0.10 * 0.29 * (0.25 - 0.52)= -0.09
-0.09 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 74%. For individuals who are male, the probability of brown eyes is 62%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.62
0.62 - 0.74 = -0.12
-0.12 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 74%. For individuals who are male, the probability of brown eyes is 62%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.62
0.62 - 0.74 = -0.12
-0.12 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 83%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 33%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 84%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 41%. For individuals who are not male and out-of-state residents, the probability of competitive department is 63%. For individuals who are not male and in-state residents, the probability of competitive department is 6%. For individuals who are male and out-of-state residents, the probability of competitive department is 93%. For individuals who are male and in-state residents, the probability of competitive department is 42%. The overall probability of in-state residency is 81%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.41
P(V3=1 | X=0, V2=0) = 0.63
P(V3=1 | X=0, V2=1) = 0.06
P(V3=1 | X=1, V2=0) = 0.93
P(V3=1 | X=1, V2=1) = 0.42
P(V2=1) = 0.81
0.81 * 0.33 * (0.42 - 0.93)+ 0.19 * 0.33 * (0.06 - 0.63)= -0.10
-0.10 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 71%. For individuals who are male, the probability of brown eyes is 68%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.68
0.68 - 0.71 = -0.03
-0.03 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 71%. For individuals who are male, the probability of brown eyes is 68%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.68
0.68 - 0.71 = -0.03
-0.03 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 71%. For individuals who are male, the probability of brown eyes is 68%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.68
0.68 - 0.71 = -0.03
-0.03 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 71%. For individuals who are male, the probability of brown eyes is 68%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.68
0.68 - 0.71 = -0.03
-0.03 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6348,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 82%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 56%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 78%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 52%. For individuals who are not male and out-of-state residents, the probability of competitive department is 69%. For individuals who are not male and in-state residents, the probability of competitive department is 38%. For individuals who are male and out-of-state residents, the probability of competitive department is 63%. For individuals who are male and in-state residents, the probability of competitive department is 31%. The overall probability of in-state residency is 84%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.52
P(V3=1 | X=0, V2=0) = 0.69
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.84
0.84 * 0.56 * (0.31 - 0.63)+ 0.16 * 0.56 * (0.38 - 0.69)= 0.02
0.02 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6349,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 82%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 56%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 78%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 52%. For individuals who are not male and out-of-state residents, the probability of competitive department is 69%. For individuals who are not male and in-state residents, the probability of competitive department is 38%. For individuals who are male and out-of-state residents, the probability of competitive department is 63%. For individuals who are male and in-state residents, the probability of competitive department is 31%. The overall probability of in-state residency is 84%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.52
P(V3=1 | X=0, V2=0) = 0.69
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.84
0.84 * 0.56 * (0.31 - 0.63)+ 0.16 * 0.56 * (0.38 - 0.69)= 0.02
0.02 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6350,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 82%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 56%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 78%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 52%. For individuals who are not male and out-of-state residents, the probability of competitive department is 69%. For individuals who are not male and in-state residents, the probability of competitive department is 38%. For individuals who are male and out-of-state residents, the probability of competitive department is 63%. For individuals who are male and in-state residents, the probability of competitive department is 31%. The overall probability of in-state residency is 84%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.52
P(V3=1 | X=0, V2=0) = 0.69
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.84
0.84 * (0.52 - 0.78) * 0.38 + 0.16 * (0.56 - 0.82) * 0.63 = -0.05
-0.05 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 89%. The probability of non-male gender and brown eyes is 8%. The probability of male gender and brown eyes is 61%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.61
0.61/0.89 - 0.08/0.11 = -0.02
-0.02 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 58%. For individuals who are male, the probability of brown eyes is 57%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.57
0.57 - 0.58 = -0.01
-0.01 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 72%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 36%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 68%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 37%. For individuals who are not male and out-of-state residents, the probability of competitive department is 64%. For individuals who are not male and in-state residents, the probability of competitive department is 39%. For individuals who are male and out-of-state residents, the probability of competitive department is 71%. For individuals who are male and in-state residents, the probability of competitive department is 36%. The overall probability of in-state residency is 97%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.68
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.64
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.71
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.97
0.97 * 0.36 * (0.36 - 0.71)+ 0.03 * 0.36 * (0.39 - 0.64)= 0.01
0.01 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 55%. For individuals who are not male, the probability of brown eyes is 58%. For individuals who are male, the probability of brown eyes is 57%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.57
0.55*0.57 - 0.45*0.58 = 0.57
0.57 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 52%. For individuals who are male, the probability of brown eyes is 48%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.48
0.48 - 0.52 = -0.05
-0.05 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 52%. For individuals who are male, the probability of brown eyes is 48%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.48
0.48 - 0.52 = -0.05
-0.05 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 86%. For individuals who are not male, the probability of brown eyes is 52%. For individuals who are male, the probability of brown eyes is 48%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.48
0.86*0.48 - 0.14*0.52 = 0.49
0.49 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 86%. For individuals who are not male, the probability of brown eyes is 52%. For individuals who are male, the probability of brown eyes is 48%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.48
0.86*0.48 - 0.14*0.52 = 0.49
0.49 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 63%. For individuals who are male, the probability of brown eyes is 55%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.55
0.55 - 0.63 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6389,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 63%. For individuals who are male, the probability of brown eyes is 55%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.55
0.55 - 0.63 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 53%. The probability of non-male gender and brown eyes is 30%. The probability of male gender and brown eyes is 29%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.29
0.29/0.53 - 0.30/0.47 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 53%. The probability of non-male gender and brown eyes is 30%. The probability of male gender and brown eyes is 29%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.29
0.29/0.53 - 0.30/0.47 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 57%. For individuals who are male, the probability of brown eyes is 52%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.52
0.52 - 0.57 = -0.05
-0.05 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 69%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 36%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 78%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 28%. For individuals who are not male and out-of-state residents, the probability of competitive department is 75%. For individuals who are not male and in-state residents, the probability of competitive department is 37%. For individuals who are male and out-of-state residents, the probability of competitive department is 79%. For individuals who are male and in-state residents, the probability of competitive department is 50%. The overall probability of in-state residency is 93%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.69
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.37
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.93
0.93 * 0.36 * (0.50 - 0.79)+ 0.07 * 0.36 * (0.37 - 0.75)= -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 69%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 36%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 78%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 28%. For individuals who are not male and out-of-state residents, the probability of competitive department is 75%. For individuals who are not male and in-state residents, the probability of competitive department is 37%. For individuals who are male and out-of-state residents, the probability of competitive department is 79%. For individuals who are male and in-state residents, the probability of competitive department is 50%. The overall probability of in-state residency is 93%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.69
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.37
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.93
0.93 * 0.36 * (0.50 - 0.79)+ 0.07 * 0.36 * (0.37 - 0.75)= -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 69%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 36%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 78%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 28%. For individuals who are not male and out-of-state residents, the probability of competitive department is 75%. For individuals who are not male and in-state residents, the probability of competitive department is 37%. For individuals who are male and out-of-state residents, the probability of competitive department is 79%. For individuals who are male and in-state residents, the probability of competitive department is 50%. The overall probability of in-state residency is 93%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.69
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.37
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.93
0.93 * (0.28 - 0.78) * 0.37 + 0.07 * (0.36 - 0.69) * 0.79 = 0.01
0.01 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 97%. For individuals who are not male, the probability of brown eyes is 57%. For individuals who are male, the probability of brown eyes is 52%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.52
0.97*0.52 - 0.03*0.57 = 0.52
0.52 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 54%. For individuals who are male, the probability of brown eyes is 60%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.60
0.60 - 0.54 = 0.06
0.06 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 54%. For individuals who are male, the probability of brown eyes is 60%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.60
0.60 - 0.54 = 0.06
0.06 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 54%. For individuals who are male, the probability of brown eyes is 60%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.60
0.60 - 0.54 = 0.06
0.06 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6419,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 65%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 28%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 69%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 22%. For individuals who are not male and out-of-state residents, the probability of competitive department is 53%. For individuals who are not male and in-state residents, the probability of competitive department is 26%. For individuals who are male and out-of-state residents, the probability of competitive department is 81%. For individuals who are male and in-state residents, the probability of competitive department is 9%. The overall probability of in-state residency is 81%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.28
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.81
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.81
0.81 * 0.28 * (0.09 - 0.81)+ 0.19 * 0.28 * (0.26 - 0.53)= 0.03
0.03 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 65%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 28%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 69%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 22%. For individuals who are not male and out-of-state residents, the probability of competitive department is 53%. For individuals who are not male and in-state residents, the probability of competitive department is 26%. For individuals who are male and out-of-state residents, the probability of competitive department is 81%. For individuals who are male and in-state residents, the probability of competitive department is 9%. The overall probability of in-state residency is 81%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.28
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.81
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.81
0.81 * (0.22 - 0.69) * 0.26 + 0.19 * (0.28 - 0.65) * 0.81 = 0.04
0.04 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 65%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 28%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 69%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 22%. For individuals who are not male and out-of-state residents, the probability of competitive department is 53%. For individuals who are not male and in-state residents, the probability of competitive department is 26%. For individuals who are male and out-of-state residents, the probability of competitive department is 81%. For individuals who are male and in-state residents, the probability of competitive department is 9%. The overall probability of in-state residency is 81%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.28
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.81
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.81
0.81 * (0.22 - 0.69) * 0.26 + 0.19 * (0.28 - 0.65) * 0.81 = 0.04
0.04 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 56%. For individuals who are not male, the probability of brown eyes is 54%. For individuals who are male, the probability of brown eyes is 60%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.60
0.56*0.60 - 0.44*0.54 = 0.57
0.57 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 56%. For individuals who are male, the probability of brown eyes is 47%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.47
0.47 - 0.56 = -0.09
-0.09 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 56%. For individuals who are male, the probability of brown eyes is 47%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.47
0.47 - 0.56 = -0.09
-0.09 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6432,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 63%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 36%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 60%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 37%. For individuals who are not male and out-of-state residents, the probability of competitive department is 67%. For individuals who are not male and in-state residents, the probability of competitive department is 28%. For individuals who are male and out-of-state residents, the probability of competitive department is 89%. For individuals who are male and in-state residents, the probability of competitive department is 57%. The overall probability of in-state residency is 99%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.63
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.28
P(V3=1 | X=1, V2=0) = 0.89
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.99
0.99 * 0.36 * (0.57 - 0.89)+ 0.01 * 0.36 * (0.28 - 0.67)= -0.08
-0.08 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6435,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 63%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 36%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 60%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 37%. For individuals who are not male and out-of-state residents, the probability of competitive department is 67%. For individuals who are not male and in-state residents, the probability of competitive department is 28%. For individuals who are male and out-of-state residents, the probability of competitive department is 89%. For individuals who are male and in-state residents, the probability of competitive department is 57%. The overall probability of in-state residency is 99%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.63
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.28
P(V3=1 | X=1, V2=0) = 0.89
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.99
0.99 * (0.37 - 0.60) * 0.28 + 0.01 * (0.36 - 0.63) * 0.89 = -0.02
-0.02 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 89%. For individuals who are not male, the probability of brown eyes is 56%. For individuals who are male, the probability of brown eyes is 47%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.47
0.89*0.47 - 0.11*0.56 = 0.48
0.48 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 89%. For individuals who are not male, the probability of brown eyes is 56%. For individuals who are male, the probability of brown eyes is 47%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.47
0.89*0.47 - 0.11*0.56 = 0.48
0.48 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 89%. The probability of non-male gender and brown eyes is 6%. The probability of male gender and brown eyes is 42%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.42
0.42/0.89 - 0.06/0.11 = -0.09
-0.09 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 89%. The probability of non-male gender and brown eyes is 6%. The probability of male gender and brown eyes is 42%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.42
0.42/0.89 - 0.06/0.11 = -0.09
-0.09 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 71%. For individuals who are male, the probability of brown eyes is 65%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.65
0.65 - 0.71 = -0.06
-0.06 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 77%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 45%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 77%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 50%. For individuals who are not male and out-of-state residents, the probability of competitive department is 47%. For individuals who are not male and in-state residents, the probability of competitive department is 12%. For individuals who are male and out-of-state residents, the probability of competitive department is 75%. For individuals who are male and in-state residents, the probability of competitive department is 40%. The overall probability of in-state residency is 81%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.77
P(Y=1 | X=1, V3=1) = 0.50
P(V3=1 | X=0, V2=0) = 0.47
P(V3=1 | X=0, V2=1) = 0.12
P(V3=1 | X=1, V2=0) = 0.75
P(V3=1 | X=1, V2=1) = 0.40
P(V2=1) = 0.81
0.81 * 0.45 * (0.40 - 0.75)+ 0.19 * 0.45 * (0.12 - 0.47)= -0.06
-0.06 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 42%. The probability of non-male gender and brown eyes is 41%. The probability of male gender and brown eyes is 27%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.27
0.27/0.42 - 0.41/0.58 = -0.07
-0.07 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 55%. For individuals who are male, the probability of brown eyes is 58%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.58
0.58 - 0.55 = 0.04
0.04 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6457,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 55%. For individuals who are male, the probability of brown eyes is 58%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.58
0.58 - 0.55 = 0.04
0.04 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 56%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 27%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 65%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 30%. For individuals who are not male and out-of-state residents, the probability of competitive department is 53%. For individuals who are not male and in-state residents, the probability of competitive department is 5%. For individuals who are male and out-of-state residents, the probability of competitive department is 61%. For individuals who are male and in-state residents, the probability of competitive department is 17%. The overall probability of in-state residency is 97%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.05
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.97
0.97 * 0.27 * (0.17 - 0.61)+ 0.03 * 0.27 * (0.05 - 0.53)= -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 56%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 27%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 65%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 30%. For individuals who are not male and out-of-state residents, the probability of competitive department is 53%. For individuals who are not male and in-state residents, the probability of competitive department is 5%. For individuals who are male and out-of-state residents, the probability of competitive department is 61%. For individuals who are male and in-state residents, the probability of competitive department is 17%. The overall probability of in-state residency is 97%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.05
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.97
0.97 * (0.30 - 0.65) * 0.05 + 0.03 * (0.27 - 0.56) * 0.61 = 0.08
0.08 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 83%. The probability of non-male gender and brown eyes is 9%. The probability of male gender and brown eyes is 49%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.49
0.49/0.83 - 0.09/0.17 = 0.04
0.04 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 74%. For individuals who are male, the probability of brown eyes is 72%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.72
0.72 - 0.74 = -0.02
-0.02 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 85%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 62%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 87%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 56%. For individuals who are not male and out-of-state residents, the probability of competitive department is 86%. For individuals who are not male and in-state residents, the probability of competitive department is 45%. For individuals who are male and out-of-state residents, the probability of competitive department is 85%. For individuals who are male and in-state residents, the probability of competitive department is 46%. The overall probability of in-state residency is 95%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.86
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.95
0.95 * 0.62 * (0.46 - 0.85)+ 0.05 * 0.62 * (0.45 - 0.86)= -0.00
0.00 = 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 85%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 62%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 87%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 56%. For individuals who are not male and out-of-state residents, the probability of competitive department is 86%. For individuals who are not male and in-state residents, the probability of competitive department is 45%. For individuals who are male and out-of-state residents, the probability of competitive department is 85%. For individuals who are male and in-state residents, the probability of competitive department is 46%. The overall probability of in-state residency is 95%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.86
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.95
0.95 * (0.56 - 0.87) * 0.45 + 0.05 * (0.62 - 0.85) * 0.85 = -0.02
-0.02 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 55%. For individuals who are not male, the probability of brown eyes is 74%. For individuals who are male, the probability of brown eyes is 72%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.72
0.55*0.72 - 0.45*0.74 = 0.73
0.73 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 55%. The probability of non-male gender and brown eyes is 33%. The probability of male gender and brown eyes is 40%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.40
0.40/0.55 - 0.33/0.45 = -0.02
-0.02 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
6482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 51%. For individuals who are male, the probability of brown eyes is 31%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.31
0.31 - 0.51 = -0.20
-0.20 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6485,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 51%. For individuals who are male, the probability of brown eyes is 31%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.31
0.31 - 0.51 = -0.20
-0.20 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6486,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 51%. For individuals who are male, the probability of brown eyes is 31%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.31
0.31 - 0.51 = -0.20
-0.20 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 54%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 14%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 42%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 9%. For individuals who are not male and out-of-state residents, the probability of competitive department is 34%. For individuals who are not male and in-state residents, the probability of competitive department is 6%. For individuals who are male and out-of-state residents, the probability of competitive department is 66%. For individuals who are male and in-state residents, the probability of competitive department is 30%. The overall probability of in-state residency is 88%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.14
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.09
P(V3=1 | X=0, V2=0) = 0.34
P(V3=1 | X=0, V2=1) = 0.06
P(V3=1 | X=1, V2=0) = 0.66
P(V3=1 | X=1, V2=1) = 0.30
P(V2=1) = 0.88
0.88 * 0.14 * (0.30 - 0.66)+ 0.12 * 0.14 * (0.06 - 0.34)= -0.10
-0.10 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 54%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 14%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 42%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 9%. For individuals who are not male and out-of-state residents, the probability of competitive department is 34%. For individuals who are not male and in-state residents, the probability of competitive department is 6%. For individuals who are male and out-of-state residents, the probability of competitive department is 66%. For individuals who are male and in-state residents, the probability of competitive department is 30%. The overall probability of in-state residency is 88%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.14
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.09
P(V3=1 | X=0, V2=0) = 0.34
P(V3=1 | X=0, V2=1) = 0.06
P(V3=1 | X=1, V2=0) = 0.66
P(V3=1 | X=1, V2=1) = 0.30
P(V2=1) = 0.88
0.88 * (0.09 - 0.42) * 0.06 + 0.12 * (0.14 - 0.54) * 0.66 = -0.12
-0.12 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6492,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 84%. For individuals who are not male, the probability of brown eyes is 51%. For individuals who are male, the probability of brown eyes is 31%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.31
0.84*0.31 - 0.16*0.51 = 0.34
0.34 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6496,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look at how gender correlates with brown eyes case by case according to department competitiveness. Method 2: We look directly at how gender correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 77%. For individuals who are male, the probability of brown eyes is 68%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.68
0.68 - 0.77 = -0.09
-0.09 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 77%. For individuals who are male, the probability of brown eyes is 68%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.68
0.68 - 0.77 = -0.09
-0.09 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 77%. For individuals who are male, the probability of brown eyes is 68%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.68
0.68 - 0.77 = -0.09
-0.09 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6512,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 48%. For individuals who are male, the probability of brown eyes is 41%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.41
0.41 - 0.48 = -0.07
-0.07 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 48%. For individuals who are male, the probability of brown eyes is 41%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.41
0.41 - 0.48 = -0.07
-0.07 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 48%. For individuals who are male, the probability of brown eyes is 41%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.41
0.41 - 0.48 = -0.07
-0.07 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 56%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 14%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 60%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 19%. For individuals who are not male and out-of-state residents, the probability of competitive department is 52%. For individuals who are not male and in-state residents, the probability of competitive department is 15%. For individuals who are male and out-of-state residents, the probability of competitive department is 78%. For individuals who are male and in-state residents, the probability of competitive department is 41%. The overall probability of in-state residency is 89%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.14
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.15
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.89
0.89 * 0.14 * (0.41 - 0.78)+ 0.11 * 0.14 * (0.15 - 0.52)= -0.11
-0.11 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 82%. For individuals who are not male, the probability of brown eyes is 48%. For individuals who are male, the probability of brown eyes is 41%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.41
0.82*0.41 - 0.18*0.48 = 0.42
0.42 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. Method 1: We look directly at how gender correlates with brown eyes in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
6529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male, the probability of brown eyes is 67%. For individuals who are male, the probability of brown eyes is 64%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.64
0.64 - 0.67 = -0.03
-0.03 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 47%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 45%. For individuals who are not male and out-of-state residents, the probability of competitive department is 76%. For individuals who are not male and in-state residents, the probability of competitive department is 27%. For individuals who are male and out-of-state residents, the probability of competitive department is 61%. For individuals who are male and in-state residents, the probability of competitive department is 36%. The overall probability of in-state residency is 96%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.45
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.27
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.96
0.96 * 0.47 * (0.36 - 0.61)+ 0.04 * 0.47 * (0.27 - 0.76)= -0.02
-0.02 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 47%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 45%. For individuals who are not male and out-of-state residents, the probability of competitive department is 76%. For individuals who are not male and in-state residents, the probability of competitive department is 27%. For individuals who are male and out-of-state residents, the probability of competitive department is 61%. For individuals who are male and in-state residents, the probability of competitive department is 36%. The overall probability of in-state residency is 96%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.45
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.27
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.96
0.96 * 0.47 * (0.36 - 0.61)+ 0.04 * 0.47 * (0.27 - 0.76)= -0.02
-0.02 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 47%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 45%. For individuals who are not male and out-of-state residents, the probability of competitive department is 76%. For individuals who are not male and in-state residents, the probability of competitive department is 27%. For individuals who are male and out-of-state residents, the probability of competitive department is 61%. For individuals who are male and in-state residents, the probability of competitive department is 36%. The overall probability of in-state residency is 96%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.45
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.27
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.96
0.96 * (0.45 - 0.76) * 0.27 + 0.04 * (0.47 - 0.76) * 0.61 = -0.01
-0.01 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6533,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are not male and applicants to a competitive department, the probability of brown eyes is 47%. For individuals who are male and applicants to a non-competitive department, the probability of brown eyes is 76%. For individuals who are male and applicants to a competitive department, the probability of brown eyes is 45%. For individuals who are not male and out-of-state residents, the probability of competitive department is 76%. For individuals who are not male and in-state residents, the probability of competitive department is 27%. For individuals who are male and out-of-state residents, the probability of competitive department is 61%. For individuals who are male and in-state residents, the probability of competitive department is 36%. The overall probability of in-state residency is 96%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.45
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.27
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.96
0.96 * (0.45 - 0.76) * 0.27 + 0.04 * (0.47 - 0.76) * 0.61 = -0.01
-0.01 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 50%. For individuals who are not male, the probability of brown eyes is 67%. For individuals who are male, the probability of brown eyes is 64%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.64
0.50*0.64 - 0.50*0.67 = 0.66
0.66 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6535,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. The overall probability of male gender is 50%. For individuals who are not male, the probability of brown eyes is 67%. For individuals who are male, the probability of brown eyes is 64%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.64
0.50*0.64 - 0.50*0.67 = 0.66
0.66 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
6541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 30%. For individuals who have visited England, the probability of high salary is 42%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.42
0.42 - 0.30 = 0.12
0.12 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 16%. For individuals who have not visited England and white-collar workers, the probability of high salary is 60%. For individuals who have visited England and blue-collar workers, the probability of high salary is 22%. For individuals who have visited England and white-collar workers, the probability of high salary is 56%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 30%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 34%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 58%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 67%. The overall probability of high skill level is 9%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.16
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.22
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.30
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.09
0.09 * (0.56 - 0.22) * 0.34 + 0.91 * (0.60 - 0.16) * 0.58 = 0.02
0.02 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 16%. For individuals who have not visited England and white-collar workers, the probability of high salary is 60%. For individuals who have visited England and blue-collar workers, the probability of high salary is 22%. For individuals who have visited England and white-collar workers, the probability of high salary is 56%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 30%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 34%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 58%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 67%. The overall probability of high skill level is 9%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.16
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.22
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.30
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.09
0.09 * (0.56 - 0.22) * 0.34 + 0.91 * (0.60 - 0.16) * 0.58 = 0.02
0.02 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6548,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. For individuals who have not visited England, the probability of high salary is 30%. For individuals who have visited England, the probability of high salary is 42%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.42
0.55*0.42 - 0.45*0.30 = 0.37
0.37 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. The probability of not having visited England and high salary is 13%. The probability of having visited England and high salary is 23%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.23
0.23/0.55 - 0.13/0.45 = 0.12
0.12 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 25%. For individuals who have visited England, the probability of high salary is 33%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.33
0.33 - 0.25 = 0.08
0.08 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 25%. For individuals who have visited England, the probability of high salary is 33%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.33
0.33 - 0.25 = 0.08
0.08 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 25%. For individuals who have visited England, the probability of high salary is 33%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.33
0.33 - 0.25 = 0.08
0.08 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6559,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 19%. For individuals who have not visited England and white-collar workers, the probability of high salary is 47%. For individuals who have visited England and blue-collar workers, the probability of high salary is 18%. For individuals who have visited England and white-collar workers, the probability of high salary is 47%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 22%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 60%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 51%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 86%. The overall probability of high skill level is 2%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.19
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.18
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.22
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.86
P(V2=1) = 0.02
0.02 * 0.47 * (0.86 - 0.51)+ 0.98 * 0.47 * (0.60 - 0.22)= 0.08
0.08 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 44%. For individuals who have not visited England, the probability of high salary is 25%. For individuals who have visited England, the probability of high salary is 33%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.33
0.44*0.33 - 0.56*0.25 = 0.28
0.28 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 14%. For individuals who have not visited England and white-collar workers, the probability of high salary is 54%. For individuals who have visited England and blue-collar workers, the probability of high salary is 45%. For individuals who have visited England and white-collar workers, the probability of high salary is 92%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 51%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 36%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 81%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 86%. The overall probability of high skill level is 2%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.14
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.92
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.36
P(V3=1 | X=1, V2=0) = 0.81
P(V3=1 | X=1, V2=1) = 0.86
P(V2=1) = 0.02
0.02 * (0.92 - 0.45) * 0.36 + 0.98 * (0.54 - 0.14) * 0.81 = 0.35
0.35 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 45%. The probability of not having visited England and high salary is 19%. The probability of having visited England and high salary is 38%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.38
0.38/0.45 - 0.19/0.55 = 0.49
0.49 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 45%. The probability of not having visited England and high salary is 19%. The probability of having visited England and high salary is 38%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.38
0.38/0.45 - 0.19/0.55 = 0.49
0.49 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 59%. For individuals who have visited England, the probability of high salary is 76%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.76
0.76 - 0.59 = 0.17
0.17 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 18%. For individuals who have not visited England and white-collar workers, the probability of high salary is 59%. For individuals who have visited England and blue-collar workers, the probability of high salary is 59%. For individuals who have visited England and white-collar workers, the probability of high salary is 83%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 100%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 91%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 70%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 44%. The overall probability of high skill level is 10%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.18
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 1.00
P(V3=1 | X=0, V2=1) = 0.91
P(V3=1 | X=1, V2=0) = 0.70
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.10
0.10 * 0.59 * (0.44 - 0.70)+ 0.90 * 0.59 * (0.91 - 1.00)= -0.07
-0.07 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 29%. For individuals who have visited England, the probability of high salary is 65%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.65
0.65 - 0.29 = 0.36
0.36 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 29%. For individuals who have visited England, the probability of high salary is 65%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.65
0.65 - 0.29 = 0.36
0.36 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6607,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 42%. The probability of not having visited England and high salary is 17%. The probability of having visited England and high salary is 27%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.27
0.27/0.42 - 0.17/0.58 = 0.36
0.36 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 39%. For individuals who have visited England, the probability of high salary is 55%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.55
0.55 - 0.39 = 0.16
0.16 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 39%. For individuals who have visited England, the probability of high salary is 55%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.55
0.55 - 0.39 = 0.16
0.16 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6614,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 27%. For individuals who have not visited England and white-collar workers, the probability of high salary is 63%. For individuals who have visited England and blue-collar workers, the probability of high salary is 33%. For individuals who have visited England and white-collar workers, the probability of high salary is 63%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 32%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 44%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 75%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 79%. The overall probability of high skill level is 8%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.27
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.63
P(V3=1 | X=0, V2=0) = 0.32
P(V3=1 | X=0, V2=1) = 0.44
P(V3=1 | X=1, V2=0) = 0.75
P(V3=1 | X=1, V2=1) = 0.79
P(V2=1) = 0.08
0.08 * 0.63 * (0.79 - 0.75)+ 0.92 * 0.63 * (0.44 - 0.32)= 0.15
0.15 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 49%. For individuals who have not visited England, the probability of high salary is 39%. For individuals who have visited England, the probability of high salary is 55%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.55
0.49*0.55 - 0.51*0.39 = 0.48
0.48 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6619,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 49%. For individuals who have not visited England, the probability of high salary is 39%. For individuals who have visited England, the probability of high salary is 55%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.55
0.49*0.55 - 0.51*0.39 = 0.48
0.48 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 49%. The probability of not having visited England and high salary is 20%. The probability of having visited England and high salary is 27%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.27
0.27/0.49 - 0.20/0.51 = 0.16
0.16 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 62%. For individuals who have visited England, the probability of high salary is 72%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.72
0.72 - 0.62 = 0.10
0.10 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6625,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 62%. For individuals who have visited England, the probability of high salary is 72%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.72
0.72 - 0.62 = 0.10
0.10 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 62%. For individuals who have visited England, the probability of high salary is 72%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.72
0.72 - 0.62 = 0.10
0.10 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 50%. For individuals who have not visited England, the probability of high salary is 62%. For individuals who have visited England, the probability of high salary is 72%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.72
0.50*0.72 - 0.50*0.62 = 0.66
0.66 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 50%. The probability of not having visited England and high salary is 31%. The probability of having visited England and high salary is 36%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.36
0.36/0.50 - 0.31/0.50 = 0.10
0.10 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6638,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 39%. For individuals who have visited England, the probability of high salary is 78%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.78
0.78 - 0.39 = 0.39
0.39 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6639,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 39%. For individuals who have visited England, the probability of high salary is 78%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.78
0.78 - 0.39 = 0.39
0.39 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 35%. For individuals who have not visited England and white-collar workers, the probability of high salary is 57%. For individuals who have visited England and blue-collar workers, the probability of high salary is 64%. For individuals who have visited England and white-collar workers, the probability of high salary is 92%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 20%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 10%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 51%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 48%. The overall probability of high skill level is 13%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.92
P(V3=1 | X=0, V2=0) = 0.20
P(V3=1 | X=0, V2=1) = 0.10
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.13
0.13 * (0.92 - 0.64) * 0.10 + 0.87 * (0.57 - 0.35) * 0.51 = 0.30
0.30 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 47%. For individuals who have not visited England, the probability of high salary is 39%. For individuals who have visited England, the probability of high salary is 78%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.78
0.47*0.78 - 0.53*0.39 = 0.57
0.57 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 47%. The probability of not having visited England and high salary is 21%. The probability of having visited England and high salary is 37%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.37
0.37/0.47 - 0.21/0.53 = 0.39
0.39 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 26%. For individuals who have not visited England and white-collar workers, the probability of high salary is 61%. For individuals who have visited England and blue-collar workers, the probability of high salary is 55%. For individuals who have visited England and white-collar workers, the probability of high salary is 68%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 40%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 15%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 2%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 24%. The overall probability of high skill level is 11%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.26
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.15
P(V3=1 | X=1, V2=0) = 0.02
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.11
0.11 * (0.68 - 0.55) * 0.15 + 0.89 * (0.61 - 0.26) * 0.02 = 0.27
0.27 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 26%. For individuals who have not visited England and white-collar workers, the probability of high salary is 61%. For individuals who have visited England and blue-collar workers, the probability of high salary is 55%. For individuals who have visited England and white-collar workers, the probability of high salary is 68%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 40%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 15%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 2%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 24%. The overall probability of high skill level is 11%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.26
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.15
P(V3=1 | X=1, V2=0) = 0.02
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.11
0.11 * (0.68 - 0.55) * 0.15 + 0.89 * (0.61 - 0.26) * 0.02 = 0.27
0.27 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 37%. For individuals who have visited England, the probability of high salary is 73%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.73
0.73 - 0.37 = 0.36
0.36 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 37%. For individuals who have visited England, the probability of high salary is 73%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.73
0.73 - 0.37 = 0.36
0.36 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 37%. For individuals who have visited England, the probability of high salary is 73%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.73
0.73 - 0.37 = 0.36
0.36 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 37%. For individuals who have visited England, the probability of high salary is 73%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.73
0.73 - 0.37 = 0.36
0.36 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6674,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 48%. For individuals who have not visited England, the probability of high salary is 37%. For individuals who have visited England, the probability of high salary is 73%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.73
0.48*0.73 - 0.52*0.37 = 0.54
0.54 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 48%. For individuals who have not visited England, the probability of high salary is 37%. For individuals who have visited England, the probability of high salary is 73%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.73
0.48*0.73 - 0.52*0.37 = 0.54
0.54 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 44%. For individuals who have not visited England and white-collar workers, the probability of high salary is 94%. For individuals who have visited England and blue-collar workers, the probability of high salary is 29%. For individuals who have visited England and white-collar workers, the probability of high salary is 74%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 39%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 29%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 83%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 75%. The overall probability of high skill level is 14%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.94
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.83
P(V3=1 | X=1, V2=1) = 0.75
P(V2=1) = 0.14
0.14 * 0.94 * (0.75 - 0.83)+ 0.86 * 0.94 * (0.29 - 0.39)= 0.22
0.22 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 44%. For individuals who have not visited England and white-collar workers, the probability of high salary is 94%. For individuals who have visited England and blue-collar workers, the probability of high salary is 29%. For individuals who have visited England and white-collar workers, the probability of high salary is 74%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 39%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 29%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 83%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 75%. The overall probability of high skill level is 14%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.94
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.83
P(V3=1 | X=1, V2=1) = 0.75
P(V2=1) = 0.14
0.14 * (0.74 - 0.29) * 0.29 + 0.86 * (0.94 - 0.44) * 0.83 = -0.18
-0.18 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 56%. For individuals who have not visited England, the probability of high salary is 63%. For individuals who have visited England, the probability of high salary is 66%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.66
0.56*0.66 - 0.44*0.63 = 0.65
0.65 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 56%. For individuals who have not visited England, the probability of high salary is 63%. For individuals who have visited England, the probability of high salary is 66%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.66
0.56*0.66 - 0.44*0.63 = 0.65
0.65 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 56%. The probability of not having visited England and high salary is 28%. The probability of having visited England and high salary is 37%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.37
0.37/0.56 - 0.28/0.44 = 0.03
0.03 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 56%. The probability of not having visited England and high salary is 28%. The probability of having visited England and high salary is 37%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.37
0.37/0.56 - 0.28/0.44 = 0.03
0.03 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6693,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 64%. For individuals who have visited England, the probability of high salary is 70%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.70
0.70 - 0.64 = 0.06
0.06 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 60%. For individuals who have not visited England and white-collar workers, the probability of high salary is 93%. For individuals who have visited England and blue-collar workers, the probability of high salary is 45%. For individuals who have visited England and white-collar workers, the probability of high salary is 84%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 9%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 48%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 62%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 88%. The overall probability of high skill level is 7%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.93
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0, V2=0) = 0.09
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.62
P(V3=1 | X=1, V2=1) = 0.88
P(V2=1) = 0.07
0.07 * 0.93 * (0.88 - 0.62)+ 0.93 * 0.93 * (0.48 - 0.09)= 0.18
0.18 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 60%. For individuals who have not visited England and white-collar workers, the probability of high salary is 93%. For individuals who have visited England and blue-collar workers, the probability of high salary is 45%. For individuals who have visited England and white-collar workers, the probability of high salary is 84%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 9%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 48%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 62%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 88%. The overall probability of high skill level is 7%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.93
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0, V2=0) = 0.09
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.62
P(V3=1 | X=1, V2=1) = 0.88
P(V2=1) = 0.07
0.07 * (0.84 - 0.45) * 0.48 + 0.93 * (0.93 - 0.60) * 0.62 = -0.14
-0.14 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 22%. For individuals who have visited England, the probability of high salary is 62%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.62
0.62 - 0.22 = 0.40
0.40 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 22%. For individuals who have visited England, the probability of high salary is 62%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.62
0.62 - 0.22 = 0.40
0.40 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 22%. For individuals who have visited England, the probability of high salary is 62%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.62
0.62 - 0.22 = 0.40
0.40 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 15%. For individuals who have not visited England and white-collar workers, the probability of high salary is 40%. For individuals who have visited England and blue-collar workers, the probability of high salary is 43%. For individuals who have visited England and white-collar workers, the probability of high salary is 73%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 29%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 19%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 61%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 72%. The overall probability of high skill level is 6%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.15
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.73
P(V3=1 | X=0, V2=0) = 0.29
P(V3=1 | X=0, V2=1) = 0.19
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.06
0.06 * 0.40 * (0.72 - 0.61)+ 0.94 * 0.40 * (0.19 - 0.29)= 0.09
0.09 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6713,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 15%. For individuals who have not visited England and white-collar workers, the probability of high salary is 40%. For individuals who have visited England and blue-collar workers, the probability of high salary is 43%. For individuals who have visited England and white-collar workers, the probability of high salary is 73%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 29%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 19%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 61%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 72%. The overall probability of high skill level is 6%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.15
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.73
P(V3=1 | X=0, V2=0) = 0.29
P(V3=1 | X=0, V2=1) = 0.19
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.06
0.06 * 0.40 * (0.72 - 0.61)+ 0.94 * 0.40 * (0.19 - 0.29)= 0.09
0.09 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 15%. For individuals who have not visited England and white-collar workers, the probability of high salary is 40%. For individuals who have visited England and blue-collar workers, the probability of high salary is 43%. For individuals who have visited England and white-collar workers, the probability of high salary is 73%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 29%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 19%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 61%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 72%. The overall probability of high skill level is 6%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.15
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.73
P(V3=1 | X=0, V2=0) = 0.29
P(V3=1 | X=0, V2=1) = 0.19
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.06
0.06 * (0.73 - 0.43) * 0.19 + 0.94 * (0.40 - 0.15) * 0.61 = 0.29
0.29 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6716,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 58%. For individuals who have not visited England, the probability of high salary is 22%. For individuals who have visited England, the probability of high salary is 62%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.62
0.58*0.62 - 0.42*0.22 = 0.45
0.45 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 58%. The probability of not having visited England and high salary is 9%. The probability of having visited England and high salary is 36%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.36
0.36/0.58 - 0.09/0.42 = 0.40
0.40 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 58%. The probability of not having visited England and high salary is 9%. The probability of having visited England and high salary is 36%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.36
0.36/0.58 - 0.09/0.42 = 0.40
0.40 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6724,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 50%. For individuals who have visited England, the probability of high salary is 73%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.73 - 0.50 = 0.23
0.23 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 52%. For individuals who have not visited England, the probability of high salary is 50%. For individuals who have visited England, the probability of high salary is 73%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.52*0.73 - 0.48*0.50 = 0.62
0.62 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6733,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 52%. The probability of not having visited England and high salary is 24%. The probability of having visited England and high salary is 38%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.38
0.38/0.52 - 0.24/0.48 = 0.23
0.23 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 46%. For individuals who have visited England, the probability of high salary is 77%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.77
0.77 - 0.46 = 0.31
0.31 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6744,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 46%. For individuals who have not visited England, the probability of high salary is 46%. For individuals who have visited England, the probability of high salary is 77%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.77
0.46*0.77 - 0.54*0.46 = 0.60
0.60 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 37%. For individuals who have not visited England and white-collar workers, the probability of high salary is 74%. For individuals who have visited England and blue-collar workers, the probability of high salary is 44%. For individuals who have visited England and white-collar workers, the probability of high salary is 70%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 6%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 26%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 60%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 64%. The overall probability of high skill level is 8%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0, V2=0) = 0.06
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.60
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.08
0.08 * 0.74 * (0.64 - 0.60)+ 0.92 * 0.74 * (0.26 - 0.06)= 0.20
0.20 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 37%. For individuals who have not visited England and white-collar workers, the probability of high salary is 74%. For individuals who have visited England and blue-collar workers, the probability of high salary is 44%. For individuals who have visited England and white-collar workers, the probability of high salary is 70%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 6%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 26%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 60%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 64%. The overall probability of high skill level is 8%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0, V2=0) = 0.06
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.60
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.08
0.08 * (0.70 - 0.44) * 0.26 + 0.92 * (0.74 - 0.37) * 0.60 = 0.06
0.06 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 44%. For individuals who have not visited England, the probability of high salary is 40%. For individuals who have visited England, the probability of high salary is 60%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.60
0.44*0.60 - 0.56*0.40 = 0.50
0.50 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 44%. The probability of not having visited England and high salary is 22%. The probability of having visited England and high salary is 26%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.26
0.26/0.44 - 0.22/0.56 = 0.20
0.20 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 40%. For individuals who have visited England, the probability of high salary is 43%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.43
0.43 - 0.40 = 0.03
0.03 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 31%. For individuals who have not visited England and white-collar workers, the probability of high salary is 62%. For individuals who have visited England and blue-collar workers, the probability of high salary is 25%. For individuals who have visited England and white-collar workers, the probability of high salary is 60%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 28%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 50%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 50%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 80%. The overall probability of high skill level is 11%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.28
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.11
0.11 * 0.62 * (0.80 - 0.50)+ 0.89 * 0.62 * (0.50 - 0.28)= 0.07
0.07 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 31%. For individuals who have not visited England and white-collar workers, the probability of high salary is 62%. For individuals who have visited England and blue-collar workers, the probability of high salary is 25%. For individuals who have visited England and white-collar workers, the probability of high salary is 60%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 28%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 50%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 50%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 80%. The overall probability of high skill level is 11%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.28
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.11
0.11 * 0.62 * (0.80 - 0.50)+ 0.89 * 0.62 * (0.50 - 0.28)= 0.07
0.07 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6770,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 31%. For individuals who have not visited England and white-collar workers, the probability of high salary is 62%. For individuals who have visited England and blue-collar workers, the probability of high salary is 25%. For individuals who have visited England and white-collar workers, the probability of high salary is 60%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 28%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 50%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 50%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 80%. The overall probability of high skill level is 11%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.28
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.11
0.11 * (0.60 - 0.25) * 0.50 + 0.89 * (0.62 - 0.31) * 0.50 = -0.05
-0.05 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 58%. For individuals who have not visited England, the probability of high salary is 40%. For individuals who have visited England, the probability of high salary is 43%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.43
0.58*0.43 - 0.42*0.40 = 0.41
0.41 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 29%. For individuals who have not visited England and white-collar workers, the probability of high salary is 57%. For individuals who have visited England and blue-collar workers, the probability of high salary is 53%. For individuals who have visited England and white-collar workers, the probability of high salary is 84%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 13%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 19%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 52%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 58%. The overall probability of high skill level is 20%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.29
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0, V2=0) = 0.13
P(V3=1 | X=0, V2=1) = 0.19
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.20
0.20 * (0.84 - 0.53) * 0.19 + 0.80 * (0.57 - 0.29) * 0.52 = 0.25
0.25 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 29%. For individuals who have not visited England and white-collar workers, the probability of high salary is 57%. For individuals who have visited England and blue-collar workers, the probability of high salary is 53%. For individuals who have visited England and white-collar workers, the probability of high salary is 84%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 13%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 19%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 52%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 58%. The overall probability of high skill level is 20%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.29
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0, V2=0) = 0.13
P(V3=1 | X=0, V2=1) = 0.19
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.20
0.20 * (0.84 - 0.53) * 0.19 + 0.80 * (0.57 - 0.29) * 0.52 = 0.25
0.25 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 42%. For individuals who have not visited England, the probability of high salary is 33%. For individuals who have visited England, the probability of high salary is 70%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.70
0.42*0.70 - 0.58*0.33 = 0.48
0.48 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 42%. The probability of not having visited England and high salary is 19%. The probability of having visited England and high salary is 29%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.29
0.29/0.42 - 0.19/0.58 = 0.37
0.37 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 42%. The probability of not having visited England and high salary is 19%. The probability of having visited England and high salary is 29%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.29
0.29/0.42 - 0.19/0.58 = 0.37
0.37 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6790,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 53%. For individuals who have visited England, the probability of high salary is 78%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.78
0.78 - 0.53 = 0.25
0.25 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 36%. For individuals who have not visited England and white-collar workers, the probability of high salary is 61%. For individuals who have visited England and blue-collar workers, the probability of high salary is 59%. For individuals who have visited England and white-collar workers, the probability of high salary is 83%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 68%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 45%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 79%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 27%. The overall probability of high skill level is 3%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.68
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.03
0.03 * 0.61 * (0.27 - 0.79)+ 0.97 * 0.61 * (0.45 - 0.68)= 0.02
0.02 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 36%. For individuals who have not visited England and white-collar workers, the probability of high salary is 61%. For individuals who have visited England and blue-collar workers, the probability of high salary is 59%. For individuals who have visited England and white-collar workers, the probability of high salary is 83%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 68%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 45%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 79%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 27%. The overall probability of high skill level is 3%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.68
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.03
0.03 * 0.61 * (0.27 - 0.79)+ 0.97 * 0.61 * (0.45 - 0.68)= 0.02
0.02 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 36%. For individuals who have not visited England and white-collar workers, the probability of high salary is 61%. For individuals who have visited England and blue-collar workers, the probability of high salary is 59%. For individuals who have visited England and white-collar workers, the probability of high salary is 83%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 68%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 45%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 79%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 27%. The overall probability of high skill level is 3%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.68
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.03
0.03 * (0.83 - 0.59) * 0.45 + 0.97 * (0.61 - 0.36) * 0.79 = 0.23
0.23 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 48%. For individuals who have not visited England, the probability of high salary is 53%. For individuals who have visited England, the probability of high salary is 78%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.78
0.48*0.78 - 0.52*0.53 = 0.65
0.65 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 48%. For individuals who have not visited England, the probability of high salary is 53%. For individuals who have visited England, the probability of high salary is 78%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.78
0.48*0.78 - 0.52*0.53 = 0.65
0.65 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 48%. The probability of not having visited England and high salary is 28%. The probability of having visited England and high salary is 37%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.37
0.37/0.48 - 0.28/0.52 = 0.25
0.25 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 31%. For individuals who have visited England, the probability of high salary is 58%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.58
0.58 - 0.31 = 0.27
0.27 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 31%. For individuals who have visited England, the probability of high salary is 58%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.58
0.58 - 0.31 = 0.27
0.27 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 22%. For individuals who have not visited England and white-collar workers, the probability of high salary is 53%. For individuals who have visited England and blue-collar workers, the probability of high salary is 51%. For individuals who have visited England and white-collar workers, the probability of high salary is 76%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 32%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 23%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 24%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 49%. The overall probability of high skill level is 19%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.22
P(Y=1 | X=0, V3=1) = 0.53
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.76
P(V3=1 | X=0, V2=0) = 0.32
P(V3=1 | X=0, V2=1) = 0.23
P(V3=1 | X=1, V2=0) = 0.24
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.19
0.19 * 0.53 * (0.49 - 0.24)+ 0.81 * 0.53 * (0.23 - 0.32)= -0.00
0.00 = 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 22%. For individuals who have not visited England and white-collar workers, the probability of high salary is 53%. For individuals who have visited England and blue-collar workers, the probability of high salary is 51%. For individuals who have visited England and white-collar workers, the probability of high salary is 76%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 32%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 23%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 24%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 49%. The overall probability of high skill level is 19%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.22
P(Y=1 | X=0, V3=1) = 0.53
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.76
P(V3=1 | X=0, V2=0) = 0.32
P(V3=1 | X=0, V2=1) = 0.23
P(V3=1 | X=1, V2=0) = 0.24
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.19
0.19 * (0.76 - 0.51) * 0.23 + 0.81 * (0.53 - 0.22) * 0.24 = 0.27
0.27 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. For individuals who have not visited England, the probability of high salary is 31%. For individuals who have visited England, the probability of high salary is 58%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.58
0.55*0.58 - 0.45*0.31 = 0.46
0.46 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. The probability of not having visited England and high salary is 14%. The probability of having visited England and high salary is 32%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.32
0.32/0.55 - 0.14/0.45 = 0.27
0.27 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 60%. For individuals who have visited England, the probability of high salary is 72%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.72
0.72 - 0.60 = 0.12
0.12 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 60%. For individuals who have visited England, the probability of high salary is 72%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.72
0.72 - 0.60 = 0.12
0.12 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6823,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 60%. For individuals who have visited England, the probability of high salary is 72%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.72
0.72 - 0.60 = 0.12
0.12 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 45%. For individuals who have not visited England and white-collar workers, the probability of high salary is 88%. For individuals who have visited England and blue-collar workers, the probability of high salary is 51%. For individuals who have visited England and white-collar workers, the probability of high salary is 77%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 32%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 43%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 80%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 73%. The overall probability of high skill level is 8%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.88
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.32
P(V3=1 | X=0, V2=1) = 0.43
P(V3=1 | X=1, V2=0) = 0.80
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.08
0.08 * 0.88 * (0.73 - 0.80)+ 0.92 * 0.88 * (0.43 - 0.32)= 0.20
0.20 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 45%. For individuals who have not visited England and white-collar workers, the probability of high salary is 88%. For individuals who have visited England and blue-collar workers, the probability of high salary is 51%. For individuals who have visited England and white-collar workers, the probability of high salary is 77%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 32%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 43%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 80%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 73%. The overall probability of high skill level is 8%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.88
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.32
P(V3=1 | X=0, V2=1) = 0.43
P(V3=1 | X=1, V2=0) = 0.80
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.08
0.08 * 0.88 * (0.73 - 0.80)+ 0.92 * 0.88 * (0.43 - 0.32)= 0.20
0.20 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6831,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 59%. The probability of not having visited England and high salary is 24%. The probability of having visited England and high salary is 42%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.42
0.42/0.59 - 0.24/0.41 = 0.12
0.12 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 50%. For individuals who have visited England, the probability of high salary is 73%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.73 - 0.50 = 0.23
0.23 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 34%. For individuals who have not visited England and white-collar workers, the probability of high salary is 74%. For individuals who have visited England and blue-collar workers, the probability of high salary is 35%. For individuals who have visited England and white-collar workers, the probability of high salary is 92%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 34%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 62%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 58%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 97%. The overall probability of high skill level is 18%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.92
P(V3=1 | X=0, V2=0) = 0.34
P(V3=1 | X=0, V2=1) = 0.62
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.97
P(V2=1) = 0.18
0.18 * 0.74 * (0.97 - 0.58)+ 0.82 * 0.74 * (0.62 - 0.34)= 0.10
0.10 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 14%. For individuals who have visited England, the probability of high salary is 55%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.55
0.55 - 0.14 = 0.41
0.41 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6850,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 14%. For individuals who have visited England, the probability of high salary is 55%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.55
0.55 - 0.14 = 0.41
0.41 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 14%. For individuals who have visited England, the probability of high salary is 55%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.55
0.55 - 0.14 = 0.41
0.41 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 6%. For individuals who have not visited England and white-collar workers, the probability of high salary is 40%. For individuals who have visited England and blue-collar workers, the probability of high salary is 36%. For individuals who have visited England and white-collar workers, the probability of high salary is 68%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 26%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 11%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 57%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 67%. The overall probability of high skill level is 19%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.26
P(V3=1 | X=0, V2=1) = 0.11
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.19
0.19 * 0.40 * (0.67 - 0.57)+ 0.81 * 0.40 * (0.11 - 0.26)= 0.12
0.12 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 6%. For individuals who have not visited England and white-collar workers, the probability of high salary is 40%. For individuals who have visited England and blue-collar workers, the probability of high salary is 36%. For individuals who have visited England and white-collar workers, the probability of high salary is 68%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 26%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 11%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 57%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 67%. The overall probability of high skill level is 19%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.26
P(V3=1 | X=0, V2=1) = 0.11
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.19
0.19 * (0.68 - 0.36) * 0.11 + 0.81 * (0.40 - 0.06) * 0.57 = 0.30
0.30 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6857,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 56%. For individuals who have not visited England, the probability of high salary is 14%. For individuals who have visited England, the probability of high salary is 55%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.55
0.56*0.55 - 0.44*0.14 = 0.37
0.37 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6858,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 56%. The probability of not having visited England and high salary is 6%. The probability of having visited England and high salary is 31%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.31
0.31/0.56 - 0.06/0.44 = 0.41
0.41 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how having visited England correlates with salary case by case according to occupation. Method 2: We look directly at how having visited England correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6866,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 25%. For individuals who have not visited England and white-collar workers, the probability of high salary is 57%. For individuals who have visited England and blue-collar workers, the probability of high salary is 51%. For individuals who have visited England and white-collar workers, the probability of high salary is 77%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 89%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 75%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 63%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 73%. The overall probability of high skill level is 14%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.25
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.89
P(V3=1 | X=0, V2=1) = 0.75
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.14
0.14 * 0.57 * (0.73 - 0.63)+ 0.86 * 0.57 * (0.75 - 0.89)= -0.06
-0.06 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 25%. For individuals who have not visited England and white-collar workers, the probability of high salary is 57%. For individuals who have visited England and blue-collar workers, the probability of high salary is 51%. For individuals who have visited England and white-collar workers, the probability of high salary is 77%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 89%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 75%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 63%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 73%. The overall probability of high skill level is 14%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.25
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.89
P(V3=1 | X=0, V2=1) = 0.75
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.14
0.14 * (0.77 - 0.51) * 0.75 + 0.86 * (0.57 - 0.25) * 0.63 = 0.21
0.21 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. For individuals who have not visited England, the probability of high salary is 53%. For individuals who have visited England, the probability of high salary is 68%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.68
0.55*0.68 - 0.45*0.53 = 0.61
0.61 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. The probability of not having visited England and high salary is 24%. The probability of having visited England and high salary is 38%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.38
0.38/0.55 - 0.24/0.45 = 0.15
0.15 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6878,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 46%. For individuals who have visited England, the probability of high salary is 73%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.73
0.73 - 0.46 = 0.26
0.26 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 46%. For individuals who have visited England, the probability of high salary is 73%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.73
0.73 - 0.46 = 0.26
0.26 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 19%. For individuals who have visited England, the probability of high salary is 29%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.29
0.29 - 0.19 = 0.11
0.11 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6892,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 19%. For individuals who have visited England, the probability of high salary is 29%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.29
0.29 - 0.19 = 0.11
0.11 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 8%. For individuals who have not visited England and white-collar workers, the probability of high salary is 41%. For individuals who have visited England and blue-collar workers, the probability of high salary is 8%. For individuals who have visited England and white-collar workers, the probability of high salary is 47%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 27%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 56%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 48%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 81%. The overall probability of high skill level is 18%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.08
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.48
P(V3=1 | X=1, V2=1) = 0.81
P(V2=1) = 0.18
0.18 * (0.47 - 0.08) * 0.56 + 0.82 * (0.41 - 0.08) * 0.48 = 0.02
0.02 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6897,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 8%. For individuals who have not visited England and white-collar workers, the probability of high salary is 41%. For individuals who have visited England and blue-collar workers, the probability of high salary is 8%. For individuals who have visited England and white-collar workers, the probability of high salary is 47%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 27%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 56%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 48%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 81%. The overall probability of high skill level is 18%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.08
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.48
P(V3=1 | X=1, V2=1) = 0.81
P(V2=1) = 0.18
0.18 * (0.47 - 0.08) * 0.56 + 0.82 * (0.41 - 0.08) * 0.48 = 0.02
0.02 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 45%. For individuals who have not visited England, the probability of high salary is 19%. For individuals who have visited England, the probability of high salary is 29%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.29
0.45*0.29 - 0.55*0.19 = 0.23
0.23 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6900,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 45%. The probability of not having visited England and high salary is 10%. The probability of having visited England and high salary is 13%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.13
0.13/0.45 - 0.10/0.55 = 0.11
0.11 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 40%. For individuals who have not visited England and white-collar workers, the probability of high salary is 97%. For individuals who have visited England and blue-collar workers, the probability of high salary is 8%. For individuals who have visited England and white-collar workers, the probability of high salary is 75%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 15%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 22%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 51%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 54%. The overall probability of high skill level is 5%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.40
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.08
P(Y=1 | X=1, V3=1) = 0.75
P(V3=1 | X=0, V2=0) = 0.15
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.05
0.05 * 0.97 * (0.54 - 0.51)+ 0.95 * 0.97 * (0.22 - 0.15)= 0.20
0.20 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 43%. For individuals who have not visited England and white-collar workers, the probability of high salary is 50%. For individuals who have visited England and blue-collar workers, the probability of high salary is 67%. For individuals who have visited England and white-collar workers, the probability of high salary is 91%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 1%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 34%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 10%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 11%. The overall probability of high skill level is 18%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.91
P(V3=1 | X=0, V2=0) = 0.01
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.10
P(V3=1 | X=1, V2=1) = 0.11
P(V2=1) = 0.18
0.18 * 0.50 * (0.11 - 0.10)+ 0.82 * 0.50 * (0.34 - 0.01)= 0.01
0.01 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6923,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 43%. For individuals who have not visited England and white-collar workers, the probability of high salary is 50%. For individuals who have visited England and blue-collar workers, the probability of high salary is 67%. For individuals who have visited England and white-collar workers, the probability of high salary is 91%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 1%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 34%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 10%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 11%. The overall probability of high skill level is 18%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.91
P(V3=1 | X=0, V2=0) = 0.01
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.10
P(V3=1 | X=1, V2=1) = 0.11
P(V2=1) = 0.18
0.18 * 0.50 * (0.11 - 0.10)+ 0.82 * 0.50 * (0.34 - 0.01)= 0.01
0.01 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 43%. For individuals who have not visited England and white-collar workers, the probability of high salary is 50%. For individuals who have visited England and blue-collar workers, the probability of high salary is 67%. For individuals who have visited England and white-collar workers, the probability of high salary is 91%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 1%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 34%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 10%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 11%. The overall probability of high skill level is 18%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.91
P(V3=1 | X=0, V2=0) = 0.01
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.10
P(V3=1 | X=1, V2=1) = 0.11
P(V2=1) = 0.18
0.18 * (0.91 - 0.67) * 0.34 + 0.82 * (0.50 - 0.43) * 0.10 = 0.25
0.25 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. For individuals who have not visited England, the probability of high salary is 44%. For individuals who have visited England, the probability of high salary is 70%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.70
0.55*0.70 - 0.45*0.44 = 0.58
0.58 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. The probability of not having visited England and high salary is 20%. The probability of having visited England and high salary is 38%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.38
0.38/0.55 - 0.20/0.45 = 0.26
0.26 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6929,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 55%. The probability of not having visited England and high salary is 20%. The probability of having visited England and high salary is 38%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.38
0.38/0.55 - 0.20/0.45 = 0.26
0.26 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6934,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 21%. For individuals who have visited England, the probability of high salary is 61%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.61
0.61 - 0.21 = 0.40
0.40 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6936,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 3%. For individuals who have not visited England and white-collar workers, the probability of high salary is 36%. For individuals who have visited England and blue-collar workers, the probability of high salary is 28%. For individuals who have visited England and white-collar workers, the probability of high salary is 76%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 52%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 88%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 69%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 68%. The overall probability of high skill level is 6%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.76
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.88
P(V3=1 | X=1, V2=0) = 0.69
P(V3=1 | X=1, V2=1) = 0.68
P(V2=1) = 0.06
0.06 * 0.36 * (0.68 - 0.69)+ 0.94 * 0.36 * (0.88 - 0.52)= 0.05
0.05 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 3%. For individuals who have not visited England and white-collar workers, the probability of high salary is 36%. For individuals who have visited England and blue-collar workers, the probability of high salary is 28%. For individuals who have visited England and white-collar workers, the probability of high salary is 76%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 52%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 88%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 69%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 68%. The overall probability of high skill level is 6%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.76
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.88
P(V3=1 | X=1, V2=0) = 0.69
P(V3=1 | X=1, V2=1) = 0.68
P(V2=1) = 0.06
0.06 * (0.76 - 0.28) * 0.88 + 0.94 * (0.36 - 0.03) * 0.69 = 0.33
0.33 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 43%. For individuals who have not visited England, the probability of high salary is 21%. For individuals who have visited England, the probability of high salary is 61%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.61
0.43*0.61 - 0.57*0.21 = 0.38
0.38 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 43%. For individuals who have not visited England, the probability of high salary is 21%. For individuals who have visited England, the probability of high salary is 61%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.61
0.43*0.61 - 0.57*0.21 = 0.38
0.38 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 43%. The probability of not having visited England and high salary is 12%. The probability of having visited England and high salary is 26%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.26
0.26/0.43 - 0.12/0.57 = 0.40
0.40 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
6946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 31%. For individuals who have visited England, the probability of high salary is 65%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.65
0.65 - 0.31 = 0.34
0.34 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6947,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 31%. For individuals who have visited England, the probability of high salary is 65%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.65
0.65 - 0.31 = 0.34
0.34 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
6948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 31%. For individuals who have visited England, the probability of high salary is 65%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.65
0.65 - 0.31 = 0.34
0.34 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England, the probability of high salary is 31%. For individuals who have visited England, the probability of high salary is 65%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.65
0.65 - 0.31 = 0.34
0.34 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
6951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 19%. For individuals who have not visited England and white-collar workers, the probability of high salary is 43%. For individuals who have visited England and blue-collar workers, the probability of high salary is 44%. For individuals who have visited England and white-collar workers, the probability of high salary is 71%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 51%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 33%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 77%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 83%. The overall probability of high skill level is 14%.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.19
P(Y=1 | X=0, V3=1) = 0.43
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.77
P(V3=1 | X=1, V2=1) = 0.83
P(V2=1) = 0.14
0.14 * 0.43 * (0.83 - 0.77)+ 0.86 * 0.43 * (0.33 - 0.51)= 0.07
0.07 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
6952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who have not visited England and blue-collar workers, the probability of high salary is 19%. For individuals who have not visited England and white-collar workers, the probability of high salary is 43%. For individuals who have visited England and blue-collar workers, the probability of high salary is 44%. For individuals who have visited England and white-collar workers, the probability of high salary is 71%. For individuals who have not visited England and with low skill levels, the probability of white-collar job is 51%. For individuals who have not visited England and with high skill levels, the probability of white-collar job is 33%. For individuals who have visited England and with low skill levels, the probability of white-collar job is 77%. For individuals who have visited England and with high skill levels, the probability of white-collar job is 83%. The overall probability of high skill level is 14%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.19
P(Y=1 | X=0, V3=1) = 0.43
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.77
P(V3=1 | X=1, V2=1) = 0.83
P(V2=1) = 0.14
0.14 * (0.71 - 0.44) * 0.33 + 0.86 * (0.43 - 0.19) * 0.77 = 0.26
0.26 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
6955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of having visited England is 43%. For individuals who have not visited England, the probability of high salary is 31%. For individuals who have visited England, the probability of high salary is 65%.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.65
0.43*0.65 - 0.57*0.31 = 0.45
0.45 > 0",arrowhead,gender_pay,1,marginal,P(Y)
6959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how having visited England correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
6966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is 0.01.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
6968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 42%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 13%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 29%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 11%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 30%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.42
P(Y=1 | X=0, V3=0) = 0.13
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.11
P(Y=1 | X=1, V3=1) = 0.30
0.30 - (0.42*0.30 + 0.58*0.29) = 0.01
0.01 > 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
6969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 42%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 13%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 29%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 11%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 30%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.42
P(Y=1 | X=0, V3=0) = 0.13
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.11
P(Y=1 | X=1, V3=1) = 0.30
0.30 - (0.42*0.30 + 0.58*0.29) = 0.01
0.01 > 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
6970,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 5%. For people with no respiratory issues, the probability of black hair is 14%. For people with respiratory issues, the probability of black hair is 14%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.14
0.05*0.14 - 0.95*0.14 = 0.14
0.14 > 0",collision,hospitalization,1,marginal,P(Y)
6971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 5%. For people with no respiratory issues, the probability of black hair is 14%. For people with respiratory issues, the probability of black hair is 14%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.14
0.05*0.14 - 0.95*0.14 = 0.14
0.14 > 0",collision,hospitalization,1,marginal,P(Y)
6978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 5%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 10%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 23%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 7%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 21%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.05
P(Y=1 | X=0, V3=0) = 0.10
P(Y=1 | X=0, V3=1) = 0.23
P(Y=1 | X=1, V3=0) = 0.07
P(Y=1 | X=1, V3=1) = 0.21
0.21 - (0.05*0.21 + 0.95*0.23) = -0.02
-0.02 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
6981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 58%. For people with no respiratory issues, the probability of black hair is 13%. For people with respiratory issues, the probability of black hair is 13%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.13
0.58*0.13 - 0.42*0.13 = 0.13
0.13 > 0",collision,hospitalization,1,marginal,P(Y)
6986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.14.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
6988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 58%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 9%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 38%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 7%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 23%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.07
P(Y=1 | X=1, V3=1) = 0.23
0.23 - (0.58*0.23 + 0.42*0.38) = -0.03
-0.03 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
6989,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 58%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 9%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 38%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 7%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 23%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.09
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.07
P(Y=1 | X=1, V3=1) = 0.23
0.23 - (0.58*0.23 + 0.42*0.38) = -0.03
-0.03 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
6990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 52%. For people with no respiratory issues, the probability of black hair is 17%. For people with respiratory issues, the probability of black hair is 17%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.17
0.52*0.17 - 0.48*0.17 = 0.17
0.17 > 0",collision,hospitalization,1,marginal,P(Y)
6991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 52%. For people with no respiratory issues, the probability of black hair is 17%. For people with respiratory issues, the probability of black hair is 17%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.17
0.52*0.17 - 0.48*0.17 = 0.17
0.17 > 0",collision,hospitalization,1,marginal,P(Y)
6995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
6996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.19.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
6997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.19.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
6998,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 52%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 7%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 54%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 10%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 35%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.52
P(Y=1 | X=0, V3=0) = 0.07
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.10
P(Y=1 | X=1, V3=1) = 0.35
0.35 - (0.52*0.35 + 0.48*0.54) = -0.08
-0.08 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7006,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.26.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 55%. For people with no respiratory issues, the probability of black hair is 14%. For people with respiratory issues, the probability of black hair is 14%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.14
0.55*0.14 - 0.45*0.14 = 0.14
0.14 > 0",collision,hospitalization,1,marginal,P(Y)
7014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is 0.02.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is 0.02.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 8%. For people with no respiratory issues, the probability of black hair is 15%. For people with respiratory issues, the probability of black hair is 15%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.15
P(Y=1 | X=1) = 0.15
0.08*0.15 - 0.92*0.15 = 0.15
0.15 > 0",collision,hospitalization,1,marginal,P(Y)
7034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 41%. For people with no respiratory issues, the probability of black hair is 6%. For people with respiratory issues, the probability of black hair is 6%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.06
0.41*0.06 - 0.59*0.06 = 0.06
0.06 > 0",collision,hospitalization,1,marginal,P(Y)
7044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 41%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 4%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 10%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 3%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 8%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.41
P(Y=1 | X=0, V3=0) = 0.04
P(Y=1 | X=0, V3=1) = 0.10
P(Y=1 | X=1, V3=0) = 0.03
P(Y=1 | X=1, V3=1) = 0.08
0.08 - (0.41*0.08 + 0.59*0.10) = -0.01
-0.01 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 59%. For people with no respiratory issues, the probability of black hair is 5%. For people with respiratory issues, the probability of black hair is 5%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.05
P(Y=1 | X=1) = 0.05
0.59*0.05 - 0.41*0.05 = 0.05
0.05 > 0",collision,hospitalization,1,marginal,P(Y)
7055,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is 0.16.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.29.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 8%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 7%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 59%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 3%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 26%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.08
P(Y=1 | X=0, V3=0) = 0.07
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.03
P(Y=1 | X=1, V3=1) = 0.26
0.26 - (0.08*0.26 + 0.92*0.59) = -0.25
-0.25 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 41%. For people with no respiratory issues, the probability of black hair is 19%. For people with respiratory issues, the probability of black hair is 19%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.19
0.41*0.19 - 0.59*0.19 = 0.19
0.19 > 0",collision,hospitalization,1,marginal,P(Y)
7074,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.07.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 48%. For people with no respiratory issues, the probability of black hair is 7%. For people with respiratory issues, the probability of black hair is 7%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.07
0.48*0.07 - 0.52*0.07 = 0.07
0.07 > 0",collision,hospitalization,1,marginal,P(Y)
7085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7086,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is 0.12.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 48%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 3%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 29%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 4%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 41%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.48
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.41
0.41 - (0.48*0.41 + 0.52*0.29) = 0.08
0.08 > 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 16%. For people with no respiratory issues, the probability of black hair is 6%. For people with respiratory issues, the probability of black hair is 6%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.06
0.16*0.06 - 0.84*0.06 = 0.06
0.06 > 0",collision,hospitalization,1,marginal,P(Y)
7095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.06.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 50%. For people with no respiratory issues, the probability of black hair is 6%. For people with respiratory issues, the probability of black hair is 6%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.06
0.50*0.06 - 0.50*0.06 = 0.06
0.06 > 0",collision,hospitalization,1,marginal,P(Y)
7104,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.04.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 50%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 4%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 12%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 3%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 10%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.50
P(Y=1 | X=0, V3=0) = 0.04
P(Y=1 | X=0, V3=1) = 0.12
P(Y=1 | X=1, V3=0) = 0.03
P(Y=1 | X=1, V3=1) = 0.10
0.10 - (0.50*0.10 + 0.50*0.12) = -0.01
-0.01 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7110,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 50%. For people with no respiratory issues, the probability of black hair is 19%. For people with respiratory issues, the probability of black hair is 19%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.19
0.50*0.19 - 0.50*0.19 = 0.19
0.19 > 0",collision,hospitalization,1,marginal,P(Y)
7114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7117,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.18.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.02.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7129,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 12%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 3%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 10%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 1%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 9%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.12
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.10
P(Y=1 | X=1, V3=0) = 0.01
P(Y=1 | X=1, V3=1) = 0.09
0.09 - (0.12*0.09 + 0.88*0.10) = -0.01
-0.01 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 47%. For people with no respiratory issues, the probability of black hair is 17%. For people with respiratory issues, the probability of black hair is 17%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.17
0.47*0.17 - 0.53*0.17 = 0.17
0.17 > 0",collision,hospitalization,1,marginal,P(Y)
7134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.28.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 48%. For people with no respiratory issues, the probability of black hair is 2%. For people with respiratory issues, the probability of black hair is 2%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.02
P(Y=1 | X=1) = 0.02
0.48*0.02 - 0.52*0.02 = 0.02
0.02 > 0",collision,hospitalization,1,marginal,P(Y)
7144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.12.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 48%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 2%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 26%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 1%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 15%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.48
P(Y=1 | X=0, V3=0) = 0.02
P(Y=1 | X=0, V3=1) = 0.26
P(Y=1 | X=1, V3=0) = 0.01
P(Y=1 | X=1, V3=1) = 0.15
0.15 - (0.48*0.15 + 0.52*0.26) = -0.03
-0.03 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7150,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 4%. For people with no respiratory issues, the probability of black hair is 16%. For people with respiratory issues, the probability of black hair is 16%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.16
0.04*0.16 - 0.96*0.16 = 0.16
0.16 > 0",collision,hospitalization,1,marginal,P(Y)
7151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 4%. For people with no respiratory issues, the probability of black hair is 16%. For people with respiratory issues, the probability of black hair is 16%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.16
0.04*0.16 - 0.96*0.16 = 0.16
0.16 > 0",collision,hospitalization,1,marginal,P(Y)
7155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.08.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.08.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 57%. For people with no respiratory issues, the probability of black hair is 18%. For people with respiratory issues, the probability of black hair is 18%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.18
0.57*0.18 - 0.43*0.18 = 0.18
0.18 > 0",collision,hospitalization,1,marginal,P(Y)
7171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 57%. For people with no respiratory issues, the probability of black hair is 18%. For people with respiratory issues, the probability of black hair is 18%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.18
0.57*0.18 - 0.43*0.18 = 0.18
0.18 > 0",collision,hospitalization,1,marginal,P(Y)
7174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 57%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 3%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 39%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 10%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 24%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.57
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.10
P(Y=1 | X=1, V3=1) = 0.24
0.24 - (0.57*0.24 + 0.43*0.39) = -0.06
-0.06 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 3%. For people with no respiratory issues, the probability of black hair is 4%. For people with respiratory issues, the probability of black hair is 4%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.04
P(Y=1 | X=1) = 0.04
0.03*0.04 - 0.97*0.04 = 0.04
0.04 > 0",collision,hospitalization,1,marginal,P(Y)
7184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7185,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.03.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 3%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 2%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 9%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 0%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 6%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.03
P(Y=1 | X=0, V3=0) = 0.02
P(Y=1 | X=0, V3=1) = 0.09
P(Y=1 | X=1, V3=0) = 0.00
P(Y=1 | X=1, V3=1) = 0.06
0.06 - (0.03*0.06 + 0.97*0.09) = -0.03
-0.03 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 55%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 3%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 21%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 3%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 9%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.55
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.21
P(Y=1 | X=1, V3=0) = 0.03
P(Y=1 | X=1, V3=1) = 0.09
0.09 - (0.55*0.09 + 0.45*0.21) = -0.02
-0.02 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 51%. For people with no respiratory issues, the probability of black hair is 3%. For people with respiratory issues, the probability of black hair is 3%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.03
P(Y=1 | X=1) = 0.03
0.51*0.03 - 0.49*0.03 = 0.03
0.03 > 0",collision,hospitalization,1,marginal,P(Y)
7209,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 51%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 0%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 5%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 1%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 5%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.51
P(Y=1 | X=0, V3=0) = 0.00
P(Y=1 | X=0, V3=1) = 0.05
P(Y=1 | X=1, V3=0) = 0.01
P(Y=1 | X=1, V3=1) = 0.05
0.05 - (0.51*0.05 + 0.49*0.05) = 0.00
0.00 = 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.03.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 18%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 10%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 25%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 7%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 22%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.18
P(Y=1 | X=0, V3=0) = 0.10
P(Y=1 | X=0, V3=1) = 0.25
P(Y=1 | X=1, V3=0) = 0.07
P(Y=1 | X=1, V3=1) = 0.22
0.22 - (0.18*0.22 + 0.82*0.25) = -0.02
-0.02 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 49%. For people with no respiratory issues, the probability of black hair is 19%. For people with respiratory issues, the probability of black hair is 19%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.19
0.49*0.19 - 0.51*0.19 = 0.19
0.19 > 0",collision,hospitalization,1,marginal,P(Y)
7227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.05.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 49%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 15%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 31%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 7%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 27%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.49
P(Y=1 | X=0, V3=0) = 0.15
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.07
P(Y=1 | X=1, V3=1) = 0.27
0.27 - (0.49*0.27 + 0.51*0.31) = -0.01
-0.01 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 17%. For people with no respiratory issues, the probability of black hair is 20%. For people with respiratory issues, the probability of black hair is 20%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.20
0.17*0.20 - 0.83*0.20 = 0.20
0.20 > 0",collision,hospitalization,1,marginal,P(Y)
7236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. For hospitalized individuals, the correlation between respiratory issues and black hair is -0.10.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 17%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 12%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 42%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 7%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 31%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.17
P(Y=1 | X=0, V3=0) = 0.12
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.07
P(Y=1 | X=1, V3=1) = 0.31
0.31 - (0.17*0.31 + 0.83*0.42) = -0.08
-0.08 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 42%. For people with no respiratory issues, the probability of black hair is 13%. For people with respiratory issues, the probability of black hair is 13%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.13
0.42*0.13 - 0.58*0.13 = 0.13
0.13 > 0",collision,hospitalization,1,marginal,P(Y)
7244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look at how respiratory issues correlates with black hair case by case according to hospitalization status. Method 2: We look directly at how respiratory issues correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 42%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 6%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 17%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 6%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 20%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.42
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.17
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.20
0.20 - (0.42*0.20 + 0.58*0.17) = 0.02
0.02 > 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 40%. For people with no respiratory issues, the probability of black hair is 11%. For people with respiratory issues, the probability of black hair is 11%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.11
0.40*0.11 - 0.60*0.11 = 0.11
0.11 > 0",collision,hospitalization,1,marginal,P(Y)
7255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. Method 1: We look directly at how respiratory issues correlates with black hair in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
7258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 40%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 8%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 24%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 5%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 18%.",no,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.40
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.24
P(Y=1 | X=1, V3=0) = 0.05
P(Y=1 | X=1, V3=1) = 0.18
0.18 - (0.40*0.18 + 0.60*0.24) = -0.02
-0.02 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Respiratory issues has a direct effect on hospitalization status. Black hair has a direct effect on hospitalization status. The overall probability of respiratory issues is 40%. For people with no respiratory issues and non-hospitalized individuals, the probability of black hair is 8%. For people with no respiratory issues and hospitalized individuals, the probability of black hair is 24%. For people with respiratory issues and non-hospitalized individuals, the probability of black hair is 5%. For people with respiratory issues and hospitalized individuals, the probability of black hair is 18%.",yes,"Let Y = black hair; X = respiratory issues; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.40
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.24
P(Y=1 | X=1, V3=0) = 0.05
P(Y=1 | X=1, V3=1) = 0.18
0.18 - (0.40*0.18 + 0.60*0.24) = -0.02
-0.02 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 84%. For people with mean personalities, the probability of freckles is 56%. For people with kind personalities, the probability of freckles is 56%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.56
0.84*0.56 - 0.16*0.56 = 0.56
0.56 > 0",collision,man_in_relationship,1,marginal,P(Y)
7266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.08.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 84%. For people with mean personalities and single people, the probability of freckles is 42%. For people with mean personalities and in a relationship, the probability of freckles is 81%. For people with kind personalities and single people, the probability of freckles is 38%. For people with kind personalities and in a relationship, the probability of freckles is 68%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.84
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.81
P(Y=1 | X=1, V3=0) = 0.38
P(Y=1 | X=1, V3=1) = 0.68
0.68 - (0.84*0.68 + 0.16*0.81) = -0.01
-0.01 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 43%. For people with mean personalities, the probability of freckles is 50%. For people with kind personalities, the probability of freckles is 50%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.50
0.43*0.50 - 0.57*0.50 = 0.50
0.50 > 0",collision,man_in_relationship,1,marginal,P(Y)
7271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 43%. For people with mean personalities, the probability of freckles is 50%. For people with kind personalities, the probability of freckles is 50%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.50
0.43*0.50 - 0.57*0.50 = 0.50
0.50 > 0",collision,man_in_relationship,1,marginal,P(Y)
7284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.05.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is 0.05.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7298,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 41%. For people with mean personalities and single people, the probability of freckles is 33%. For people with mean personalities and in a relationship, the probability of freckles is 62%. For people with kind personalities and single people, the probability of freckles is 29%. For people with kind personalities and in a relationship, the probability of freckles is 67%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.41
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.67
0.67 - (0.41*0.67 + 0.59*0.62) = 0.03
0.03 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 41%. For people with mean personalities and single people, the probability of freckles is 33%. For people with mean personalities and in a relationship, the probability of freckles is 62%. For people with kind personalities and single people, the probability of freckles is 29%. For people with kind personalities and in a relationship, the probability of freckles is 67%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.41
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.67
0.67 - (0.41*0.67 + 0.59*0.62) = 0.03
0.03 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 56%. For people with mean personalities, the probability of freckles is 7%. For people with kind personalities, the probability of freckles is 7%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.07
0.56*0.07 - 0.44*0.07 = 0.07
0.07 > 0",collision,man_in_relationship,1,marginal,P(Y)
7314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 56%. For people with mean personalities and single people, the probability of freckles is 8%. For people with mean personalities and in a relationship, the probability of freckles is 3%. For people with kind personalities and single people, the probability of freckles is 6%. For people with kind personalities and in a relationship, the probability of freckles is 8%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.56
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.08
0.08 - (0.56*0.08 + 0.44*0.03) = 0.01
0.01 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 56%. For people with mean personalities and single people, the probability of freckles is 8%. For people with mean personalities and in a relationship, the probability of freckles is 3%. For people with kind personalities and single people, the probability of freckles is 6%. For people with kind personalities and in a relationship, the probability of freckles is 8%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.56
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.08
0.08 - (0.56*0.08 + 0.44*0.03) = 0.01
0.01 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.01.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 46%. For people with mean personalities and single people, the probability of freckles is 8%. For people with mean personalities and in a relationship, the probability of freckles is 13%. For people with kind personalities and single people, the probability of freckles is 6%. For people with kind personalities and in a relationship, the probability of freckles is 12%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.46
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.13
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.12
0.12 - (0.46*0.12 + 0.54*0.13) = -0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities and single people, the probability of freckles is 8%. For people with mean personalities and in a relationship, the probability of freckles is 24%. For people with kind personalities and single people, the probability of freckles is 4%. For people with kind personalities and in a relationship, the probability of freckles is 31%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.24
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.31
0.31 - (0.45*0.31 + 0.55*0.24) = 0.04
0.04 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7339,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities and single people, the probability of freckles is 8%. For people with mean personalities and in a relationship, the probability of freckles is 24%. For people with kind personalities and single people, the probability of freckles is 4%. For people with kind personalities and in a relationship, the probability of freckles is 31%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.24
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.31
0.31 - (0.45*0.31 + 0.55*0.24) = 0.04
0.04 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 86%. For people with mean personalities, the probability of freckles is 60%. For people with kind personalities, the probability of freckles is 60%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.60
0.86*0.60 - 0.14*0.60 = 0.60
0.60 > 0",collision,man_in_relationship,1,marginal,P(Y)
7344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.04.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7360,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 58%. For people with mean personalities, the probability of freckles is 40%. For people with kind personalities, the probability of freckles is 40%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.40
0.58*0.40 - 0.42*0.40 = 0.40
0.40 > 0",collision,man_in_relationship,1,marginal,P(Y)
7364,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.04.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 58%. For people with mean personalities and single people, the probability of freckles is 53%. For people with mean personalities and in a relationship, the probability of freckles is 34%. For people with kind personalities and single people, the probability of freckles is 97%. For people with kind personalities and in a relationship, the probability of freckles is 31%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.34
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.31
0.31 - (0.58*0.31 + 0.42*0.34) = -0.01
-0.01 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 85%. For people with mean personalities, the probability of freckles is 9%. For people with kind personalities, the probability of freckles is 9%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.85*0.09 - 0.15*0.09 = 0.09
0.09 > 0",collision,man_in_relationship,1,marginal,P(Y)
7381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 85%. For people with mean personalities, the probability of freckles is 9%. For people with kind personalities, the probability of freckles is 9%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.85*0.09 - 0.15*0.09 = 0.09
0.09 > 0",collision,man_in_relationship,1,marginal,P(Y)
7384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.05.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 85%. For people with mean personalities and single people, the probability of freckles is 5%. For people with mean personalities and in a relationship, the probability of freckles is 18%. For people with kind personalities and single people, the probability of freckles is 4%. For people with kind personalities and in a relationship, the probability of freckles is 12%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.85
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.18
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.12
0.12 - (0.85*0.12 + 0.15*0.18) = -0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 44%. For people with mean personalities, the probability of freckles is 9%. For people with kind personalities, the probability of freckles is 9%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.44*0.09 - 0.56*0.09 = 0.09
0.09 > 0",collision,man_in_relationship,1,marginal,P(Y)
7395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 44%. For people with mean personalities and single people, the probability of freckles is 11%. For people with mean personalities and in a relationship, the probability of freckles is 7%. For people with kind personalities and single people, the probability of freckles is 11%. For people with kind personalities and in a relationship, the probability of freckles is 9%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.44
P(Y=1 | X=0, V3=0) = 0.11
P(Y=1 | X=0, V3=1) = 0.07
P(Y=1 | X=1, V3=0) = 0.11
P(Y=1 | X=1, V3=1) = 0.09
0.09 - (0.44*0.09 + 0.56*0.07) = 0.01
0.01 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is 0.03.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 47%. For people with mean personalities and single people, the probability of freckles is 3%. For people with mean personalities and in a relationship, the probability of freckles is 1%. For people with kind personalities and single people, the probability of freckles is 2%. For people with kind personalities and in a relationship, the probability of freckles is 2%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.47
P(Y=1 | X=0, V3=0) = 0.03
P(Y=1 | X=0, V3=1) = 0.01
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.02
0.02 - (0.47*0.02 + 0.53*0.01) = 0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities, the probability of freckles is 13%. For people with kind personalities, the probability of freckles is 13%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.13
0.45*0.13 - 0.55*0.13 = 0.13
0.13 > 0",collision,man_in_relationship,1,marginal,P(Y)
7419,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities and single people, the probability of freckles is 6%. For people with mean personalities and in a relationship, the probability of freckles is 32%. For people with kind personalities and single people, the probability of freckles is 8%. For people with kind personalities and in a relationship, the probability of freckles is 25%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.06
P(Y=1 | X=0, V3=1) = 0.32
P(Y=1 | X=1, V3=0) = 0.08
P(Y=1 | X=1, V3=1) = 0.25
0.25 - (0.45*0.25 + 0.55*0.32) = -0.04
-0.04 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 94%. For people with mean personalities, the probability of freckles is 42%. For people with kind personalities, the probability of freckles is 42%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.42
0.94*0.42 - 0.06*0.42 = 0.42
0.42 > 0",collision,man_in_relationship,1,marginal,P(Y)
7421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 94%. For people with mean personalities, the probability of freckles is 42%. For people with kind personalities, the probability of freckles is 42%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.42
0.94*0.42 - 0.06*0.42 = 0.42
0.42 > 0",collision,man_in_relationship,1,marginal,P(Y)
7429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 94%. For people with mean personalities and single people, the probability of freckles is 31%. For people with mean personalities and in a relationship, the probability of freckles is 62%. For people with kind personalities and single people, the probability of freckles is 25%. For people with kind personalities and in a relationship, the probability of freckles is 55%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.94
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.55
0.55 - (0.94*0.55 + 0.06*0.62) = -0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7434,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.05.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 57%. For people with mean personalities and single people, the probability of freckles is 38%. For people with mean personalities and in a relationship, the probability of freckles is 43%. For people with kind personalities and single people, the probability of freckles is 61%. For people with kind personalities and in a relationship, the probability of freckles is 37%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.57
P(Y=1 | X=0, V3=0) = 0.38
P(Y=1 | X=0, V3=1) = 0.43
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.37
0.37 - (0.57*0.37 + 0.43*0.43) = -0.02
-0.02 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities, the probability of freckles is 40%. For people with kind personalities, the probability of freckles is 40%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.40
0.45*0.40 - 0.55*0.40 = 0.40
0.40 > 0",collision,man_in_relationship,1,marginal,P(Y)
7444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is 0.20.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities and single people, the probability of freckles is 38%. For people with mean personalities and in a relationship, the probability of freckles is 44%. For people with kind personalities and single people, the probability of freckles is 36%. For people with kind personalities and in a relationship, the probability of freckles is 69%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.38
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.69
0.69 - (0.45*0.69 + 0.55*0.44) = 0.21
0.21 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities, the probability of freckles is 49%. For people with kind personalities, the probability of freckles is 49%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.45*0.49 - 0.55*0.49 = 0.49
0.49 > 0",collision,man_in_relationship,1,marginal,P(Y)
7460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 95%. For people with mean personalities, the probability of freckles is 11%. For people with kind personalities, the probability of freckles is 11%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.11
0.95*0.11 - 0.05*0.11 = 0.11
0.11 > 0",collision,man_in_relationship,1,marginal,P(Y)
7465,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.05.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 95%. For people with mean personalities and single people, the probability of freckles is 8%. For people with mean personalities and in a relationship, the probability of freckles is 34%. For people with kind personalities and single people, the probability of freckles is 6%. For people with kind personalities and in a relationship, the probability of freckles is 16%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.95
P(Y=1 | X=0, V3=0) = 0.08
P(Y=1 | X=0, V3=1) = 0.34
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.16
0.16 - (0.95*0.16 + 0.05*0.34) = -0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 49%. For people with mean personalities, the probability of freckles is 10%. For people with kind personalities, the probability of freckles is 10%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.10
0.49*0.10 - 0.51*0.10 = 0.10
0.10 > 0",collision,man_in_relationship,1,marginal,P(Y)
7474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is 0.09.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is 0.09.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 49%. For people with mean personalities and single people, the probability of freckles is 12%. For people with mean personalities and in a relationship, the probability of freckles is 7%. For people with kind personalities and single people, the probability of freckles is 6%. For people with kind personalities and in a relationship, the probability of freckles is 12%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.49
P(Y=1 | X=0, V3=0) = 0.12
P(Y=1 | X=0, V3=1) = 0.07
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.12
0.12 - (0.49*0.12 + 0.51*0.07) = 0.02
0.02 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 49%. For people with mean personalities and single people, the probability of freckles is 12%. For people with mean personalities and in a relationship, the probability of freckles is 7%. For people with kind personalities and single people, the probability of freckles is 6%. For people with kind personalities and in a relationship, the probability of freckles is 12%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.49
P(Y=1 | X=0, V3=0) = 0.12
P(Y=1 | X=0, V3=1) = 0.07
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.12
0.12 - (0.49*0.12 + 0.51*0.07) = 0.02
0.02 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 47%. For people with mean personalities, the probability of freckles is 13%. For people with kind personalities, the probability of freckles is 13%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.13
P(Y=1 | X=1) = 0.13
0.47*0.13 - 0.53*0.13 = 0.13
0.13 > 0",collision,man_in_relationship,1,marginal,P(Y)
7487,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is 0.14.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 47%. For people with mean personalities and single people, the probability of freckles is 20%. For people with mean personalities and in a relationship, the probability of freckles is 11%. For people with kind personalities and single people, the probability of freckles is 2%. For people with kind personalities and in a relationship, the probability of freckles is 21%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.47
P(Y=1 | X=0, V3=0) = 0.20
P(Y=1 | X=0, V3=1) = 0.11
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.21
0.21 - (0.47*0.21 + 0.53*0.11) = 0.06
0.06 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 48%. For people with mean personalities, the probability of freckles is 9%. For people with kind personalities, the probability of freckles is 9%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.09
P(Y=1 | X=1) = 0.09
0.48*0.09 - 0.52*0.09 = 0.09
0.09 > 0",collision,man_in_relationship,1,marginal,P(Y)
7494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 48%. For people with mean personalities and single people, the probability of freckles is 5%. For people with mean personalities and in a relationship, the probability of freckles is 15%. For people with kind personalities and single people, the probability of freckles is 4%. For people with kind personalities and in a relationship, the probability of freckles is 15%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.48
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.15
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.15
0.15 - (0.48*0.15 + 0.52*0.15) = -0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 50%. For people with mean personalities, the probability of freckles is 6%. For people with kind personalities, the probability of freckles is 6%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.06
0.50*0.06 - 0.50*0.06 = 0.06
0.06 > 0",collision,man_in_relationship,1,marginal,P(Y)
7501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 50%. For people with mean personalities, the probability of freckles is 6%. For people with kind personalities, the probability of freckles is 6%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.06
0.50*0.06 - 0.50*0.06 = 0.06
0.06 > 0",collision,man_in_relationship,1,marginal,P(Y)
7504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.01.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.01.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 50%. For people with mean personalities and single people, the probability of freckles is 5%. For people with mean personalities and in a relationship, the probability of freckles is 7%. For people with kind personalities and single people, the probability of freckles is 5%. For people with kind personalities and in a relationship, the probability of freckles is 7%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.50
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.07
P(Y=1 | X=1, V3=0) = 0.05
P(Y=1 | X=1, V3=1) = 0.07
0.07 - (0.50*0.07 + 0.50*0.07) = -0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 53%. For people with mean personalities, the probability of freckles is 42%. For people with kind personalities, the probability of freckles is 42%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.42
0.53*0.42 - 0.47*0.42 = 0.42
0.42 > 0",collision,man_in_relationship,1,marginal,P(Y)
7515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.06.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.06.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 52%. For people with mean personalities, the probability of freckles is 54%. For people with kind personalities, the probability of freckles is 54%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.54
0.52*0.54 - 0.48*0.54 = 0.54
0.54 > 0",collision,man_in_relationship,1,marginal,P(Y)
7521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 52%. For people with mean personalities, the probability of freckles is 54%. For people with kind personalities, the probability of freckles is 54%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.54
0.52*0.54 - 0.48*0.54 = 0.54
0.54 > 0",collision,man_in_relationship,1,marginal,P(Y)
7525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 52%. For people with mean personalities and single people, the probability of freckles is 33%. For people with mean personalities and in a relationship, the probability of freckles is 82%. For people with kind personalities and single people, the probability of freckles is 39%. For people with kind personalities and in a relationship, the probability of freckles is 72%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.52
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.72
0.72 - (0.52*0.72 + 0.48*0.82) = -0.05
-0.05 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 52%. For people with mean personalities and single people, the probability of freckles is 33%. For people with mean personalities and in a relationship, the probability of freckles is 82%. For people with kind personalities and single people, the probability of freckles is 39%. For people with kind personalities and in a relationship, the probability of freckles is 72%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.52
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.72
0.72 - (0.52*0.72 + 0.48*0.82) = -0.05
-0.05 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities, the probability of freckles is 51%. For people with kind personalities, the probability of freckles is 51%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.51
0.45*0.51 - 0.55*0.51 = 0.51
0.51 > 0",collision,man_in_relationship,1,marginal,P(Y)
7534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look at how personality correlates with freckles case by case according to relationship status. Method 2: We look directly at how personality correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities and single people, the probability of freckles is 54%. For people with mean personalities and in a relationship, the probability of freckles is 45%. For people with kind personalities and single people, the probability of freckles is 22%. For people with kind personalities and in a relationship, the probability of freckles is 56%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.22
P(Y=1 | X=1, V3=1) = 0.56
0.56 - (0.45*0.56 + 0.55*0.45) = 0.03
0.03 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7539,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 45%. For people with mean personalities and single people, the probability of freckles is 54%. For people with mean personalities and in a relationship, the probability of freckles is 45%. For people with kind personalities and single people, the probability of freckles is 22%. For people with kind personalities and in a relationship, the probability of freckles is 56%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.22
P(Y=1 | X=1, V3=1) = 0.56
0.56 - (0.45*0.56 + 0.55*0.45) = 0.03
0.03 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 85%. For people with mean personalities, the probability of freckles is 47%. For people with kind personalities, the probability of freckles is 47%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.47
0.85*0.47 - 0.15*0.47 = 0.47
0.47 > 0",collision,man_in_relationship,1,marginal,P(Y)
7545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is -0.08.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 85%. For people with mean personalities and single people, the probability of freckles is 38%. For people with mean personalities and in a relationship, the probability of freckles is 71%. For people with kind personalities and single people, the probability of freckles is 32%. For people with kind personalities and in a relationship, the probability of freckles is 57%.",yes,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.85
P(Y=1 | X=0, V3=0) = 0.38
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.57
0.57 - (0.85*0.57 + 0.15*0.71) = -0.01
-0.01 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
7550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. The overall probability of kindness is 57%. For people with mean personalities, the probability of freckles is 10%. For people with kind personalities, the probability of freckles is 10%.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.10
0.57*0.10 - 0.43*0.10 = 0.10
0.10 > 0",collision,man_in_relationship,1,marginal,P(Y)
7555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. Method 1: We look directly at how personality correlates with freckles in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
7556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Personality has a direct effect on relationship status. Freckles has a direct effect on relationship status. For people in a relationship, the correlation between kindness and freckles is 0.07.",no,"Let Y = freckles; X = personality; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
7561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 34%. For children who like spicy food, the probability of intelligent child is 67%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.67
0.67 - 0.34 = 0.34
0.34 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 34%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 37%. For children who like spicy food and with low parental social status, the probability of intelligent child is 68%. For children who like spicy food and with high parental social status, the probability of intelligent child is 65%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 4%. For children who do not like spicy food and confounder active, the probability of high parental social status is 9%. For children who like spicy food and confounder inactive, the probability of high parental social status is 79%. For children who like spicy food and confounder active, the probability of high parental social status is 56%. The overall probability of confounder active is 47%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.37
P(Y=1 | X=1, V3=0) = 0.68
P(Y=1 | X=1, V3=1) = 0.65
P(V3=1 | X=0, V2=0) = 0.04
P(V3=1 | X=0, V2=1) = 0.09
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.56
P(V2=1) = 0.47
0.47 * 0.37 * (0.56 - 0.79)+ 0.53 * 0.37 * (0.09 - 0.04)= 0.03
0.03 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 54%. For children who do not like spicy food, the probability of intelligent child is 34%. For children who like spicy food, the probability of intelligent child is 67%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.67
0.54*0.67 - 0.46*0.34 = 0.53
0.53 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 42%. For children who like spicy food, the probability of intelligent child is 56%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.56
0.56 - 0.42 = 0.14
0.14 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 42%. For children who like spicy food, the probability of intelligent child is 56%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.56
0.56 - 0.42 = 0.14
0.14 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 42%. For children who like spicy food, the probability of intelligent child is 56%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.56
0.56 - 0.42 = 0.14
0.14 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 54%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 26%. For children who like spicy food and with low parental social status, the probability of intelligent child is 79%. For children who like spicy food and with high parental social status, the probability of intelligent child is 51%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 37%. For children who do not like spicy food and confounder active, the probability of high parental social status is 46%. For children who like spicy food and confounder inactive, the probability of high parental social status is 76%. For children who like spicy food and confounder active, the probability of high parental social status is 85%. The overall probability of confounder active is 48%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.26
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.37
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.76
P(V3=1 | X=1, V2=1) = 0.85
P(V2=1) = 0.48
0.48 * 0.26 * (0.85 - 0.76)+ 0.52 * 0.26 * (0.46 - 0.37)= -0.11
-0.11 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 54%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 26%. For children who like spicy food and with low parental social status, the probability of intelligent child is 79%. For children who like spicy food and with high parental social status, the probability of intelligent child is 51%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 37%. For children who do not like spicy food and confounder active, the probability of high parental social status is 46%. For children who like spicy food and confounder inactive, the probability of high parental social status is 76%. For children who like spicy food and confounder active, the probability of high parental social status is 85%. The overall probability of confounder active is 48%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.26
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.37
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.76
P(V3=1 | X=1, V2=1) = 0.85
P(V2=1) = 0.48
0.48 * 0.26 * (0.85 - 0.76)+ 0.52 * 0.26 * (0.46 - 0.37)= -0.11
-0.11 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 54%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 26%. For children who like spicy food and with low parental social status, the probability of intelligent child is 79%. For children who like spicy food and with high parental social status, the probability of intelligent child is 51%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 37%. For children who do not like spicy food and confounder active, the probability of high parental social status is 46%. For children who like spicy food and confounder inactive, the probability of high parental social status is 76%. For children who like spicy food and confounder active, the probability of high parental social status is 85%. The overall probability of confounder active is 48%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.26
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.37
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.76
P(V3=1 | X=1, V2=1) = 0.85
P(V2=1) = 0.48
0.48 * (0.51 - 0.79) * 0.46 + 0.52 * (0.26 - 0.54) * 0.76 = 0.25
0.25 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 49%. For children who do not like spicy food, the probability of intelligent child is 42%. For children who like spicy food, the probability of intelligent child is 56%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.56
0.49*0.56 - 0.51*0.42 = 0.49
0.49 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 31%. For children who like spicy food, the probability of intelligent child is 68%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.68
0.68 - 0.31 = 0.37
0.37 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 31%. For children who like spicy food, the probability of intelligent child is 68%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.68
0.68 - 0.31 = 0.37
0.37 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 36%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 29%. For children who like spicy food and with low parental social status, the probability of intelligent child is 64%. For children who like spicy food and with high parental social status, the probability of intelligent child is 68%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 63%. For children who do not like spicy food and confounder active, the probability of high parental social status is 83%. For children who like spicy food and confounder inactive, the probability of high parental social status is 85%. For children who like spicy food and confounder active, the probability of high parental social status is 41%. The overall probability of confounder active is 59%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.63
P(V3=1 | X=0, V2=1) = 0.83
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.59
0.59 * 0.29 * (0.41 - 0.85)+ 0.41 * 0.29 * (0.83 - 0.63)= 0.01
0.01 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 36%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 29%. For children who like spicy food and with low parental social status, the probability of intelligent child is 64%. For children who like spicy food and with high parental social status, the probability of intelligent child is 68%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 63%. For children who do not like spicy food and confounder active, the probability of high parental social status is 83%. For children who like spicy food and confounder inactive, the probability of high parental social status is 85%. For children who like spicy food and confounder active, the probability of high parental social status is 41%. The overall probability of confounder active is 59%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.63
P(V3=1 | X=0, V2=1) = 0.83
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.59
0.59 * 0.29 * (0.41 - 0.85)+ 0.41 * 0.29 * (0.83 - 0.63)= 0.01
0.01 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 45%. The probability of not liking spicy food and intelligent child is 17%. The probability of liking spicy food and intelligent child is 30%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.30
0.30/0.45 - 0.17/0.55 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7600,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7602,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 75%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.75
0.75 - 0.35 = 0.40
0.40 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7603,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 75%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.75
0.75 - 0.35 = 0.40
0.40 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 45%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 32%. For children who like spicy food and with low parental social status, the probability of intelligent child is 75%. For children who like spicy food and with high parental social status, the probability of intelligent child is 74%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 66%. For children who do not like spicy food and confounder active, the probability of high parental social status is 83%. For children who like spicy food and confounder inactive, the probability of high parental social status is 34%. For children who like spicy food and confounder active, the probability of high parental social status is 44%. The overall probability of confounder active is 58%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.32
P(Y=1 | X=1, V3=0) = 0.75
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.66
P(V3=1 | X=0, V2=1) = 0.83
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.58
0.58 * (0.74 - 0.75) * 0.83 + 0.42 * (0.32 - 0.45) * 0.34 = 0.39
0.39 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 42%. The probability of not liking spicy food and intelligent child is 20%. The probability of liking spicy food and intelligent child is 31%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.31
0.31/0.42 - 0.20/0.58 = 0.39
0.39 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 32%. For children who like spicy food, the probability of intelligent child is 80%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.80
0.80 - 0.32 = 0.48
0.48 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7617,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 32%. For children who like spicy food, the probability of intelligent child is 80%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.80
0.80 - 0.32 = 0.48
0.48 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7619,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 32%. For children who like spicy food, the probability of intelligent child is 80%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.80
0.80 - 0.32 = 0.48
0.48 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 47%. For children who do not like spicy food, the probability of intelligent child is 32%. For children who like spicy food, the probability of intelligent child is 80%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.80
0.47*0.80 - 0.53*0.32 = 0.56
0.56 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 47%. The probability of not liking spicy food and intelligent child is 17%. The probability of liking spicy food and intelligent child is 38%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.38
0.38/0.47 - 0.17/0.53 = 0.49
0.49 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 36%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.36
0.36 - 0.35 = 0.02
0.02 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 38%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 1%. For children who like spicy food and with low parental social status, the probability of intelligent child is 61%. For children who like spicy food and with high parental social status, the probability of intelligent child is 31%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 3%. For children who do not like spicy food and confounder active, the probability of high parental social status is 11%. For children who like spicy food and confounder inactive, the probability of high parental social status is 70%. For children who like spicy food and confounder active, the probability of high parental social status is 91%. The overall probability of confounder active is 57%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.38
P(Y=1 | X=0, V3=1) = 0.01
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.31
P(V3=1 | X=0, V2=0) = 0.03
P(V3=1 | X=0, V2=1) = 0.11
P(V3=1 | X=1, V2=0) = 0.70
P(V3=1 | X=1, V2=1) = 0.91
P(V2=1) = 0.57
0.57 * 0.01 * (0.91 - 0.70)+ 0.43 * 0.01 * (0.11 - 0.03)= -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 38%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 1%. For children who like spicy food and with low parental social status, the probability of intelligent child is 61%. For children who like spicy food and with high parental social status, the probability of intelligent child is 31%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 3%. For children who do not like spicy food and confounder active, the probability of high parental social status is 11%. For children who like spicy food and confounder inactive, the probability of high parental social status is 70%. For children who like spicy food and confounder active, the probability of high parental social status is 91%. The overall probability of confounder active is 57%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.38
P(Y=1 | X=0, V3=1) = 0.01
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.31
P(V3=1 | X=0, V2=0) = 0.03
P(V3=1 | X=0, V2=1) = 0.11
P(V3=1 | X=1, V2=0) = 0.70
P(V3=1 | X=1, V2=1) = 0.91
P(V2=1) = 0.57
0.57 * (0.31 - 0.61) * 0.11 + 0.43 * (0.01 - 0.38) * 0.70 = 0.24
0.24 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 20%. For children who like spicy food, the probability of intelligent child is 82%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.82
0.82 - 0.20 = 0.62
0.62 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 21%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 25%. For children who like spicy food and with low parental social status, the probability of intelligent child is 81%. For children who like spicy food and with high parental social status, the probability of intelligent child is 83%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 55%. For children who do not like spicy food and confounder active, the probability of high parental social status is 30%. For children who like spicy food and confounder inactive, the probability of high parental social status is 33%. For children who like spicy food and confounder active, the probability of high parental social status is 73%. The overall probability of confounder active is 56%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.21
P(Y=1 | X=0, V3=1) = 0.25
P(Y=1 | X=1, V3=0) = 0.81
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.55
P(V3=1 | X=0, V2=1) = 0.30
P(V3=1 | X=1, V2=0) = 0.33
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.56
0.56 * 0.25 * (0.73 - 0.33)+ 0.44 * 0.25 * (0.30 - 0.55)= 0.00
0.00 = 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 21%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 25%. For children who like spicy food and with low parental social status, the probability of intelligent child is 81%. For children who like spicy food and with high parental social status, the probability of intelligent child is 83%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 55%. For children who do not like spicy food and confounder active, the probability of high parental social status is 30%. For children who like spicy food and confounder inactive, the probability of high parental social status is 33%. For children who like spicy food and confounder active, the probability of high parental social status is 73%. The overall probability of confounder active is 56%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.21
P(Y=1 | X=0, V3=1) = 0.25
P(Y=1 | X=1, V3=0) = 0.81
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.55
P(V3=1 | X=0, V2=1) = 0.30
P(V3=1 | X=1, V2=0) = 0.33
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.56
0.56 * (0.83 - 0.81) * 0.30 + 0.44 * (0.25 - 0.21) * 0.33 = 0.60
0.60 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7652,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 57%. For children who do not like spicy food, the probability of intelligent child is 20%. For children who like spicy food, the probability of intelligent child is 82%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.82
0.57*0.82 - 0.43*0.20 = 0.55
0.55 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 57%. The probability of not liking spicy food and intelligent child is 10%. The probability of liking spicy food and intelligent child is 46%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.46
0.46/0.57 - 0.10/0.43 = 0.60
0.60 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7656,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 50%. For children who like spicy food, the probability of intelligent child is 86%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.86
0.86 - 0.50 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 50%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 50%. For children who like spicy food and with low parental social status, the probability of intelligent child is 86%. For children who like spicy food and with high parental social status, the probability of intelligent child is 86%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 72%. For children who do not like spicy food and confounder active, the probability of high parental social status is 60%. For children who like spicy food and confounder inactive, the probability of high parental social status is 27%. For children who like spicy food and confounder active, the probability of high parental social status is 37%. The overall probability of confounder active is 60%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.50
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.86
P(V3=1 | X=0, V2=0) = 0.72
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.27
P(V3=1 | X=1, V2=1) = 0.37
P(V2=1) = 0.60
0.60 * 0.50 * (0.37 - 0.27)+ 0.40 * 0.50 * (0.60 - 0.72)= 0.00
0.00 = 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 50%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 50%. For children who like spicy food and with low parental social status, the probability of intelligent child is 86%. For children who like spicy food and with high parental social status, the probability of intelligent child is 86%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 72%. For children who do not like spicy food and confounder active, the probability of high parental social status is 60%. For children who like spicy food and confounder inactive, the probability of high parental social status is 27%. For children who like spicy food and confounder active, the probability of high parental social status is 37%. The overall probability of confounder active is 60%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.50
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.86
P(V3=1 | X=0, V2=0) = 0.72
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.27
P(V3=1 | X=1, V2=1) = 0.37
P(V2=1) = 0.60
0.60 * (0.86 - 0.86) * 0.60 + 0.40 * (0.50 - 0.50) * 0.27 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 50%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 50%. For children who like spicy food and with low parental social status, the probability of intelligent child is 86%. For children who like spicy food and with high parental social status, the probability of intelligent child is 86%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 72%. For children who do not like spicy food and confounder active, the probability of high parental social status is 60%. For children who like spicy food and confounder inactive, the probability of high parental social status is 27%. For children who like spicy food and confounder active, the probability of high parental social status is 37%. The overall probability of confounder active is 60%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.50
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.86
P(V3=1 | X=0, V2=0) = 0.72
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.27
P(V3=1 | X=1, V2=1) = 0.37
P(V2=1) = 0.60
0.60 * (0.86 - 0.86) * 0.60 + 0.40 * (0.50 - 0.50) * 0.27 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 55%. For children who do not like spicy food, the probability of intelligent child is 50%. For children who like spicy food, the probability of intelligent child is 86%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.86
0.55*0.86 - 0.45*0.50 = 0.70
0.70 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 55%. The probability of not liking spicy food and intelligent child is 23%. The probability of liking spicy food and intelligent child is 47%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.47
0.47/0.55 - 0.23/0.45 = 0.36
0.36 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 55%. The probability of not liking spicy food and intelligent child is 23%. The probability of liking spicy food and intelligent child is 47%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.47
0.47/0.55 - 0.23/0.45 = 0.36
0.36 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 7%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 10%. For children who like spicy food and with low parental social status, the probability of intelligent child is 49%. For children who like spicy food and with high parental social status, the probability of intelligent child is 44%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 10%. For children who do not like spicy food and confounder active, the probability of high parental social status is 3%. For children who like spicy food and confounder inactive, the probability of high parental social status is 53%. For children who like spicy food and confounder active, the probability of high parental social status is 79%. The overall probability of confounder active is 44%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.07
P(Y=1 | X=0, V3=1) = 0.10
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.10
P(V3=1 | X=0, V2=1) = 0.03
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.79
P(V2=1) = 0.44
0.44 * 0.10 * (0.79 - 0.53)+ 0.56 * 0.10 * (0.03 - 0.10)= 0.01
0.01 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7681,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 54%. For children who do not like spicy food, the probability of intelligent child is 7%. For children who like spicy food, the probability of intelligent child is 48%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.48
0.54*0.48 - 0.46*0.07 = 0.30
0.30 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 54%. The probability of not liking spicy food and intelligent child is 3%. The probability of liking spicy food and intelligent child is 24%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.24
0.24/0.54 - 0.03/0.46 = 0.39
0.39 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 48%. For children who like spicy food, the probability of intelligent child is 73%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.73
0.73 - 0.48 = 0.24
0.24 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7692,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 59%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 29%. For children who like spicy food and with low parental social status, the probability of intelligent child is 90%. For children who like spicy food and with high parental social status, the probability of intelligent child is 61%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 36%. For children who do not like spicy food and confounder active, the probability of high parental social status is 35%. For children who like spicy food and confounder inactive, the probability of high parental social status is 60%. For children who like spicy food and confounder active, the probability of high parental social status is 62%. The overall probability of confounder active is 46%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.59
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.90
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.36
P(V3=1 | X=0, V2=1) = 0.35
P(V3=1 | X=1, V2=0) = 0.60
P(V3=1 | X=1, V2=1) = 0.62
P(V2=1) = 0.46
0.46 * (0.61 - 0.90) * 0.35 + 0.54 * (0.29 - 0.59) * 0.60 = 0.31
0.31 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 60%. For children who do not like spicy food, the probability of intelligent child is 48%. For children who like spicy food, the probability of intelligent child is 73%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.73
0.60*0.73 - 0.40*0.48 = 0.63
0.63 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 60%. The probability of not liking spicy food and intelligent child is 20%. The probability of liking spicy food and intelligent child is 43%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.43
0.43/0.60 - 0.20/0.40 = 0.24
0.24 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7703,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 32%. For children who like spicy food, the probability of intelligent child is 68%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.68
0.68 - 0.32 = 0.36
0.36 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 34%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 30%. For children who like spicy food and with low parental social status, the probability of intelligent child is 73%. For children who like spicy food and with high parental social status, the probability of intelligent child is 64%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 62%. For children who do not like spicy food and confounder active, the probability of high parental social status is 80%. For children who like spicy food and confounder inactive, the probability of high parental social status is 48%. For children who like spicy food and confounder active, the probability of high parental social status is 64%. The overall probability of confounder active is 56%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.30
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.64
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.80
P(V3=1 | X=1, V2=0) = 0.48
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.56
0.56 * 0.30 * (0.64 - 0.48)+ 0.44 * 0.30 * (0.80 - 0.62)= 0.00
0.00 = 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 34%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 30%. For children who like spicy food and with low parental social status, the probability of intelligent child is 73%. For children who like spicy food and with high parental social status, the probability of intelligent child is 64%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 62%. For children who do not like spicy food and confounder active, the probability of high parental social status is 80%. For children who like spicy food and confounder inactive, the probability of high parental social status is 48%. For children who like spicy food and confounder active, the probability of high parental social status is 64%. The overall probability of confounder active is 56%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.30
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.64
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.80
P(V3=1 | X=1, V2=0) = 0.48
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.56
0.56 * (0.64 - 0.73) * 0.80 + 0.44 * (0.30 - 0.34) * 0.48 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 51%. The probability of not liking spicy food and intelligent child is 15%. The probability of liking spicy food and intelligent child is 35%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.35
0.35/0.51 - 0.15/0.49 = 0.36
0.36 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 51%. The probability of not liking spicy food and intelligent child is 15%. The probability of liking spicy food and intelligent child is 35%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.35
0.35/0.51 - 0.15/0.49 = 0.36
0.36 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 38%. For children who like spicy food, the probability of intelligent child is 68%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.68
0.68 - 0.38 = 0.30
0.30 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 38%. For children who like spicy food, the probability of intelligent child is 68%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.68
0.68 - 0.38 = 0.30
0.30 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 36%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 39%. For children who like spicy food and with low parental social status, the probability of intelligent child is 68%. For children who like spicy food and with high parental social status, the probability of intelligent child is 67%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 56%. For children who do not like spicy food and confounder active, the probability of high parental social status is 55%. For children who like spicy food and confounder inactive, the probability of high parental social status is 8%. For children who like spicy food and confounder active, the probability of high parental social status is 24%. The overall probability of confounder active is 42%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.68
P(Y=1 | X=1, V3=1) = 0.67
P(V3=1 | X=0, V2=0) = 0.56
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.08
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.42
0.42 * 0.39 * (0.24 - 0.08)+ 0.58 * 0.39 * (0.55 - 0.56)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7721,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 36%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 39%. For children who like spicy food and with low parental social status, the probability of intelligent child is 68%. For children who like spicy food and with high parental social status, the probability of intelligent child is 67%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 56%. For children who do not like spicy food and confounder active, the probability of high parental social status is 55%. For children who like spicy food and confounder inactive, the probability of high parental social status is 8%. For children who like spicy food and confounder active, the probability of high parental social status is 24%. The overall probability of confounder active is 42%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.68
P(Y=1 | X=1, V3=1) = 0.67
P(V3=1 | X=0, V2=0) = 0.56
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.08
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.42
0.42 * (0.67 - 0.68) * 0.55 + 0.58 * (0.39 - 0.36) * 0.08 = 0.29
0.29 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 47%. For children who do not like spicy food, the probability of intelligent child is 38%. For children who like spicy food, the probability of intelligent child is 68%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.68
0.47*0.68 - 0.53*0.38 = 0.52
0.52 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7724,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 47%. The probability of not liking spicy food and intelligent child is 20%. The probability of liking spicy food and intelligent child is 32%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.32
0.32/0.47 - 0.20/0.53 = 0.30
0.30 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 17%. For children who like spicy food, the probability of intelligent child is 59%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.59
0.59 - 0.17 = 0.42
0.42 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7732,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 17%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 19%. For children who like spicy food and with low parental social status, the probability of intelligent child is 60%. For children who like spicy food and with high parental social status, the probability of intelligent child is 58%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 21%. For children who do not like spicy food and confounder active, the probability of high parental social status is 13%. For children who like spicy food and confounder inactive, the probability of high parental social status is 69%. For children who like spicy food and confounder active, the probability of high parental social status is 80%. The overall probability of confounder active is 52%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.17
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.13
P(V3=1 | X=1, V2=0) = 0.69
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.52
0.52 * 0.19 * (0.80 - 0.69)+ 0.48 * 0.19 * (0.13 - 0.21)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7740,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 46%. For children who do not like spicy food, the probability of intelligent child is 41%. For children who like spicy food, the probability of intelligent child is 66%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.66
0.46*0.66 - 0.54*0.41 = 0.53
0.53 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 46%. For children who do not like spicy food, the probability of intelligent child is 41%. For children who like spicy food, the probability of intelligent child is 66%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.66
0.46*0.66 - 0.54*0.41 = 0.53
0.53 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 16%. For children who like spicy food, the probability of intelligent child is 52%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.52
0.52 - 0.16 = 0.37
0.37 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 16%. For children who like spicy food, the probability of intelligent child is 52%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.16
P(Y=1 | X=1) = 0.52
0.52 - 0.16 = 0.37
0.37 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 19%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 14%. For children who like spicy food and with low parental social status, the probability of intelligent child is 57%. For children who like spicy food and with high parental social status, the probability of intelligent child is 46%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 59%. For children who do not like spicy food and confounder active, the probability of high parental social status is 45%. For children who like spicy food and confounder inactive, the probability of high parental social status is 27%. For children who like spicy food and confounder active, the probability of high parental social status is 60%. The overall probability of confounder active is 55%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.19
P(Y=1 | X=0, V3=1) = 0.14
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.46
P(V3=1 | X=0, V2=0) = 0.59
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.27
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.55
0.55 * 0.14 * (0.60 - 0.27)+ 0.45 * 0.14 * (0.45 - 0.59)= 0.00
0.00 = 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 19%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 14%. For children who like spicy food and with low parental social status, the probability of intelligent child is 57%. For children who like spicy food and with high parental social status, the probability of intelligent child is 46%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 59%. For children who do not like spicy food and confounder active, the probability of high parental social status is 45%. For children who like spicy food and confounder inactive, the probability of high parental social status is 27%. For children who like spicy food and confounder active, the probability of high parental social status is 60%. The overall probability of confounder active is 55%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.19
P(Y=1 | X=0, V3=1) = 0.14
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.46
P(V3=1 | X=0, V2=0) = 0.59
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.27
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.55
0.55 * (0.46 - 0.57) * 0.45 + 0.45 * (0.14 - 0.19) * 0.27 = 0.36
0.36 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 60%. The probability of not liking spicy food and intelligent child is 7%. The probability of liking spicy food and intelligent child is 31%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.31
0.31/0.60 - 0.07/0.40 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7773,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 70%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.70
0.70 - 0.35 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 35%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 35%. For children who like spicy food and with low parental social status, the probability of intelligent child is 69%. For children who like spicy food and with high parental social status, the probability of intelligent child is 70%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 57%. For children who do not like spicy food and confounder active, the probability of high parental social status is 69%. For children who like spicy food and confounder inactive, the probability of high parental social status is 35%. For children who like spicy food and confounder active, the probability of high parental social status is 28%. The overall probability of confounder active is 60%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0, V2=0) = 0.57
P(V3=1 | X=0, V2=1) = 0.69
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.60
0.60 * 0.35 * (0.28 - 0.35)+ 0.40 * 0.35 * (0.69 - 0.57)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7777,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 35%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 35%. For children who like spicy food and with low parental social status, the probability of intelligent child is 69%. For children who like spicy food and with high parental social status, the probability of intelligent child is 70%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 57%. For children who do not like spicy food and confounder active, the probability of high parental social status is 69%. For children who like spicy food and confounder inactive, the probability of high parental social status is 35%. For children who like spicy food and confounder active, the probability of high parental social status is 28%. The overall probability of confounder active is 60%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0, V2=0) = 0.57
P(V3=1 | X=0, V2=1) = 0.69
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.60
0.60 * (0.70 - 0.69) * 0.69 + 0.40 * (0.35 - 0.35) * 0.35 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 46%. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 70%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.70
0.46*0.70 - 0.54*0.35 = 0.51
0.51 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 46%. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 70%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.70
0.46*0.70 - 0.54*0.35 = 0.51
0.51 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 46%. The probability of not liking spicy food and intelligent child is 19%. The probability of liking spicy food and intelligent child is 32%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.32
0.32/0.46 - 0.19/0.54 = 0.34
0.34 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 77%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.77
0.77 - 0.35 = 0.42
0.42 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 77%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.77
0.77 - 0.35 = 0.42
0.42 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 36%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 33%. For children who like spicy food and with low parental social status, the probability of intelligent child is 91%. For children who like spicy food and with high parental social status, the probability of intelligent child is 74%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 42%. For children who do not like spicy food and confounder active, the probability of high parental social status is 33%. For children who like spicy food and confounder inactive, the probability of high parental social status is 79%. For children who like spicy food and confounder active, the probability of high parental social status is 83%. The overall probability of confounder active is 55%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.83
P(V2=1) = 0.55
0.55 * 0.33 * (0.83 - 0.79)+ 0.45 * 0.33 * (0.33 - 0.42)= -0.02
-0.02 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7792,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 43%. For children who do not like spicy food, the probability of intelligent child is 35%. For children who like spicy food, the probability of intelligent child is 77%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.77
0.43*0.77 - 0.57*0.35 = 0.55
0.55 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 42%. For children who like spicy food, the probability of intelligent child is 56%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.56
0.56 - 0.42 = 0.15
0.15 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 42%. For children who like spicy food, the probability of intelligent child is 56%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.56
0.56 - 0.42 = 0.15
0.15 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 53%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 22%. For children who like spicy food and with low parental social status, the probability of intelligent child is 75%. For children who like spicy food and with high parental social status, the probability of intelligent child is 49%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 40%. For children who do not like spicy food and confounder active, the probability of high parental social status is 31%. For children who like spicy food and confounder inactive, the probability of high parental social status is 70%. For children who like spicy food and confounder active, the probability of high parental social status is 76%. The overall probability of confounder active is 41%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.22
P(Y=1 | X=1, V3=0) = 0.75
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.31
P(V3=1 | X=1, V2=0) = 0.70
P(V3=1 | X=1, V2=1) = 0.76
P(V2=1) = 0.41
0.41 * 0.22 * (0.76 - 0.70)+ 0.59 * 0.22 * (0.31 - 0.40)= -0.11
-0.11 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 53%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 22%. For children who like spicy food and with low parental social status, the probability of intelligent child is 75%. For children who like spicy food and with high parental social status, the probability of intelligent child is 49%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 40%. For children who do not like spicy food and confounder active, the probability of high parental social status is 31%. For children who like spicy food and confounder inactive, the probability of high parental social status is 70%. For children who like spicy food and confounder active, the probability of high parental social status is 76%. The overall probability of confounder active is 41%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.22
P(Y=1 | X=1, V3=0) = 0.75
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.31
P(V3=1 | X=1, V2=0) = 0.70
P(V3=1 | X=1, V2=1) = 0.76
P(V2=1) = 0.41
0.41 * 0.22 * (0.76 - 0.70)+ 0.59 * 0.22 * (0.31 - 0.40)= -0.11
-0.11 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 53%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 22%. For children who like spicy food and with low parental social status, the probability of intelligent child is 75%. For children who like spicy food and with high parental social status, the probability of intelligent child is 49%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 40%. For children who do not like spicy food and confounder active, the probability of high parental social status is 31%. For children who like spicy food and confounder inactive, the probability of high parental social status is 70%. For children who like spicy food and confounder active, the probability of high parental social status is 76%. The overall probability of confounder active is 41%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.22
P(Y=1 | X=1, V3=0) = 0.75
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.31
P(V3=1 | X=1, V2=0) = 0.70
P(V3=1 | X=1, V2=1) = 0.76
P(V2=1) = 0.41
0.41 * (0.49 - 0.75) * 0.31 + 0.59 * (0.22 - 0.53) * 0.70 = 0.24
0.24 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 52%. The probability of not liking spicy food and intelligent child is 20%. The probability of liking spicy food and intelligent child is 29%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.29
0.29/0.52 - 0.20/0.48 = 0.15
0.15 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 30%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 24%. For children who like spicy food and with low parental social status, the probability of intelligent child is 61%. For children who like spicy food and with high parental social status, the probability of intelligent child is 65%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 53%. For children who do not like spicy food and confounder active, the probability of high parental social status is 48%. For children who like spicy food and confounder inactive, the probability of high parental social status is 64%. For children who like spicy food and confounder active, the probability of high parental social status is 57%. The overall probability of confounder active is 48%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.24
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.65
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.48
0.48 * 0.24 * (0.57 - 0.64)+ 0.52 * 0.24 * (0.48 - 0.53)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 30%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 24%. For children who like spicy food and with low parental social status, the probability of intelligent child is 61%. For children who like spicy food and with high parental social status, the probability of intelligent child is 65%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 53%. For children who do not like spicy food and confounder active, the probability of high parental social status is 48%. For children who like spicy food and confounder inactive, the probability of high parental social status is 64%. For children who like spicy food and confounder active, the probability of high parental social status is 57%. The overall probability of confounder active is 48%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.24
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.65
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.48
0.48 * 0.24 * (0.57 - 0.64)+ 0.52 * 0.24 * (0.48 - 0.53)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 52%. For children who do not like spicy food, the probability of intelligent child is 27%. For children who like spicy food, the probability of intelligent child is 63%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.63
0.52*0.63 - 0.48*0.27 = 0.46
0.46 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 52%. For children who do not like spicy food, the probability of intelligent child is 27%. For children who like spicy food, the probability of intelligent child is 63%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.63
0.52*0.63 - 0.48*0.27 = 0.46
0.46 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 52%. The probability of not liking spicy food and intelligent child is 13%. The probability of liking spicy food and intelligent child is 33%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.33
0.33/0.52 - 0.13/0.48 = 0.36
0.36 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 31%. For children who like spicy food, the probability of intelligent child is 65%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.65
0.65 - 0.31 = 0.34
0.34 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 33%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 31%. For children who like spicy food and with low parental social status, the probability of intelligent child is 63%. For children who like spicy food and with high parental social status, the probability of intelligent child is 67%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 96%. For children who do not like spicy food and confounder active, the probability of high parental social status is 90%. For children who like spicy food and confounder inactive, the probability of high parental social status is 50%. For children who like spicy food and confounder active, the probability of high parental social status is 50%. The overall probability of confounder active is 47%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.67
P(V3=1 | X=0, V2=0) = 0.96
P(V3=1 | X=0, V2=1) = 0.90
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.47
0.47 * 0.31 * (0.50 - 0.50)+ 0.53 * 0.31 * (0.90 - 0.96)= 0.01
0.01 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7833,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 33%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 31%. For children who like spicy food and with low parental social status, the probability of intelligent child is 63%. For children who like spicy food and with high parental social status, the probability of intelligent child is 67%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 96%. For children who do not like spicy food and confounder active, the probability of high parental social status is 90%. For children who like spicy food and confounder inactive, the probability of high parental social status is 50%. For children who like spicy food and confounder active, the probability of high parental social status is 50%. The overall probability of confounder active is 47%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.67
P(V3=1 | X=0, V2=0) = 0.96
P(V3=1 | X=0, V2=1) = 0.90
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.47
0.47 * (0.67 - 0.63) * 0.90 + 0.53 * (0.31 - 0.33) * 0.50 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 25%. For children who like spicy food, the probability of intelligent child is 53%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.53
0.53 - 0.25 = 0.29
0.29 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 23%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 28%. For children who like spicy food and with low parental social status, the probability of intelligent child is 51%. For children who like spicy food and with high parental social status, the probability of intelligent child is 53%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 42%. For children who do not like spicy food and confounder active, the probability of high parental social status is 25%. For children who like spicy food and confounder inactive, the probability of high parental social status is 93%. For children who like spicy food and confounder active, the probability of high parental social status is 74%. The overall probability of confounder active is 44%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.28
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.93
P(V3=1 | X=1, V2=1) = 0.74
P(V2=1) = 0.44
0.44 * (0.53 - 0.51) * 0.25 + 0.56 * (0.28 - 0.23) * 0.93 = 0.28
0.28 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 41%. For children who do not like spicy food, the probability of intelligent child is 25%. For children who like spicy food, the probability of intelligent child is 53%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.53
0.41*0.53 - 0.59*0.25 = 0.37
0.37 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7850,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 41%. The probability of not liking spicy food and intelligent child is 15%. The probability of liking spicy food and intelligent child is 22%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.22
0.22/0.41 - 0.15/0.59 = 0.28
0.28 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 41%. The probability of not liking spicy food and intelligent child is 15%. The probability of liking spicy food and intelligent child is 22%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.22
0.22/0.41 - 0.15/0.59 = 0.28
0.28 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7858,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 47%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 11%. For children who like spicy food and with low parental social status, the probability of intelligent child is 71%. For children who like spicy food and with high parental social status, the probability of intelligent child is 40%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 41%. For children who do not like spicy food and confounder active, the probability of high parental social status is 57%. For children who like spicy food and confounder inactive, the probability of high parental social status is 89%. For children who like spicy food and confounder active, the probability of high parental social status is 82%. The overall probability of confounder active is 56%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.47
P(Y=1 | X=0, V3=1) = 0.11
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.41
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.89
P(V3=1 | X=1, V2=1) = 0.82
P(V2=1) = 0.56
0.56 * 0.11 * (0.82 - 0.89)+ 0.44 * 0.11 * (0.57 - 0.41)= -0.13
-0.13 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 47%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 11%. For children who like spicy food and with low parental social status, the probability of intelligent child is 71%. For children who like spicy food and with high parental social status, the probability of intelligent child is 40%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 41%. For children who do not like spicy food and confounder active, the probability of high parental social status is 57%. For children who like spicy food and confounder inactive, the probability of high parental social status is 89%. For children who like spicy food and confounder active, the probability of high parental social status is 82%. The overall probability of confounder active is 56%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.47
P(Y=1 | X=0, V3=1) = 0.11
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.41
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.89
P(V3=1 | X=1, V2=1) = 0.82
P(V2=1) = 0.56
0.56 * 0.11 * (0.82 - 0.89)+ 0.44 * 0.11 * (0.57 - 0.41)= -0.13
-0.13 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 49%. For children who like spicy food, the probability of intelligent child is 84%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.84
0.84 - 0.49 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7871,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 49%. For children who like spicy food, the probability of intelligent child is 84%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.84
0.84 - 0.49 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7873,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 46%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 54%. For children who like spicy food and with low parental social status, the probability of intelligent child is 82%. For children who like spicy food and with high parental social status, the probability of intelligent child is 85%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 35%. For children who do not like spicy food and confounder active, the probability of high parental social status is 20%. For children who like spicy food and confounder inactive, the probability of high parental social status is 56%. For children who like spicy food and confounder active, the probability of high parental social status is 43%. The overall probability of confounder active is 43%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.85
P(V3=1 | X=0, V2=0) = 0.35
P(V3=1 | X=0, V2=1) = 0.20
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.43
P(V2=1) = 0.43
0.43 * 0.54 * (0.43 - 0.56)+ 0.57 * 0.54 * (0.20 - 0.35)= 0.02
0.02 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 41%. For children who do not like spicy food, the probability of intelligent child is 49%. For children who like spicy food, the probability of intelligent child is 84%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.84
0.41*0.84 - 0.59*0.49 = 0.64
0.64 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 41%. The probability of not liking spicy food and intelligent child is 29%. The probability of liking spicy food and intelligent child is 34%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.34
0.34/0.41 - 0.29/0.59 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7883,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 33%. For children who like spicy food, the probability of intelligent child is 74%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.74
0.74 - 0.33 = 0.41
0.41 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 34%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 33%. For children who like spicy food and with low parental social status, the probability of intelligent child is 76%. For children who like spicy food and with high parental social status, the probability of intelligent child is 70%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 77%. For children who do not like spicy food and confounder active, the probability of high parental social status is 80%. For children who like spicy food and confounder inactive, the probability of high parental social status is 37%. For children who like spicy food and confounder active, the probability of high parental social status is 55%. The overall probability of confounder active is 56%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0, V2=0) = 0.77
P(V3=1 | X=0, V2=1) = 0.80
P(V3=1 | X=1, V2=0) = 0.37
P(V3=1 | X=1, V2=1) = 0.55
P(V2=1) = 0.56
0.56 * 0.33 * (0.55 - 0.37)+ 0.44 * 0.33 * (0.80 - 0.77)= 0.00
0.00 = 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7895,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 32%. For children who like spicy food, the probability of intelligent child is 61%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.61
0.61 - 0.32 = 0.29
0.29 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 31%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 34%. For children who like spicy food and with low parental social status, the probability of intelligent child is 59%. For children who like spicy food and with high parental social status, the probability of intelligent child is 62%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 31%. For children who do not like spicy food and confounder active, the probability of high parental social status is 34%. For children who like spicy food and confounder inactive, the probability of high parental social status is 62%. For children who like spicy food and confounder active, the probability of high parental social status is 69%. The overall probability of confounder active is 44%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.34
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.62
P(V3=1 | X=0, V2=0) = 0.31
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.62
P(V3=1 | X=1, V2=1) = 0.69
P(V2=1) = 0.44
0.44 * (0.62 - 0.59) * 0.34 + 0.56 * (0.34 - 0.31) * 0.62 = 0.28
0.28 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 31%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 34%. For children who like spicy food and with low parental social status, the probability of intelligent child is 59%. For children who like spicy food and with high parental social status, the probability of intelligent child is 62%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 31%. For children who do not like spicy food and confounder active, the probability of high parental social status is 34%. For children who like spicy food and confounder inactive, the probability of high parental social status is 62%. For children who like spicy food and confounder active, the probability of high parental social status is 69%. The overall probability of confounder active is 44%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.34
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.62
P(V3=1 | X=0, V2=0) = 0.31
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.62
P(V3=1 | X=1, V2=1) = 0.69
P(V2=1) = 0.44
0.44 * (0.62 - 0.59) * 0.34 + 0.56 * (0.34 - 0.31) * 0.62 = 0.28
0.28 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 28%. For children who like spicy food, the probability of intelligent child is 46%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.46
0.46 - 0.28 = 0.18
0.18 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 28%. For children who like spicy food, the probability of intelligent child is 46%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.46
0.46 - 0.28 = 0.18
0.18 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7913,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 28%. For children who like spicy food, the probability of intelligent child is 46%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.46
0.46 - 0.28 = 0.18
0.18 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 37%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 3%. For children who like spicy food and with low parental social status, the probability of intelligent child is 65%. For children who like spicy food and with high parental social status, the probability of intelligent child is 35%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 25%. For children who do not like spicy food and confounder active, the probability of high parental social status is 29%. For children who like spicy food and confounder inactive, the probability of high parental social status is 59%. For children who like spicy food and confounder active, the probability of high parental social status is 66%. The overall probability of confounder active is 44%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.35
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.66
P(V2=1) = 0.44
0.44 * 0.03 * (0.66 - 0.59)+ 0.56 * 0.03 * (0.29 - 0.25)= -0.12
-0.12 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 37%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 3%. For children who like spicy food and with low parental social status, the probability of intelligent child is 65%. For children who like spicy food and with high parental social status, the probability of intelligent child is 35%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 25%. For children who do not like spicy food and confounder active, the probability of high parental social status is 29%. For children who like spicy food and confounder inactive, the probability of high parental social status is 59%. For children who like spicy food and confounder active, the probability of high parental social status is 66%. The overall probability of confounder active is 44%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.35
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.66
P(V2=1) = 0.44
0.44 * 0.03 * (0.66 - 0.59)+ 0.56 * 0.03 * (0.29 - 0.25)= -0.12
-0.12 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7916,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 37%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 3%. For children who like spicy food and with low parental social status, the probability of intelligent child is 65%. For children who like spicy food and with high parental social status, the probability of intelligent child is 35%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 25%. For children who do not like spicy food and confounder active, the probability of high parental social status is 29%. For children who like spicy food and confounder inactive, the probability of high parental social status is 59%. For children who like spicy food and confounder active, the probability of high parental social status is 66%. The overall probability of confounder active is 44%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.35
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.66
P(V2=1) = 0.44
0.44 * (0.35 - 0.65) * 0.29 + 0.56 * (0.03 - 0.37) * 0.59 = 0.29
0.29 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7923,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 6%. For children who like spicy food, the probability of intelligent child is 44%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.44
0.44 - 0.06 = 0.38
0.38 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 6%. For children who like spicy food, the probability of intelligent child is 44%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.44
0.44 - 0.06 = 0.38
0.38 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7929,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 5%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 6%. For children who like spicy food and with low parental social status, the probability of intelligent child is 37%. For children who like spicy food and with high parental social status, the probability of intelligent child is 52%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 67%. For children who do not like spicy food and confounder active, the probability of high parental social status is 38%. For children who like spicy food and confounder inactive, the probability of high parental social status is 51%. For children who like spicy food and confounder active, the probability of high parental social status is 52%. The overall probability of confounder active is 49%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.05
P(Y=1 | X=0, V3=1) = 0.06
P(Y=1 | X=1, V3=0) = 0.37
P(Y=1 | X=1, V3=1) = 0.52
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.52
P(V2=1) = 0.49
0.49 * 0.06 * (0.52 - 0.51)+ 0.51 * 0.06 * (0.38 - 0.67)= -0.00
0.00 = 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7932,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 59%. For children who do not like spicy food, the probability of intelligent child is 6%. For children who like spicy food, the probability of intelligent child is 44%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.06
P(Y=1 | X=1) = 0.44
0.59*0.44 - 0.41*0.06 = 0.28
0.28 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
7934,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 59%. The probability of not liking spicy food and intelligent child is 2%. The probability of liking spicy food and intelligent child is 26%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.26
0.26/0.59 - 0.02/0.41 = 0.39
0.39 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look directly at how liking spicy food correlates with child's intelligence in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 40%. For children who like spicy food, the probability of intelligent child is 84%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.84
0.84 - 0.40 = 0.43
0.43 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 40%. For children who like spicy food, the probability of intelligent child is 84%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.84
0.84 - 0.40 = 0.43
0.43 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 40%. For children who like spicy food, the probability of intelligent child is 84%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.84
0.84 - 0.40 = 0.43
0.43 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 42%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 41%. For children who like spicy food and with low parental social status, the probability of intelligent child is 79%. For children who like spicy food and with high parental social status, the probability of intelligent child is 90%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 74%. For children who do not like spicy food and confounder active, the probability of high parental social status is 87%. For children who like spicy food and confounder inactive, the probability of high parental social status is 34%. For children who like spicy food and confounder active, the probability of high parental social status is 40%. The overall probability of confounder active is 59%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.90
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.87
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.40
P(V2=1) = 0.59
0.59 * (0.90 - 0.79) * 0.87 + 0.41 * (0.41 - 0.42) * 0.34 = 0.48
0.48 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 39%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 35%. For children who like spicy food and with low parental social status, the probability of intelligent child is 65%. For children who like spicy food and with high parental social status, the probability of intelligent child is 68%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 39%. For children who do not like spicy food and confounder active, the probability of high parental social status is 48%. For children who like spicy food and confounder inactive, the probability of high parental social status is 79%. For children who like spicy food and confounder active, the probability of high parental social status is 82%. The overall probability of confounder active is 47%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.39
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.82
P(V2=1) = 0.47
0.47 * 0.35 * (0.82 - 0.79)+ 0.53 * 0.35 * (0.48 - 0.39)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 39%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 35%. For children who like spicy food and with low parental social status, the probability of intelligent child is 65%. For children who like spicy food and with high parental social status, the probability of intelligent child is 68%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 39%. For children who do not like spicy food and confounder active, the probability of high parental social status is 48%. For children who like spicy food and confounder inactive, the probability of high parental social status is 79%. For children who like spicy food and confounder active, the probability of high parental social status is 82%. The overall probability of confounder active is 47%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.39
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.82
P(V2=1) = 0.47
0.47 * 0.35 * (0.82 - 0.79)+ 0.53 * 0.35 * (0.48 - 0.39)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 51%. The probability of not liking spicy food and intelligent child is 18%. The probability of liking spicy food and intelligent child is 34%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.34
0.34/0.51 - 0.18/0.49 = 0.31
0.31 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. The overall probability of liking spicy food is 51%. The probability of not liking spicy food and intelligent child is 18%. The probability of liking spicy food and intelligent child is 34%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.34
0.34/0.51 - 0.18/0.49 = 0.31
0.31 > 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
7964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. Method 1: We look at how liking spicy food correlates with child's intelligence case by case according to parents' social status. Method 2: We look directly at how liking spicy food correlates with child's intelligence in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
7966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 31%. For children who like spicy food, the probability of intelligent child is 62%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.62
0.62 - 0.31 = 0.31
0.31 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 31%. For children who like spicy food, the probability of intelligent child is 62%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.62
0.62 - 0.31 = 0.31
0.31 > 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food, the probability of intelligent child is 31%. For children who like spicy food, the probability of intelligent child is 62%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.62
0.62 - 0.31 = 0.31
0.31 > 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
7971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 32%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 31%. For children who like spicy food and with low parental social status, the probability of intelligent child is 58%. For children who like spicy food and with high parental social status, the probability of intelligent child is 68%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 75%. For children who do not like spicy food and confounder active, the probability of high parental social status is 71%. For children who like spicy food and confounder inactive, the probability of high parental social status is 34%. For children who like spicy food and confounder active, the probability of high parental social status is 40%. The overall probability of confounder active is 46%.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.71
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.40
P(V2=1) = 0.46
0.46 * 0.31 * (0.40 - 0.34)+ 0.54 * 0.31 * (0.71 - 0.75)= 0.00
0.00 = 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
7972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. For children who do not like spicy food and with low parental social status, the probability of intelligent child is 32%. For children who do not like spicy food and with high parental social status, the probability of intelligent child is 31%. For children who like spicy food and with low parental social status, the probability of intelligent child is 58%. For children who like spicy food and with high parental social status, the probability of intelligent child is 68%. For children who do not like spicy food and confounder inactive, the probability of high parental social status is 75%. For children who do not like spicy food and confounder active, the probability of high parental social status is 71%. For children who like spicy food and confounder inactive, the probability of high parental social status is 34%. For children who like spicy food and confounder active, the probability of high parental social status is 40%. The overall probability of confounder active is 46%.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.71
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.40
P(V2=1) = 0.46
0.46 * (0.68 - 0.58) * 0.71 + 0.54 * (0.31 - 0.32) * 0.34 = 0.35
0.35 > 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
7986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 45%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 72%. For smokers and are lazy, the probability of being lactose intolerant is 25%. For smokers and are hard-working, the probability of being lactose intolerant is 46%. For nonsmokers, the probability of being hard-working is 22%. For smokers, the probability of being hard-working is 95%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.45
P(Y=1 | X=0, V2=1) = 0.72
P(Y=1 | X=1, V2=0) = 0.25
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.22
P(V2=1 | X=1) = 0.95
0.22 * (0.46 - 0.25) + 0.95 * (0.72 - 0.45) = -0.22
-0.22 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
7989,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 7%. For nonsmokers, the probability of being lactose intolerant is 51%. For smokers, the probability of being lactose intolerant is 45%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.45
0.07*0.45 - 0.93*0.51 = 0.51
0.51 > 0",mediation,neg_mediation,1,marginal,P(Y)
7990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 7%. The probability of nonsmoking and being lactose intolerant is 48%. The probability of smoking and being lactose intolerant is 3%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.03
0.03/0.07 - 0.48/0.93 = -0.06
-0.06 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
7994,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 65%. For smokers, the probability of being lactose intolerant is 51%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.51
0.51 - 0.65 = -0.14
-0.14 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 65%. For smokers, the probability of being lactose intolerant is 51%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.51
0.51 - 0.65 = -0.14
-0.14 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
7999,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 36%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 74%. For smokers and are lazy, the probability of being lactose intolerant is 46%. For smokers and are hard-working, the probability of being lactose intolerant is 69%. For nonsmokers, the probability of being hard-working is 78%. For smokers, the probability of being hard-working is 21%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.74
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.69
P(V2=1 | X=0) = 0.78
P(V2=1 | X=1) = 0.21
0.21 * (0.74 - 0.36)+ 0.78 * (0.69 - 0.46)= -0.21
-0.21 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 36%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 74%. For smokers and are lazy, the probability of being lactose intolerant is 46%. For smokers and are hard-working, the probability of being lactose intolerant is 69%. For nonsmokers, the probability of being hard-working is 78%. For smokers, the probability of being hard-working is 21%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.74
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.69
P(V2=1 | X=0) = 0.78
P(V2=1 | X=1) = 0.21
0.78 * (0.69 - 0.46) + 0.21 * (0.74 - 0.36) = -0.01
-0.01 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 36%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 74%. For smokers and are lazy, the probability of being lactose intolerant is 46%. For smokers and are hard-working, the probability of being lactose intolerant is 69%. For nonsmokers, the probability of being hard-working is 78%. For smokers, the probability of being hard-working is 21%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.74
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.69
P(V2=1 | X=0) = 0.78
P(V2=1 | X=1) = 0.21
0.78 * (0.69 - 0.46) + 0.21 * (0.74 - 0.36) = -0.01
-0.01 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8006,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 5%. For nonsmokers, the probability of being lactose intolerant is 78%. For smokers, the probability of being lactose intolerant is 46%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.46
0.05*0.46 - 0.95*0.78 = 0.75
0.75 > 0",mediation,neg_mediation,1,marginal,P(Y)
8019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 5%. The probability of nonsmoking and being lactose intolerant is 74%. The probability of smoking and being lactose intolerant is 2%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.74
P(Y=1, X=1=1) = 0.02
0.02/0.05 - 0.74/0.95 = -0.32
-0.32 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8022,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 89%. For smokers, the probability of being lactose intolerant is 29%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.29
0.29 - 0.89 = -0.60
-0.60 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 89%. For smokers, the probability of being lactose intolerant is 29%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.29
0.29 - 0.89 = -0.60
-0.60 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8028,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 53%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 95%. For smokers and are lazy, the probability of being lactose intolerant is 26%. For smokers and are hard-working, the probability of being lactose intolerant is 63%. For nonsmokers, the probability of being hard-working is 86%. For smokers, the probability of being hard-working is 7%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.95
P(Y=1 | X=1, V2=0) = 0.26
P(Y=1 | X=1, V2=1) = 0.63
P(V2=1 | X=0) = 0.86
P(V2=1 | X=1) = 0.07
0.86 * (0.63 - 0.26) + 0.07 * (0.95 - 0.53) = -0.31
-0.31 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8033,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 8%. The probability of nonsmoking and being lactose intolerant is 82%. The probability of smoking and being lactose intolerant is 2%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.82
P(Y=1, X=1=1) = 0.02
0.02/0.08 - 0.82/0.92 = -0.60
-0.60 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 71%. For smokers, the probability of being lactose intolerant is 34%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.34
0.34 - 0.71 = -0.38
-0.38 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 71%. For smokers, the probability of being lactose intolerant is 34%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.34
0.34 - 0.71 = -0.38
-0.38 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 47%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 84%. For smokers and are lazy, the probability of being lactose intolerant is 20%. For smokers and are hard-working, the probability of being lactose intolerant is 58%. For nonsmokers, the probability of being hard-working is 66%. For smokers, the probability of being hard-working is 36%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.58
P(V2=1 | X=0) = 0.66
P(V2=1 | X=1) = 0.36
0.36 * (0.84 - 0.47)+ 0.66 * (0.58 - 0.20)= -0.11
-0.11 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 47%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 84%. For smokers and are lazy, the probability of being lactose intolerant is 20%. For smokers and are hard-working, the probability of being lactose intolerant is 58%. For nonsmokers, the probability of being hard-working is 66%. For smokers, the probability of being hard-working is 36%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.58
P(V2=1 | X=0) = 0.66
P(V2=1 | X=1) = 0.36
0.66 * (0.58 - 0.20) + 0.36 * (0.84 - 0.47) = -0.26
-0.26 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 15%. The probability of nonsmoking and being lactose intolerant is 61%. The probability of smoking and being lactose intolerant is 5%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.05
0.05/0.15 - 0.61/0.85 = -0.38
-0.38 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 31%. For smokers, the probability of being lactose intolerant is 59%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.59
0.59 - 0.31 = 0.28
0.28 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 15%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 53%. For smokers and are lazy, the probability of being lactose intolerant is 30%. For smokers and are hard-working, the probability of being lactose intolerant is 72%. For nonsmokers, the probability of being hard-working is 42%. For smokers, the probability of being hard-working is 70%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.53
P(Y=1 | X=1, V2=0) = 0.30
P(Y=1 | X=1, V2=1) = 0.72
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.70
0.70 * (0.53 - 0.15)+ 0.42 * (0.72 - 0.30)= 0.11
0.11 > 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 15%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 53%. For smokers and are lazy, the probability of being lactose intolerant is 30%. For smokers and are hard-working, the probability of being lactose intolerant is 72%. For nonsmokers, the probability of being hard-working is 42%. For smokers, the probability of being hard-working is 70%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.15
P(Y=1 | X=0, V2=1) = 0.53
P(Y=1 | X=1, V2=0) = 0.30
P(Y=1 | X=1, V2=1) = 0.72
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.70
0.42 * (0.72 - 0.30) + 0.70 * (0.53 - 0.15) = 0.16
0.16 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 3%. The probability of nonsmoking and being lactose intolerant is 30%. The probability of smoking and being lactose intolerant is 2%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.30/0.97 = 0.28
0.28 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
8061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 3%. The probability of nonsmoking and being lactose intolerant is 30%. The probability of smoking and being lactose intolerant is 2%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.30/0.97 = 0.28
0.28 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
8063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 53%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 80%. For smokers and are lazy, the probability of being lactose intolerant is 39%. For smokers and are hard-working, the probability of being lactose intolerant is 87%. For nonsmokers, the probability of being hard-working is 56%. For smokers, the probability of being hard-working is 9%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.80
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.87
P(V2=1 | X=0) = 0.56
P(V2=1 | X=1) = 0.09
0.56 * (0.87 - 0.39) + 0.09 * (0.80 - 0.53) = -0.02
-0.02 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 2%. For nonsmokers, the probability of being lactose intolerant is 68%. For smokers, the probability of being lactose intolerant is 43%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.43
0.02*0.43 - 0.98*0.68 = 0.68
0.68 > 0",mediation,neg_mediation,1,marginal,P(Y)
8073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 2%. For nonsmokers, the probability of being lactose intolerant is 68%. For smokers, the probability of being lactose intolerant is 43%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.43
0.02*0.43 - 0.98*0.68 = 0.68
0.68 > 0",mediation,neg_mediation,1,marginal,P(Y)
8074,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 2%. The probability of nonsmoking and being lactose intolerant is 67%. The probability of smoking and being lactose intolerant is 1%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.67
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.67/0.98 = -0.25
-0.25 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 50%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 90%. For smokers and are lazy, the probability of being lactose intolerant is 29%. For smokers and are hard-working, the probability of being lactose intolerant is 64%. For nonsmokers, the probability of being hard-working is 70%. For smokers, the probability of being hard-working is 10%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.50
P(Y=1 | X=0, V2=1) = 0.90
P(Y=1 | X=1, V2=0) = 0.29
P(Y=1 | X=1, V2=1) = 0.64
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.10
0.10 * (0.90 - 0.50)+ 0.70 * (0.64 - 0.29)= -0.24
-0.24 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8093,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 68%. For smokers, the probability of being lactose intolerant is 31%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.31
0.31 - 0.68 = -0.37
-0.37 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 49%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 75%. For smokers and are lazy, the probability of being lactose intolerant is 16%. For smokers and are hard-working, the probability of being lactose intolerant is 47%. For nonsmokers, the probability of being hard-working is 75%. For smokers, the probability of being hard-working is 49%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.49
P(Y=1 | X=0, V2=1) = 0.75
P(Y=1 | X=1, V2=0) = 0.16
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.49
0.49 * (0.75 - 0.49)+ 0.75 * (0.47 - 0.16)= -0.07
-0.07 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8100,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 14%. For nonsmokers, the probability of being lactose intolerant is 68%. For smokers, the probability of being lactose intolerant is 31%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.31
0.14*0.31 - 0.86*0.68 = 0.63
0.63 > 0",mediation,neg_mediation,1,marginal,P(Y)
8105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 66%. For smokers, the probability of being lactose intolerant is 36%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.36
0.36 - 0.66 = -0.30
-0.30 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 66%. For smokers, the probability of being lactose intolerant is 36%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.36
0.36 - 0.66 = -0.30
-0.30 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 13%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 96%. For smokers and are lazy, the probability of being lactose intolerant is 3%. For smokers and are hard-working, the probability of being lactose intolerant is 69%. For nonsmokers, the probability of being hard-working is 64%. For smokers, the probability of being hard-working is 49%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.13
P(Y=1 | X=0, V2=1) = 0.96
P(Y=1 | X=1, V2=0) = 0.03
P(Y=1 | X=1, V2=1) = 0.69
P(V2=1 | X=0) = 0.64
P(V2=1 | X=1) = 0.49
0.64 * (0.69 - 0.03) + 0.49 * (0.96 - 0.13) = -0.21
-0.21 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 19%. For nonsmokers, the probability of being lactose intolerant is 66%. For smokers, the probability of being lactose intolerant is 36%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.36
0.19*0.36 - 0.81*0.66 = 0.59
0.59 > 0",mediation,neg_mediation,1,marginal,P(Y)
8117,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 19%. The probability of nonsmoking and being lactose intolerant is 53%. The probability of smoking and being lactose intolerant is 7%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.07
0.07/0.19 - 0.53/0.81 = -0.30
-0.30 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8129,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 10%. For nonsmokers, the probability of being lactose intolerant is 52%. For smokers, the probability of being lactose intolerant is 28%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.28
0.10*0.28 - 0.90*0.52 = 0.51
0.51 > 0",mediation,neg_mediation,1,marginal,P(Y)
8136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 76%. For smokers, the probability of being lactose intolerant is 22%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.22
0.22 - 0.76 = -0.54
-0.54 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 76%. For smokers, the probability of being lactose intolerant is 22%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.22
0.22 - 0.76 = -0.54
-0.54 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 53%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 85%. For smokers and are lazy, the probability of being lactose intolerant is 21%. For smokers and are hard-working, the probability of being lactose intolerant is 51%. For nonsmokers, the probability of being hard-working is 72%. For smokers, the probability of being hard-working is 1%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.85
P(Y=1 | X=1, V2=0) = 0.21
P(Y=1 | X=1, V2=1) = 0.51
P(V2=1 | X=0) = 0.72
P(V2=1 | X=1) = 0.01
0.01 * (0.85 - 0.53)+ 0.72 * (0.51 - 0.21)= -0.23
-0.23 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 9%. For nonsmokers, the probability of being lactose intolerant is 76%. For smokers, the probability of being lactose intolerant is 22%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.22
0.09*0.22 - 0.91*0.76 = 0.71
0.71 > 0",mediation,neg_mediation,1,marginal,P(Y)
8145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 9%. The probability of nonsmoking and being lactose intolerant is 69%. The probability of smoking and being lactose intolerant is 2%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.69
P(Y=1, X=1=1) = 0.02
0.02/0.09 - 0.69/0.91 = -0.54
-0.54 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 53%. For smokers, the probability of being lactose intolerant is 27%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.27
0.27 - 0.53 = -0.26
-0.26 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 53%. For smokers, the probability of being lactose intolerant is 27%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.27
0.27 - 0.53 = -0.26
-0.26 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 53%. For smokers, the probability of being lactose intolerant is 27%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.27
0.27 - 0.53 = -0.26
-0.26 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 33%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 72%. For smokers and are lazy, the probability of being lactose intolerant is 5%. For smokers and are hard-working, the probability of being lactose intolerant is 52%. For nonsmokers, the probability of being hard-working is 51%. For smokers, the probability of being hard-working is 46%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.33
P(Y=1 | X=0, V2=1) = 0.72
P(Y=1 | X=1, V2=0) = 0.05
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.51
P(V2=1 | X=1) = 0.46
0.46 * (0.72 - 0.33)+ 0.51 * (0.52 - 0.05)= -0.02
-0.02 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 3%. The probability of nonsmoking and being lactose intolerant is 52%. The probability of smoking and being lactose intolerant is 1%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.52/0.97 = -0.26
-0.26 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8160,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8163,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 64%. For smokers, the probability of being lactose intolerant is 19%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.19
0.19 - 0.64 = -0.45
-0.45 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 0%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 66%. For smokers and are lazy, the probability of being lactose intolerant is 14%. For smokers and are hard-working, the probability of being lactose intolerant is 43%. For nonsmokers, the probability of being hard-working is 97%. For smokers, the probability of being hard-working is 18%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.00
P(Y=1 | X=0, V2=1) = 0.66
P(Y=1 | X=1, V2=0) = 0.14
P(Y=1 | X=1, V2=1) = 0.43
P(V2=1 | X=0) = 0.97
P(V2=1 | X=1) = 0.18
0.97 * (0.43 - 0.14) + 0.18 * (0.66 - 0.00) = -0.22
-0.22 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 3%. For nonsmokers, the probability of being lactose intolerant is 64%. For smokers, the probability of being lactose intolerant is 19%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.19
0.03*0.19 - 0.97*0.64 = 0.62
0.62 > 0",mediation,neg_mediation,1,marginal,P(Y)
8177,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 55%. For smokers, the probability of being lactose intolerant is 43%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.43
0.43 - 0.55 = -0.12
-0.12 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 55%. For smokers, the probability of being lactose intolerant is 43%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.43
0.43 - 0.55 = -0.12
-0.12 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 35%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 61%. For smokers and are lazy, the probability of being lactose intolerant is 23%. For smokers and are hard-working, the probability of being lactose intolerant is 60%. For nonsmokers, the probability of being hard-working is 75%. For smokers, the probability of being hard-working is 54%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.35
P(Y=1 | X=0, V2=1) = 0.61
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.60
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.54
0.54 * (0.61 - 0.35)+ 0.75 * (0.60 - 0.23)= -0.06
-0.06 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 5%. For nonsmokers, the probability of being lactose intolerant is 55%. For smokers, the probability of being lactose intolerant is 43%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.43
0.05*0.43 - 0.95*0.55 = 0.54
0.54 > 0",mediation,neg_mediation,1,marginal,P(Y)
8188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 86%. For smokers, the probability of being lactose intolerant is 26%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.26
0.26 - 0.86 = -0.60
-0.60 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 86%. For smokers, the probability of being lactose intolerant is 26%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.26
0.26 - 0.86 = -0.60
-0.60 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 86%. For smokers, the probability of being lactose intolerant is 26%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.26
0.26 - 0.86 = -0.60
-0.60 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8195,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 51%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 89%. For smokers and are lazy, the probability of being lactose intolerant is 11%. For smokers and are hard-working, the probability of being lactose intolerant is 34%. For nonsmokers, the probability of being hard-working is 91%. For smokers, the probability of being hard-working is 63%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.89
P(Y=1 | X=1, V2=0) = 0.11
P(Y=1 | X=1, V2=1) = 0.34
P(V2=1 | X=0) = 0.91
P(V2=1 | X=1) = 0.63
0.63 * (0.89 - 0.51)+ 0.91 * (0.34 - 0.11)= -0.10
-0.10 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 51%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 89%. For smokers and are lazy, the probability of being lactose intolerant is 11%. For smokers and are hard-working, the probability of being lactose intolerant is 34%. For nonsmokers, the probability of being hard-working is 91%. For smokers, the probability of being hard-working is 63%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.89
P(Y=1 | X=1, V2=0) = 0.11
P(Y=1 | X=1, V2=1) = 0.34
P(V2=1 | X=0) = 0.91
P(V2=1 | X=1) = 0.63
0.91 * (0.34 - 0.11) + 0.63 * (0.89 - 0.51) = -0.54
-0.54 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8197,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 51%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 89%. For smokers and are lazy, the probability of being lactose intolerant is 11%. For smokers and are hard-working, the probability of being lactose intolerant is 34%. For nonsmokers, the probability of being hard-working is 91%. For smokers, the probability of being hard-working is 63%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.89
P(Y=1 | X=1, V2=0) = 0.11
P(Y=1 | X=1, V2=1) = 0.34
P(V2=1 | X=0) = 0.91
P(V2=1 | X=1) = 0.63
0.91 * (0.34 - 0.11) + 0.63 * (0.89 - 0.51) = -0.54
-0.54 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 11%. The probability of nonsmoking and being lactose intolerant is 76%. The probability of smoking and being lactose intolerant is 3%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.03
0.03/0.11 - 0.76/0.89 = -0.60
-0.60 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 11%. The probability of nonsmoking and being lactose intolerant is 76%. The probability of smoking and being lactose intolerant is 3%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.03
0.03/0.11 - 0.76/0.89 = -0.60
-0.60 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8202,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8203,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 58%. For smokers, the probability of being lactose intolerant is 48%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.48
0.48 - 0.58 = -0.10
-0.10 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 58%. For smokers, the probability of being lactose intolerant is 48%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.48
0.48 - 0.58 = -0.10
-0.10 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8209,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 38%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 87%. For smokers and are lazy, the probability of being lactose intolerant is 2%. For smokers and are hard-working, the probability of being lactose intolerant is 52%. For nonsmokers, the probability of being hard-working is 41%. For smokers, the probability of being hard-working is 92%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.87
P(Y=1 | X=1, V2=0) = 0.02
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.92
0.92 * (0.87 - 0.38)+ 0.41 * (0.52 - 0.02)= 0.25
0.25 > 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 38%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 87%. For smokers and are lazy, the probability of being lactose intolerant is 2%. For smokers and are hard-working, the probability of being lactose intolerant is 52%. For nonsmokers, the probability of being hard-working is 41%. For smokers, the probability of being hard-working is 92%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.87
P(Y=1 | X=1, V2=0) = 0.02
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.92
0.41 * (0.52 - 0.02) + 0.92 * (0.87 - 0.38) = -0.35
-0.35 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 7%. The probability of nonsmoking and being lactose intolerant is 54%. The probability of smoking and being lactose intolerant is 3%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.03
0.03/0.07 - 0.54/0.93 = -0.10
-0.10 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 44%. For smokers, the probability of being lactose intolerant is 62%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.62
0.62 - 0.44 = 0.18
0.18 > 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 44%. For smokers, the probability of being lactose intolerant is 62%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.62
0.62 - 0.44 = 0.18
0.18 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 26%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 66%. For smokers and are lazy, the probability of being lactose intolerant is 9%. For smokers and are hard-working, the probability of being lactose intolerant is 62%. For nonsmokers, the probability of being hard-working is 44%. For smokers, the probability of being hard-working is 100%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.66
P(Y=1 | X=1, V2=0) = 0.09
P(Y=1 | X=1, V2=1) = 0.62
P(V2=1 | X=0) = 0.44
P(V2=1 | X=1) = 1.00
1.00 * (0.66 - 0.26)+ 0.44 * (0.62 - 0.09)= 0.22
0.22 > 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 26%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 66%. For smokers and are lazy, the probability of being lactose intolerant is 9%. For smokers and are hard-working, the probability of being lactose intolerant is 62%. For nonsmokers, the probability of being hard-working is 44%. For smokers, the probability of being hard-working is 100%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.66
P(Y=1 | X=1, V2=0) = 0.09
P(Y=1 | X=1, V2=1) = 0.62
P(V2=1 | X=0) = 0.44
P(V2=1 | X=1) = 1.00
0.44 * (0.62 - 0.09) + 1.00 * (0.66 - 0.26) = -0.11
-0.11 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 26%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 66%. For smokers and are lazy, the probability of being lactose intolerant is 9%. For smokers and are hard-working, the probability of being lactose intolerant is 62%. For nonsmokers, the probability of being hard-working is 44%. For smokers, the probability of being hard-working is 100%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.66
P(Y=1 | X=1, V2=0) = 0.09
P(Y=1 | X=1, V2=1) = 0.62
P(V2=1 | X=0) = 0.44
P(V2=1 | X=1) = 1.00
0.44 * (0.62 - 0.09) + 1.00 * (0.66 - 0.26) = -0.11
-0.11 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 8%. For nonsmokers, the probability of being lactose intolerant is 44%. For smokers, the probability of being lactose intolerant is 62%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.62
0.08*0.62 - 0.92*0.44 = 0.44
0.44 > 0",mediation,neg_mediation,1,marginal,P(Y)
8229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 8%. The probability of nonsmoking and being lactose intolerant is 40%. The probability of smoking and being lactose intolerant is 5%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.05
0.05/0.08 - 0.40/0.92 = 0.18
0.18 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
8232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 45%. For smokers, the probability of being lactose intolerant is 42%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.42
0.42 - 0.45 = -0.02
-0.02 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 45%. For smokers, the probability of being lactose intolerant is 42%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.42
0.42 - 0.45 = -0.02
-0.02 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 19%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 56%. For smokers and are lazy, the probability of being lactose intolerant is 34%. For smokers and are hard-working, the probability of being lactose intolerant is 68%. For nonsmokers, the probability of being hard-working is 69%. For smokers, the probability of being hard-working is 24%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.19
P(Y=1 | X=0, V2=1) = 0.56
P(Y=1 | X=1, V2=0) = 0.34
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.69
P(V2=1 | X=1) = 0.24
0.24 * (0.56 - 0.19)+ 0.69 * (0.68 - 0.34)= -0.17
-0.17 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 19%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 56%. For smokers and are lazy, the probability of being lactose intolerant is 34%. For smokers and are hard-working, the probability of being lactose intolerant is 68%. For nonsmokers, the probability of being hard-working is 69%. For smokers, the probability of being hard-working is 24%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.19
P(Y=1 | X=0, V2=1) = 0.56
P(Y=1 | X=1, V2=0) = 0.34
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.69
P(V2=1 | X=1) = 0.24
0.69 * (0.68 - 0.34) + 0.24 * (0.56 - 0.19) = 0.13
0.13 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 12%. The probability of nonsmoking and being lactose intolerant is 39%. The probability of smoking and being lactose intolerant is 5%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.05
0.05/0.12 - 0.39/0.88 = -0.02
-0.02 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8248,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 84%. For smokers, the probability of being lactose intolerant is 32%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.32
0.32 - 0.84 = -0.52
-0.52 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 68%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 98%. For smokers and are lazy, the probability of being lactose intolerant is 29%. For smokers and are hard-working, the probability of being lactose intolerant is 55%. For nonsmokers, the probability of being hard-working is 54%. For smokers, the probability of being hard-working is 11%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.68
P(Y=1 | X=0, V2=1) = 0.98
P(Y=1 | X=1, V2=0) = 0.29
P(Y=1 | X=1, V2=1) = 0.55
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.11
0.11 * (0.98 - 0.68)+ 0.54 * (0.55 - 0.29)= -0.13
-0.13 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 68%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 98%. For smokers and are lazy, the probability of being lactose intolerant is 29%. For smokers and are hard-working, the probability of being lactose intolerant is 55%. For nonsmokers, the probability of being hard-working is 54%. For smokers, the probability of being hard-working is 11%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.68
P(Y=1 | X=0, V2=1) = 0.98
P(Y=1 | X=1, V2=0) = 0.29
P(Y=1 | X=1, V2=1) = 0.55
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.11
0.54 * (0.55 - 0.29) + 0.11 * (0.98 - 0.68) = -0.41
-0.41 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 68%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 98%. For smokers and are lazy, the probability of being lactose intolerant is 29%. For smokers and are hard-working, the probability of being lactose intolerant is 55%. For nonsmokers, the probability of being hard-working is 54%. For smokers, the probability of being hard-working is 11%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.68
P(Y=1 | X=0, V2=1) = 0.98
P(Y=1 | X=1, V2=0) = 0.29
P(Y=1 | X=1, V2=1) = 0.55
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.11
0.54 * (0.55 - 0.29) + 0.11 * (0.98 - 0.68) = -0.41
-0.41 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 18%. The probability of nonsmoking and being lactose intolerant is 69%. The probability of smoking and being lactose intolerant is 6%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.69
P(Y=1, X=1=1) = 0.06
0.06/0.18 - 0.69/0.82 = -0.52
-0.52 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 63%. For smokers, the probability of being lactose intolerant is 42%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.42
0.42 - 0.63 = -0.21
-0.21 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 47%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 88%. For smokers and are lazy, the probability of being lactose intolerant is 23%. For smokers and are hard-working, the probability of being lactose intolerant is 54%. For nonsmokers, the probability of being hard-working is 40%. For smokers, the probability of being hard-working is 61%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.88
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.54
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.61
0.61 * (0.88 - 0.47)+ 0.40 * (0.54 - 0.23)= 0.08
0.08 > 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 47%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 88%. For smokers and are lazy, the probability of being lactose intolerant is 23%. For smokers and are hard-working, the probability of being lactose intolerant is 54%. For nonsmokers, the probability of being hard-working is 40%. For smokers, the probability of being hard-working is 61%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.88
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.54
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.61
0.40 * (0.54 - 0.23) + 0.61 * (0.88 - 0.47) = -0.28
-0.28 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 3%. The probability of nonsmoking and being lactose intolerant is 61%. The probability of smoking and being lactose intolerant is 1%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.61/0.97 = -0.21
-0.21 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 52%. For smokers, the probability of being lactose intolerant is 43%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.43
0.43 - 0.52 = -0.09
-0.09 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 52%. For smokers, the probability of being lactose intolerant is 43%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.43
0.43 - 0.52 = -0.09
-0.09 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8278,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 38%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 63%. For smokers and are lazy, the probability of being lactose intolerant is 27%. For smokers and are hard-working, the probability of being lactose intolerant is 59%. For nonsmokers, the probability of being hard-working is 53%. For smokers, the probability of being hard-working is 51%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.27
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.53
P(V2=1 | X=1) = 0.51
0.51 * (0.63 - 0.38)+ 0.53 * (0.59 - 0.27)= -0.01
-0.01 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look directly at how smoking correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 79%. For smokers, the probability of being lactose intolerant is 48%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.48
0.48 - 0.79 = -0.31
-0.31 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 79%. For smokers, the probability of being lactose intolerant is 48%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.48
0.48 - 0.79 = -0.31
-0.31 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 79%. For smokers, the probability of being lactose intolerant is 48%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.48
0.48 - 0.79 = -0.31
-0.31 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 79%. For smokers, the probability of being lactose intolerant is 48%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.48
0.48 - 0.79 = -0.31
-0.31 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 5%. The probability of nonsmoking and being lactose intolerant is 75%. The probability of smoking and being lactose intolerant is 2%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.75
P(Y=1, X=1=1) = 0.02
0.02/0.05 - 0.75/0.95 = -0.31
-0.31 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 27%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 94%. For smokers and are lazy, the probability of being lactose intolerant is 6%. For smokers and are hard-working, the probability of being lactose intolerant is 67%. For nonsmokers, the probability of being hard-working is 50%. For smokers, the probability of being hard-working is 14%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.27
P(Y=1 | X=0, V2=1) = 0.94
P(Y=1 | X=1, V2=0) = 0.06
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.14
0.14 * (0.94 - 0.27)+ 0.50 * (0.67 - 0.06)= -0.24
-0.24 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 27%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 94%. For smokers and are lazy, the probability of being lactose intolerant is 6%. For smokers and are hard-working, the probability of being lactose intolerant is 67%. For nonsmokers, the probability of being hard-working is 50%. For smokers, the probability of being hard-working is 14%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.27
P(Y=1 | X=0, V2=1) = 0.94
P(Y=1 | X=1, V2=0) = 0.06
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.14
0.50 * (0.67 - 0.06) + 0.14 * (0.94 - 0.27) = -0.24
-0.24 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8310,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 17%. For nonsmokers, the probability of being lactose intolerant is 60%. For smokers, the probability of being lactose intolerant is 15%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.15
0.17*0.15 - 0.83*0.60 = 0.52
0.52 > 0",mediation,neg_mediation,1,marginal,P(Y)
8312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 17%. The probability of nonsmoking and being lactose intolerant is 50%. The probability of smoking and being lactose intolerant is 2%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.02
0.02/0.17 - 0.50/0.83 = -0.46
-0.46 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 17%. The probability of nonsmoking and being lactose intolerant is 50%. The probability of smoking and being lactose intolerant is 2%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.02
0.02/0.17 - 0.50/0.83 = -0.46
-0.46 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 82%. For smokers, the probability of being lactose intolerant is 42%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.42
0.42 - 0.82 = -0.40
-0.40 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 82%. For smokers, the probability of being lactose intolerant is 42%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.42
0.42 - 0.82 = -0.40
-0.40 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8323,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 57%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 95%. For smokers and are lazy, the probability of being lactose intolerant is 34%. For smokers and are hard-working, the probability of being lactose intolerant is 63%. For nonsmokers, the probability of being hard-working is 65%. For smokers, the probability of being hard-working is 28%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.57
P(Y=1 | X=0, V2=1) = 0.95
P(Y=1 | X=1, V2=0) = 0.34
P(Y=1 | X=1, V2=1) = 0.63
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.28
0.65 * (0.63 - 0.34) + 0.28 * (0.95 - 0.57) = -0.29
-0.29 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 9%. For nonsmokers, the probability of being lactose intolerant is 82%. For smokers, the probability of being lactose intolerant is 42%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.42
0.09*0.42 - 0.91*0.82 = 0.78
0.78 > 0",mediation,neg_mediation,1,marginal,P(Y)
8327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 9%. The probability of nonsmoking and being lactose intolerant is 75%. The probability of smoking and being lactose intolerant is 4%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.75
P(Y=1, X=1=1) = 0.04
0.04/0.09 - 0.75/0.91 = -0.40
-0.40 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 36%. For smokers, the probability of being lactose intolerant is 15%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.15
0.15 - 0.36 = -0.22
-0.22 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 36%. For smokers, the probability of being lactose intolerant is 15%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.15
0.15 - 0.36 = -0.22
-0.22 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 36%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 84%. For smokers and are lazy, the probability of being lactose intolerant is 4%. For smokers and are hard-working, the probability of being lactose intolerant is 64%. For nonsmokers, the probability of being hard-working is 0%. For smokers, the probability of being hard-working is 18%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.04
P(Y=1 | X=1, V2=1) = 0.64
P(V2=1 | X=0) = 0.00
P(V2=1 | X=1) = 0.18
0.18 * (0.84 - 0.36)+ 0.00 * (0.64 - 0.04)= 0.08
0.08 > 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8335,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 36%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 84%. For smokers and are lazy, the probability of being lactose intolerant is 4%. For smokers and are hard-working, the probability of being lactose intolerant is 64%. For nonsmokers, the probability of being hard-working is 0%. For smokers, the probability of being hard-working is 18%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.04
P(Y=1 | X=1, V2=1) = 0.64
P(V2=1 | X=0) = 0.00
P(V2=1 | X=1) = 0.18
0.18 * (0.84 - 0.36)+ 0.00 * (0.64 - 0.04)= 0.08
0.08 > 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 36%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 84%. For smokers and are lazy, the probability of being lactose intolerant is 4%. For smokers and are hard-working, the probability of being lactose intolerant is 64%. For nonsmokers, the probability of being hard-working is 0%. For smokers, the probability of being hard-working is 18%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.04
P(Y=1 | X=1, V2=1) = 0.64
P(V2=1 | X=0) = 0.00
P(V2=1 | X=1) = 0.18
0.00 * (0.64 - 0.04) + 0.18 * (0.84 - 0.36) = -0.32
-0.32 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 17%. For nonsmokers, the probability of being lactose intolerant is 36%. For smokers, the probability of being lactose intolerant is 15%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.15
0.17*0.15 - 0.83*0.36 = 0.32
0.32 > 0",mediation,neg_mediation,1,marginal,P(Y)
8341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 17%. The probability of nonsmoking and being lactose intolerant is 30%. The probability of smoking and being lactose intolerant is 3%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.03
0.03/0.17 - 0.30/0.83 = -0.22
-0.22 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 60%. For smokers, the probability of being lactose intolerant is 51%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.51
0.51 - 0.60 = -0.10
-0.10 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 39%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 69%. For smokers and are lazy, the probability of being lactose intolerant is 46%. For smokers and are hard-working, the probability of being lactose intolerant is 74%. For nonsmokers, the probability of being hard-working is 72%. For smokers, the probability of being hard-working is 16%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.39
P(Y=1 | X=0, V2=1) = 0.69
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.74
P(V2=1 | X=0) = 0.72
P(V2=1 | X=1) = 0.16
0.72 * (0.74 - 0.46) + 0.16 * (0.69 - 0.39) = 0.06
0.06 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 10%. For nonsmokers, the probability of being lactose intolerant is 60%. For smokers, the probability of being lactose intolerant is 51%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.51
0.10*0.51 - 0.90*0.60 = 0.59
0.59 > 0",mediation,neg_mediation,1,marginal,P(Y)
8354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 10%. The probability of nonsmoking and being lactose intolerant is 54%. The probability of smoking and being lactose intolerant is 5%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.05
0.05/0.10 - 0.54/0.90 = -0.10
-0.10 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers, the probability of being lactose intolerant is 77%. For smokers, the probability of being lactose intolerant is 37%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.37
0.37 - 0.77 = -0.40
-0.40 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 48%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 80%. For smokers and are lazy, the probability of being lactose intolerant is 26%. For smokers and are hard-working, the probability of being lactose intolerant is 52%. For nonsmokers, the probability of being hard-working is 88%. For smokers, the probability of being hard-working is 41%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.80
P(Y=1 | X=1, V2=0) = 0.26
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.88
P(V2=1 | X=1) = 0.41
0.41 * (0.80 - 0.48)+ 0.88 * (0.52 - 0.26)= -0.15
-0.15 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 4%. The probability of nonsmoking and being lactose intolerant is 73%. The probability of smoking and being lactose intolerant is 2%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.73
P(Y=1, X=1=1) = 0.02
0.02/0.04 - 0.73/0.96 = -0.40
-0.40 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
8370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 37%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 66%. For smokers and are lazy, the probability of being lactose intolerant is 41%. For smokers and are hard-working, the probability of being lactose intolerant is 73%. For nonsmokers, the probability of being hard-working is 71%. For smokers, the probability of being hard-working is 33%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.37
P(Y=1 | X=0, V2=1) = 0.66
P(Y=1 | X=1, V2=0) = 0.41
P(Y=1 | X=1, V2=1) = 0.73
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.33
0.33 * (0.66 - 0.37)+ 0.71 * (0.73 - 0.41)= -0.11
-0.11 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. For nonsmokers and are lazy, the probability of being lactose intolerant is 37%. For nonsmokers and are hard-working, the probability of being lactose intolerant is 66%. For smokers and are lazy, the probability of being lactose intolerant is 41%. For smokers and are hard-working, the probability of being lactose intolerant is 73%. For nonsmokers, the probability of being hard-working is 71%. For smokers, the probability of being hard-working is 33%.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.37
P(Y=1 | X=0, V2=1) = 0.66
P(Y=1 | X=1, V2=0) = 0.41
P(Y=1 | X=1, V2=1) = 0.73
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.33
0.71 * (0.73 - 0.41) + 0.33 * (0.66 - 0.37) = 0.06
0.06 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
8380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 4%. For nonsmokers, the probability of being lactose intolerant is 58%. For smokers, the probability of being lactose intolerant is 52%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.52
0.04*0.52 - 0.96*0.58 = 0.57
0.57 > 0",mediation,neg_mediation,1,marginal,P(Y)
8384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. The overall probability of smoking is 17%. For nonsmokers, the probability of being lactose intolerant is 73%. For smokers, the probability of being lactose intolerant is 29%.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.29
0.17*0.29 - 0.83*0.73 = 0.65
0.65 > 0",mediation,neg_mediation,1,marginal,P(Y)
8398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. Method 1: We look at how smoking correlates with lactose intolerance case by case according to effort. Method 2: We look directly at how smoking correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
8402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 41%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.41
0.41 - 0.70 = -0.30
-0.30 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 77%. For people who do not speak english and with diabetes, the probability of long lifespan is 48%. For people who speak english and without diabetes, the probability of long lifespan is 56%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 22%. For people who do not speak english and smokers, the probability of having diabetes is 59%. For people who speak english and nonsmokers, the probability of having diabetes is 49%. For people who speak english and smokers, the probability of having diabetes is 86%. The overall probability of smoker is 4%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.48
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.22
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.49
P(V3=1 | X=1, V2=1) = 0.86
P(V2=1) = 0.04
0.04 * 0.48 * (0.86 - 0.49)+ 0.96 * 0.48 * (0.59 - 0.22)= -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 5%. The probability of not speaking english and long lifespan is 67%. The probability of speaking english and long lifespan is 2%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.67
P(Y=1, X=1=1) = 0.02
0.02/0.05 - 0.67/0.95 = -0.30
-0.30 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8416,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 65%. For people who speak english, the probability of long lifespan is 32%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.32
0.32 - 0.65 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 65%. For people who speak english, the probability of long lifespan is 32%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.32
0.32 - 0.65 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 72%. For people who do not speak english and with diabetes, the probability of long lifespan is 47%. For people who speak english and without diabetes, the probability of long lifespan is 48%. For people who speak english and with diabetes, the probability of long lifespan is 22%. For people who do not speak english and nonsmokers, the probability of having diabetes is 30%. For people who do not speak english and smokers, the probability of having diabetes is 15%. For people who speak english and nonsmokers, the probability of having diabetes is 61%. For people who speak english and smokers, the probability of having diabetes is 60%. The overall probability of smoker is 17%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.30
P(V3=1 | X=0, V2=1) = 0.15
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.17
0.17 * (0.22 - 0.48) * 0.15 + 0.83 * (0.47 - 0.72) * 0.61 = -0.24
-0.24 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 72%. For people who do not speak english and with diabetes, the probability of long lifespan is 47%. For people who speak english and without diabetes, the probability of long lifespan is 48%. For people who speak english and with diabetes, the probability of long lifespan is 22%. For people who do not speak english and nonsmokers, the probability of having diabetes is 30%. For people who do not speak english and smokers, the probability of having diabetes is 15%. For people who speak english and nonsmokers, the probability of having diabetes is 61%. For people who speak english and smokers, the probability of having diabetes is 60%. The overall probability of smoker is 17%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.30
P(V3=1 | X=0, V2=1) = 0.15
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.17
0.17 * (0.22 - 0.48) * 0.15 + 0.83 * (0.47 - 0.72) * 0.61 = -0.24
-0.24 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 16%. The probability of not speaking english and long lifespan is 54%. The probability of speaking english and long lifespan is 5%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.05
0.05/0.16 - 0.54/0.84 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 58%. For people who speak english, the probability of long lifespan is 25%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.25
0.25 - 0.58 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8434,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 71%. For people who do not speak english and with diabetes, the probability of long lifespan is 46%. For people who speak english and without diabetes, the probability of long lifespan is 40%. For people who speak english and with diabetes, the probability of long lifespan is 22%. For people who do not speak english and nonsmokers, the probability of having diabetes is 49%. For people who do not speak english and smokers, the probability of having diabetes is 55%. For people who speak english and nonsmokers, the probability of having diabetes is 94%. For people who speak english and smokers, the probability of having diabetes is 76%. The overall probability of smoker is 52%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.71
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.49
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.94
P(V3=1 | X=1, V2=1) = 0.76
P(V2=1) = 0.52
0.52 * (0.22 - 0.40) * 0.55 + 0.48 * (0.46 - 0.71) * 0.94 = -0.25
-0.25 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 10%. For people who do not speak english, the probability of long lifespan is 58%. For people who speak english, the probability of long lifespan is 25%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.25
0.10*0.25 - 0.90*0.58 = 0.55
0.55 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 79%. For people who speak english, the probability of long lifespan is 72%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.72
0.72 - 0.79 = -0.07
-0.07 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 79%. For people who speak english, the probability of long lifespan is 72%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.72
0.72 - 0.79 = -0.07
-0.07 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 88%. For people who do not speak english and with diabetes, the probability of long lifespan is 54%. For people who speak english and without diabetes, the probability of long lifespan is 91%. For people who speak english and with diabetes, the probability of long lifespan is 58%. For people who do not speak english and nonsmokers, the probability of having diabetes is 22%. For people who do not speak english and smokers, the probability of having diabetes is 48%. For people who speak english and nonsmokers, the probability of having diabetes is 51%. For people who speak english and smokers, the probability of having diabetes is 81%. The overall probability of smoker is 14%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.22
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.81
P(V2=1) = 0.14
0.14 * (0.58 - 0.91) * 0.48 + 0.86 * (0.54 - 0.88) * 0.51 = 0.02
0.02 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 6%. For people who do not speak english, the probability of long lifespan is 79%. For people who speak english, the probability of long lifespan is 72%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.72
0.06*0.72 - 0.94*0.79 = 0.79
0.79 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 68%. For people who speak english, the probability of long lifespan is 37%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.37
0.37 - 0.68 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 76%. For people who do not speak english and with diabetes, the probability of long lifespan is 47%. For people who speak english and without diabetes, the probability of long lifespan is 53%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 25%. For people who do not speak english and smokers, the probability of having diabetes is 48%. For people who speak english and nonsmokers, the probability of having diabetes is 61%. For people who speak english and smokers, the probability of having diabetes is 89%. The overall probability of smoker is 2%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.89
P(V2=1) = 0.02
0.02 * 0.47 * (0.89 - 0.61)+ 0.98 * 0.47 * (0.48 - 0.25)= -0.10
-0.10 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 76%. For people who do not speak english and with diabetes, the probability of long lifespan is 47%. For people who speak english and without diabetes, the probability of long lifespan is 53%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 25%. For people who do not speak english and smokers, the probability of having diabetes is 48%. For people who speak english and nonsmokers, the probability of having diabetes is 61%. For people who speak english and smokers, the probability of having diabetes is 89%. The overall probability of smoker is 2%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.89
P(V2=1) = 0.02
0.02 * (0.27 - 0.53) * 0.48 + 0.98 * (0.47 - 0.76) * 0.61 = -0.22
-0.22 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8464,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 8%. For people who do not speak english, the probability of long lifespan is 68%. For people who speak english, the probability of long lifespan is 37%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.37
0.08*0.37 - 0.92*0.68 = 0.66
0.66 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8466,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 8%. The probability of not speaking english and long lifespan is 63%. The probability of speaking english and long lifespan is 3%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.63/0.92 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 8%. The probability of not speaking english and long lifespan is 63%. The probability of speaking english and long lifespan is 3%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.63/0.92 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 74%. For people who do not speak english and with diabetes, the probability of long lifespan is 50%. For people who speak english and without diabetes, the probability of long lifespan is 52%. For people who speak english and with diabetes, the probability of long lifespan is 20%. For people who do not speak english and nonsmokers, the probability of having diabetes is 31%. For people who do not speak english and smokers, the probability of having diabetes is 20%. For people who speak english and nonsmokers, the probability of having diabetes is 53%. For people who speak english and smokers, the probability of having diabetes is 59%. The overall probability of smoker is 13%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.74
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.20
P(V3=1 | X=0, V2=0) = 0.31
P(V3=1 | X=0, V2=1) = 0.20
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.59
P(V2=1) = 0.13
0.13 * (0.20 - 0.52) * 0.20 + 0.87 * (0.50 - 0.74) * 0.53 = -0.25
-0.25 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 5%. The probability of not speaking english and long lifespan is 64%. The probability of speaking english and long lifespan is 2%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.64
P(Y=1, X=1=1) = 0.02
0.02/0.05 - 0.64/0.95 = -0.32
-0.32 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 76%. For people who do not speak english and with diabetes, the probability of long lifespan is 52%. For people who speak english and without diabetes, the probability of long lifespan is 53%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 46%. For people who do not speak english and smokers, the probability of having diabetes is 34%. For people who speak english and nonsmokers, the probability of having diabetes is 68%. For people who speak english and smokers, the probability of having diabetes is 77%. The overall probability of smoker is 55%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.46
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.77
P(V2=1) = 0.55
0.55 * 0.52 * (0.77 - 0.68)+ 0.45 * 0.52 * (0.34 - 0.46)= -0.09
-0.09 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 76%. For people who do not speak english and with diabetes, the probability of long lifespan is 52%. For people who speak english and without diabetes, the probability of long lifespan is 53%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 46%. For people who do not speak english and smokers, the probability of having diabetes is 34%. For people who speak english and nonsmokers, the probability of having diabetes is 68%. For people who speak english and smokers, the probability of having diabetes is 77%. The overall probability of smoker is 55%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.46
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.77
P(V2=1) = 0.55
0.55 * 0.52 * (0.77 - 0.68)+ 0.45 * 0.52 * (0.34 - 0.46)= -0.09
-0.09 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8491,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 76%. For people who do not speak english and with diabetes, the probability of long lifespan is 52%. For people who speak english and without diabetes, the probability of long lifespan is 53%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 46%. For people who do not speak english and smokers, the probability of having diabetes is 34%. For people who speak english and nonsmokers, the probability of having diabetes is 68%. For people who speak english and smokers, the probability of having diabetes is 77%. The overall probability of smoker is 55%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.46
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.77
P(V2=1) = 0.55
0.55 * (0.27 - 0.53) * 0.34 + 0.45 * (0.52 - 0.76) * 0.68 = -0.25
-0.25 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8493,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 17%. For people who do not speak english, the probability of long lifespan is 66%. For people who speak english, the probability of long lifespan is 34%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.34
0.17*0.34 - 0.83*0.66 = 0.60
0.60 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 53%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.53 - 0.70 = -0.17
-0.17 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 53%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.53 - 0.70 = -0.17
-0.17 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 80%. For people who do not speak english and with diabetes, the probability of long lifespan is 44%. For people who speak english and without diabetes, the probability of long lifespan is 87%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 27%. For people who do not speak english and smokers, the probability of having diabetes is 63%. For people who speak english and nonsmokers, the probability of having diabetes is 52%. For people who speak english and smokers, the probability of having diabetes is 89%. The overall probability of smoker is 8%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.89
P(V2=1) = 0.08
0.08 * 0.44 * (0.89 - 0.52)+ 0.92 * 0.44 * (0.63 - 0.27)= -0.08
-0.08 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 80%. For people who do not speak english and with diabetes, the probability of long lifespan is 44%. For people who speak english and without diabetes, the probability of long lifespan is 87%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 27%. For people who do not speak english and smokers, the probability of having diabetes is 63%. For people who speak english and nonsmokers, the probability of having diabetes is 52%. For people who speak english and smokers, the probability of having diabetes is 89%. The overall probability of smoker is 8%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.89
P(V2=1) = 0.08
0.08 * (0.27 - 0.87) * 0.63 + 0.92 * (0.44 - 0.80) * 0.52 = -0.03
-0.03 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 7%. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 53%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.07*0.53 - 0.93*0.70 = 0.69
0.69 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 77%. For people who speak english, the probability of long lifespan is 45%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.45
0.45 - 0.77 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8514,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 77%. For people who speak english, the probability of long lifespan is 45%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.45
0.45 - 0.77 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 77%. For people who speak english, the probability of long lifespan is 45%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.45
0.45 - 0.77 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 80%. For people who do not speak english and with diabetes, the probability of long lifespan is 54%. For people who speak english and without diabetes, the probability of long lifespan is 59%. For people who speak english and with diabetes, the probability of long lifespan is 29%. For people who do not speak english and nonsmokers, the probability of having diabetes is 8%. For people who do not speak english and smokers, the probability of having diabetes is 41%. For people who speak english and nonsmokers, the probability of having diabetes is 46%. For people who speak english and smokers, the probability of having diabetes is 73%. The overall probability of smoker is 3%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.29
P(V3=1 | X=0, V2=0) = 0.08
P(V3=1 | X=0, V2=1) = 0.41
P(V3=1 | X=1, V2=0) = 0.46
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.03
0.03 * 0.54 * (0.73 - 0.46)+ 0.97 * 0.54 * (0.41 - 0.08)= -0.09
-0.09 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 80%. For people who do not speak english and with diabetes, the probability of long lifespan is 54%. For people who speak english and without diabetes, the probability of long lifespan is 59%. For people who speak english and with diabetes, the probability of long lifespan is 29%. For people who do not speak english and nonsmokers, the probability of having diabetes is 8%. For people who do not speak english and smokers, the probability of having diabetes is 41%. For people who speak english and nonsmokers, the probability of having diabetes is 46%. For people who speak english and smokers, the probability of having diabetes is 73%. The overall probability of smoker is 3%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.29
P(V3=1 | X=0, V2=0) = 0.08
P(V3=1 | X=0, V2=1) = 0.41
P(V3=1 | X=1, V2=0) = 0.46
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.03
0.03 * 0.54 * (0.73 - 0.46)+ 0.97 * 0.54 * (0.41 - 0.08)= -0.09
-0.09 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 16%. For people who do not speak english, the probability of long lifespan is 77%. For people who speak english, the probability of long lifespan is 45%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.45
0.16*0.45 - 0.84*0.77 = 0.72
0.72 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 82%. For people who speak english, the probability of long lifespan is 51%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.51
0.51 - 0.82 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 82%. For people who speak english, the probability of long lifespan is 51%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.51
0.51 - 0.82 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 84%. For people who do not speak english and with diabetes, the probability of long lifespan is 64%. For people who speak english and without diabetes, the probability of long lifespan is 62%. For people who speak english and with diabetes, the probability of long lifespan is 38%. For people who do not speak english and nonsmokers, the probability of having diabetes is 9%. For people who do not speak english and smokers, the probability of having diabetes is 4%. For people who speak english and nonsmokers, the probability of having diabetes is 47%. For people who speak english and smokers, the probability of having diabetes is 48%. The overall probability of smoker is 8%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 0.09
P(V3=1 | X=0, V2=1) = 0.04
P(V3=1 | X=1, V2=0) = 0.47
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.08
0.08 * 0.64 * (0.48 - 0.47)+ 0.92 * 0.64 * (0.04 - 0.09)= -0.08
-0.08 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 84%. For people who do not speak english and with diabetes, the probability of long lifespan is 64%. For people who speak english and without diabetes, the probability of long lifespan is 62%. For people who speak english and with diabetes, the probability of long lifespan is 38%. For people who do not speak english and nonsmokers, the probability of having diabetes is 9%. For people who do not speak english and smokers, the probability of having diabetes is 4%. For people who speak english and nonsmokers, the probability of having diabetes is 47%. For people who speak english and smokers, the probability of having diabetes is 48%. The overall probability of smoker is 8%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 0.09
P(V3=1 | X=0, V2=1) = 0.04
P(V3=1 | X=1, V2=0) = 0.47
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.08
0.08 * 0.64 * (0.48 - 0.47)+ 0.92 * 0.64 * (0.04 - 0.09)= -0.08
-0.08 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 84%. For people who do not speak english and with diabetes, the probability of long lifespan is 64%. For people who speak english and without diabetes, the probability of long lifespan is 62%. For people who speak english and with diabetes, the probability of long lifespan is 38%. For people who do not speak english and nonsmokers, the probability of having diabetes is 9%. For people who do not speak english and smokers, the probability of having diabetes is 4%. For people who speak english and nonsmokers, the probability of having diabetes is 47%. For people who speak english and smokers, the probability of having diabetes is 48%. The overall probability of smoker is 8%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 0.09
P(V3=1 | X=0, V2=1) = 0.04
P(V3=1 | X=1, V2=0) = 0.47
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.08
0.08 * (0.38 - 0.62) * 0.04 + 0.92 * (0.64 - 0.84) * 0.47 = -0.22
-0.22 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8535,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 19%. For people who do not speak english, the probability of long lifespan is 82%. For people who speak english, the probability of long lifespan is 51%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.51
0.19*0.51 - 0.81*0.82 = 0.76
0.76 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8537,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 19%. The probability of not speaking english and long lifespan is 66%. The probability of speaking english and long lifespan is 10%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.10
0.10/0.19 - 0.66/0.81 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 75%. For people who do not speak english and with diabetes, the probability of long lifespan is 52%. For people who speak english and without diabetes, the probability of long lifespan is 54%. For people who speak english and with diabetes, the probability of long lifespan is 28%. For people who do not speak english and nonsmokers, the probability of having diabetes is 37%. For people who do not speak english and smokers, the probability of having diabetes is 33%. For people who speak english and nonsmokers, the probability of having diabetes is 65%. For people who speak english and smokers, the probability of having diabetes is 67%. The overall probability of smoker is 50%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.37
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.50
0.50 * 0.52 * (0.67 - 0.65)+ 0.50 * 0.52 * (0.33 - 0.37)= -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 75%. For people who do not speak english and with diabetes, the probability of long lifespan is 52%. For people who speak english and without diabetes, the probability of long lifespan is 54%. For people who speak english and with diabetes, the probability of long lifespan is 28%. For people who do not speak english and nonsmokers, the probability of having diabetes is 37%. For people who do not speak english and smokers, the probability of having diabetes is 33%. For people who speak english and nonsmokers, the probability of having diabetes is 65%. For people who speak english and smokers, the probability of having diabetes is 67%. The overall probability of smoker is 50%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.37
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.50
0.50 * (0.28 - 0.54) * 0.33 + 0.50 * (0.52 - 0.75) * 0.65 = -0.22
-0.22 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 12%. For people who do not speak english, the probability of long lifespan is 67%. For people who speak english, the probability of long lifespan is 37%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.37
0.12*0.37 - 0.88*0.67 = 0.63
0.63 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 12%. The probability of not speaking english and long lifespan is 59%. The probability of speaking english and long lifespan is 4%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.04
0.04/0.12 - 0.59/0.88 = -0.30
-0.30 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 12%. The probability of not speaking english and long lifespan is 59%. The probability of speaking english and long lifespan is 4%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.04
0.04/0.12 - 0.59/0.88 = -0.30
-0.30 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8559,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 86%. For people who do not speak english and with diabetes, the probability of long lifespan is 47%. For people who speak english and without diabetes, the probability of long lifespan is 82%. For people who speak english and with diabetes, the probability of long lifespan is 44%. For people who do not speak english and nonsmokers, the probability of having diabetes is 9%. For people who do not speak english and smokers, the probability of having diabetes is 35%. For people who speak english and nonsmokers, the probability of having diabetes is 45%. For people who speak english and smokers, the probability of having diabetes is 67%. The overall probability of smoker is 7%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.86
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.09
P(V3=1 | X=0, V2=1) = 0.35
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.07
0.07 * 0.47 * (0.67 - 0.45)+ 0.93 * 0.47 * (0.35 - 0.09)= -0.12
-0.12 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 86%. For people who do not speak english and with diabetes, the probability of long lifespan is 47%. For people who speak english and without diabetes, the probability of long lifespan is 82%. For people who speak english and with diabetes, the probability of long lifespan is 44%. For people who do not speak english and nonsmokers, the probability of having diabetes is 9%. For people who do not speak english and smokers, the probability of having diabetes is 35%. For people who speak english and nonsmokers, the probability of having diabetes is 45%. For people who speak english and smokers, the probability of having diabetes is 67%. The overall probability of smoker is 7%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.86
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.09
P(V3=1 | X=0, V2=1) = 0.35
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.07
0.07 * (0.44 - 0.82) * 0.35 + 0.93 * (0.47 - 0.86) * 0.45 = -0.04
-0.04 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 11%. The probability of not speaking english and long lifespan is 73%. The probability of speaking english and long lifespan is 7%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.73
P(Y=1, X=1=1) = 0.07
0.07/0.11 - 0.73/0.89 = -0.17
-0.17 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 81%. For people who speak english, the probability of long lifespan is 44%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.44
0.44 - 0.81 = -0.37
-0.37 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 91%. For people who do not speak english and with diabetes, the probability of long lifespan is 59%. For people who speak english and without diabetes, the probability of long lifespan is 59%. For people who speak english and with diabetes, the probability of long lifespan is 35%. For people who do not speak english and nonsmokers, the probability of having diabetes is 26%. For people who do not speak english and smokers, the probability of having diabetes is 67%. For people who speak english and nonsmokers, the probability of having diabetes is 56%. For people who speak english and smokers, the probability of having diabetes is 92%. The overall probability of smoker is 15%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.35
P(V3=1 | X=0, V2=0) = 0.26
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.92
P(V2=1) = 0.15
0.15 * (0.35 - 0.59) * 0.67 + 0.85 * (0.59 - 0.91) * 0.56 = -0.30
-0.30 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 6%. For people who do not speak english, the probability of long lifespan is 81%. For people who speak english, the probability of long lifespan is 44%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.44
0.06*0.44 - 0.94*0.81 = 0.78
0.78 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 6%. The probability of not speaking english and long lifespan is 76%. The probability of speaking english and long lifespan is 3%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.03
0.03/0.06 - 0.76/0.94 = -0.37
-0.37 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8580,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 75%. For people who speak english, the probability of long lifespan is 34%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.34
0.34 - 0.75 = -0.40
-0.40 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 75%. For people who speak english, the probability of long lifespan is 34%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.34
0.34 - 0.75 = -0.40
-0.40 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 79%. For people who do not speak english and with diabetes, the probability of long lifespan is 55%. For people who speak english and without diabetes, the probability of long lifespan is 50%. For people who speak english and with diabetes, the probability of long lifespan is 25%. For people who do not speak english and nonsmokers, the probability of having diabetes is 18%. For people who do not speak english and smokers, the probability of having diabetes is 23%. For people who speak english and nonsmokers, the probability of having diabetes is 65%. For people who speak english and smokers, the probability of having diabetes is 50%. The overall probability of smoker is 13%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.25
P(V3=1 | X=0, V2=0) = 0.18
P(V3=1 | X=0, V2=1) = 0.23
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.13
0.13 * 0.55 * (0.50 - 0.65)+ 0.87 * 0.55 * (0.23 - 0.18)= -0.10
-0.10 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 79%. For people who do not speak english and with diabetes, the probability of long lifespan is 55%. For people who speak english and without diabetes, the probability of long lifespan is 50%. For people who speak english and with diabetes, the probability of long lifespan is 25%. For people who do not speak english and nonsmokers, the probability of having diabetes is 18%. For people who do not speak english and smokers, the probability of having diabetes is 23%. For people who speak english and nonsmokers, the probability of having diabetes is 65%. For people who speak english and smokers, the probability of having diabetes is 50%. The overall probability of smoker is 13%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.25
P(V3=1 | X=0, V2=0) = 0.18
P(V3=1 | X=0, V2=1) = 0.23
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.13
0.13 * (0.25 - 0.50) * 0.23 + 0.87 * (0.55 - 0.79) * 0.65 = -0.28
-0.28 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 79%. For people who do not speak english and with diabetes, the probability of long lifespan is 55%. For people who speak english and without diabetes, the probability of long lifespan is 50%. For people who speak english and with diabetes, the probability of long lifespan is 25%. For people who do not speak english and nonsmokers, the probability of having diabetes is 18%. For people who do not speak english and smokers, the probability of having diabetes is 23%. For people who speak english and nonsmokers, the probability of having diabetes is 65%. For people who speak english and smokers, the probability of having diabetes is 50%. The overall probability of smoker is 13%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.25
P(V3=1 | X=0, V2=0) = 0.18
P(V3=1 | X=0, V2=1) = 0.23
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.13
0.13 * (0.25 - 0.50) * 0.23 + 0.87 * (0.55 - 0.79) * 0.65 = -0.28
-0.28 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 20%. For people who do not speak english, the probability of long lifespan is 75%. For people who speak english, the probability of long lifespan is 34%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.34
0.20*0.34 - 0.80*0.75 = 0.67
0.67 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 69%. For people who speak english, the probability of long lifespan is 38%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.38
0.38 - 0.69 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 77%. For people who do not speak english and with diabetes, the probability of long lifespan is 50%. For people who speak english and without diabetes, the probability of long lifespan is 54%. For people who speak english and with diabetes, the probability of long lifespan is 30%. For people who do not speak english and nonsmokers, the probability of having diabetes is 25%. For people who do not speak english and smokers, the probability of having diabetes is 35%. For people who speak english and nonsmokers, the probability of having diabetes is 64%. For people who speak english and smokers, the probability of having diabetes is 69%. The overall probability of smoker is 48%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.35
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.69
P(V2=1) = 0.48
0.48 * 0.50 * (0.69 - 0.64)+ 0.52 * 0.50 * (0.35 - 0.25)= -0.09
-0.09 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 83%. For people who speak english, the probability of long lifespan is 71%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.71
0.71 - 0.83 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 83%. For people who speak english, the probability of long lifespan is 71%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.71
0.71 - 0.83 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 96%. For people who do not speak english and with diabetes, the probability of long lifespan is 54%. For people who speak english and without diabetes, the probability of long lifespan is 92%. For people who speak english and with diabetes, the probability of long lifespan is 60%. For people who do not speak english and nonsmokers, the probability of having diabetes is 25%. For people who do not speak english and smokers, the probability of having diabetes is 55%. For people who speak english and nonsmokers, the probability of having diabetes is 59%. For people who speak english and smokers, the probability of having diabetes is 80%. The overall probability of smoker is 18%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.18
0.18 * (0.60 - 0.92) * 0.55 + 0.82 * (0.54 - 0.96) * 0.59 = -0.03
-0.03 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8617,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 96%. For people who do not speak english and with diabetes, the probability of long lifespan is 54%. For people who speak english and without diabetes, the probability of long lifespan is 92%. For people who speak english and with diabetes, the probability of long lifespan is 60%. For people who do not speak english and nonsmokers, the probability of having diabetes is 25%. For people who do not speak english and smokers, the probability of having diabetes is 55%. For people who speak english and nonsmokers, the probability of having diabetes is 59%. For people who speak english and smokers, the probability of having diabetes is 80%. The overall probability of smoker is 18%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.18
0.18 * (0.60 - 0.92) * 0.55 + 0.82 * (0.54 - 0.96) * 0.59 = -0.03
-0.03 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 2%. For people who do not speak english, the probability of long lifespan is 83%. For people who speak english, the probability of long lifespan is 71%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.71
0.02*0.71 - 0.98*0.83 = 0.83
0.83 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 78%. For people who speak english, the probability of long lifespan is 47%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.47
0.47 - 0.78 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 88%. For people who do not speak english and with diabetes, the probability of long lifespan is 62%. For people who speak english and without diabetes, the probability of long lifespan is 66%. For people who speak english and with diabetes, the probability of long lifespan is 38%. For people who do not speak english and nonsmokers, the probability of having diabetes is 35%. For people who do not speak english and smokers, the probability of having diabetes is 56%. For people who speak english and nonsmokers, the probability of having diabetes is 63%. For people who speak english and smokers, the probability of having diabetes is 86%. The overall probability of smoker is 19%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 0.35
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.86
P(V2=1) = 0.19
0.19 * 0.62 * (0.86 - 0.63)+ 0.81 * 0.62 * (0.56 - 0.35)= -0.06
-0.06 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 88%. For people who do not speak english and with diabetes, the probability of long lifespan is 62%. For people who speak english and without diabetes, the probability of long lifespan is 66%. For people who speak english and with diabetes, the probability of long lifespan is 38%. For people who do not speak english and nonsmokers, the probability of having diabetes is 35%. For people who do not speak english and smokers, the probability of having diabetes is 56%. For people who speak english and nonsmokers, the probability of having diabetes is 63%. For people who speak english and smokers, the probability of having diabetes is 86%. The overall probability of smoker is 19%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 0.35
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.86
P(V2=1) = 0.19
0.19 * 0.62 * (0.86 - 0.63)+ 0.81 * 0.62 * (0.56 - 0.35)= -0.06
-0.06 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 88%. For people who do not speak english and with diabetes, the probability of long lifespan is 62%. For people who speak english and without diabetes, the probability of long lifespan is 66%. For people who speak english and with diabetes, the probability of long lifespan is 38%. For people who do not speak english and nonsmokers, the probability of having diabetes is 35%. For people who do not speak english and smokers, the probability of having diabetes is 56%. For people who speak english and nonsmokers, the probability of having diabetes is 63%. For people who speak english and smokers, the probability of having diabetes is 86%. The overall probability of smoker is 19%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 0.35
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.86
P(V2=1) = 0.19
0.19 * (0.38 - 0.66) * 0.56 + 0.81 * (0.62 - 0.88) * 0.63 = -0.24
-0.24 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 19%. For people who do not speak english, the probability of long lifespan is 78%. For people who speak english, the probability of long lifespan is 47%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.47
0.19*0.47 - 0.81*0.78 = 0.72
0.72 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 19%. The probability of not speaking english and long lifespan is 63%. The probability of speaking english and long lifespan is 9%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.09
0.09/0.19 - 0.63/0.81 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 19%. The probability of not speaking english and long lifespan is 63%. The probability of speaking english and long lifespan is 9%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.09
0.09/0.19 - 0.63/0.81 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 91%. For people who do not speak english and with diabetes, the probability of long lifespan is 71%. For people who speak english and without diabetes, the probability of long lifespan is 69%. For people who speak english and with diabetes, the probability of long lifespan is 43%. For people who do not speak english and nonsmokers, the probability of having diabetes is 28%. For people who do not speak english and smokers, the probability of having diabetes is 20%. For people who speak english and nonsmokers, the probability of having diabetes is 57%. For people who speak english and smokers, the probability of having diabetes is 70%. The overall probability of smoker is 8%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0, V2=0) = 0.28
P(V3=1 | X=0, V2=1) = 0.20
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.08
0.08 * (0.43 - 0.69) * 0.20 + 0.92 * (0.71 - 0.91) * 0.57 = -0.24
-0.24 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 91%. For people who do not speak english and with diabetes, the probability of long lifespan is 71%. For people who speak english and without diabetes, the probability of long lifespan is 69%. For people who speak english and with diabetes, the probability of long lifespan is 43%. For people who do not speak english and nonsmokers, the probability of having diabetes is 28%. For people who do not speak english and smokers, the probability of having diabetes is 20%. For people who speak english and nonsmokers, the probability of having diabetes is 57%. For people who speak english and smokers, the probability of having diabetes is 70%. The overall probability of smoker is 8%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0, V2=0) = 0.28
P(V3=1 | X=0, V2=1) = 0.20
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.08
0.08 * (0.43 - 0.69) * 0.20 + 0.92 * (0.71 - 0.91) * 0.57 = -0.24
-0.24 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 10%. For people who do not speak english, the probability of long lifespan is 86%. For people who speak english, the probability of long lifespan is 54%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.54
0.10*0.54 - 0.90*0.86 = 0.83
0.83 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 10%. The probability of not speaking english and long lifespan is 77%. The probability of speaking english and long lifespan is 6%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.77
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.77/0.90 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 10%. The probability of not speaking english and long lifespan is 77%. The probability of speaking english and long lifespan is 6%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.77
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.77/0.90 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8652,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 71%. For people who speak english, the probability of long lifespan is 33%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.33
0.33 - 0.71 = -0.38
-0.38 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 71%. For people who speak english, the probability of long lifespan is 33%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.33
0.33 - 0.71 = -0.38
-0.38 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8654,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 71%. For people who speak english, the probability of long lifespan is 33%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.33
0.33 - 0.71 = -0.38
-0.38 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 75%. For people who do not speak english and with diabetes, the probability of long lifespan is 57%. For people who speak english and without diabetes, the probability of long lifespan is 56%. For people who speak english and with diabetes, the probability of long lifespan is 19%. For people who do not speak english and nonsmokers, the probability of having diabetes is 27%. For people who do not speak english and smokers, the probability of having diabetes is 8%. For people who speak english and nonsmokers, the probability of having diabetes is 54%. For people who speak english and smokers, the probability of having diabetes is 73%. The overall probability of smoker is 43%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.08
P(V3=1 | X=1, V2=0) = 0.54
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.43
0.43 * 0.57 * (0.73 - 0.54)+ 0.57 * 0.57 * (0.08 - 0.27)= -0.11
-0.11 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 75%. For people who do not speak english and with diabetes, the probability of long lifespan is 57%. For people who speak english and without diabetes, the probability of long lifespan is 56%. For people who speak english and with diabetes, the probability of long lifespan is 19%. For people who do not speak english and nonsmokers, the probability of having diabetes is 27%. For people who do not speak english and smokers, the probability of having diabetes is 8%. For people who speak english and nonsmokers, the probability of having diabetes is 54%. For people who speak english and smokers, the probability of having diabetes is 73%. The overall probability of smoker is 43%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.08
P(V3=1 | X=1, V2=0) = 0.54
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.43
0.43 * (0.19 - 0.56) * 0.08 + 0.57 * (0.57 - 0.75) * 0.54 = -0.24
-0.24 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 12%. For people who do not speak english, the probability of long lifespan is 71%. For people who speak english, the probability of long lifespan is 33%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.33
0.12*0.33 - 0.88*0.71 = 0.67
0.67 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how ability to speak english correlates with lifespan case by case according to diabetes. Method 2: We look directly at how ability to speak english correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 59%. For people who speak english, the probability of long lifespan is 59%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.59
0.59 - 0.59 = -0.01
-0.01 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 17%. The probability of not speaking english and long lifespan is 49%. The probability of speaking english and long lifespan is 10%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.10
0.10/0.17 - 0.49/0.83 = -0.01
-0.01 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 17%. The probability of not speaking english and long lifespan is 49%. The probability of speaking english and long lifespan is 10%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.10
0.10/0.17 - 0.49/0.83 = -0.01
-0.01 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8681,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 93%. For people who speak english, the probability of long lifespan is 59%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.59
0.59 - 0.93 = -0.34
-0.34 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 93%. For people who speak english, the probability of long lifespan is 59%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.59
0.59 - 0.93 = -0.34
-0.34 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 18%. For people who do not speak english, the probability of long lifespan is 93%. For people who speak english, the probability of long lifespan is 59%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.59
0.18*0.59 - 0.82*0.93 = 0.87
0.87 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 18%. The probability of not speaking english and long lifespan is 76%. The probability of speaking english and long lifespan is 11%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.11
0.11/0.18 - 0.76/0.82 = -0.34
-0.34 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8693,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 75%. For people who speak english, the probability of long lifespan is 44%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.44
0.44 - 0.75 = -0.31
-0.31 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 83%. For people who do not speak english and with diabetes, the probability of long lifespan is 60%. For people who speak english and without diabetes, the probability of long lifespan is 59%. For people who speak english and with diabetes, the probability of long lifespan is 37%. For people who do not speak english and nonsmokers, the probability of having diabetes is 35%. For people who do not speak english and smokers, the probability of having diabetes is 24%. For people who speak english and nonsmokers, the probability of having diabetes is 67%. For people who speak english and smokers, the probability of having diabetes is 56%. The overall probability of smoker is 5%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.35
P(V3=1 | X=0, V2=1) = 0.24
P(V3=1 | X=1, V2=0) = 0.67
P(V3=1 | X=1, V2=1) = 0.56
P(V2=1) = 0.05
0.05 * 0.60 * (0.56 - 0.67)+ 0.95 * 0.60 * (0.24 - 0.35)= -0.08
-0.08 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 83%. For people who do not speak english and with diabetes, the probability of long lifespan is 60%. For people who speak english and without diabetes, the probability of long lifespan is 59%. For people who speak english and with diabetes, the probability of long lifespan is 37%. For people who do not speak english and nonsmokers, the probability of having diabetes is 35%. For people who do not speak english and smokers, the probability of having diabetes is 24%. For people who speak english and nonsmokers, the probability of having diabetes is 67%. For people who speak english and smokers, the probability of having diabetes is 56%. The overall probability of smoker is 5%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.35
P(V3=1 | X=0, V2=1) = 0.24
P(V3=1 | X=1, V2=0) = 0.67
P(V3=1 | X=1, V2=1) = 0.56
P(V2=1) = 0.05
0.05 * 0.60 * (0.56 - 0.67)+ 0.95 * 0.60 * (0.24 - 0.35)= -0.08
-0.08 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 8%. For people who do not speak english, the probability of long lifespan is 75%. For people who speak english, the probability of long lifespan is 44%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.44
0.08*0.44 - 0.92*0.75 = 0.73
0.73 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8703,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 8%. For people who do not speak english, the probability of long lifespan is 75%. For people who speak english, the probability of long lifespan is 44%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.44
0.08*0.44 - 0.92*0.75 = 0.73
0.73 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 72%. For people who do not speak english and with diabetes, the probability of long lifespan is 55%. For people who speak english and without diabetes, the probability of long lifespan is 47%. For people who speak english and with diabetes, the probability of long lifespan is 27%. For people who do not speak english and nonsmokers, the probability of having diabetes is 30%. For people who do not speak english and smokers, the probability of having diabetes is 6%. For people who speak english and nonsmokers, the probability of having diabetes is 84%. For people who speak english and smokers, the probability of having diabetes is 70%. The overall probability of smoker is 41%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0, V2=0) = 0.30
P(V3=1 | X=0, V2=1) = 0.06
P(V3=1 | X=1, V2=0) = 0.84
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.41
0.41 * 0.55 * (0.70 - 0.84)+ 0.59 * 0.55 * (0.06 - 0.30)= -0.14
-0.14 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8716,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 8%. For people who do not speak english, the probability of long lifespan is 69%. For people who speak english, the probability of long lifespan is 32%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.32
0.08*0.32 - 0.92*0.69 = 0.66
0.66 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 8%. The probability of not speaking english and long lifespan is 63%. The probability of speaking english and long lifespan is 3%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.63/0.92 = -0.37
-0.37 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 8%. The probability of not speaking english and long lifespan is 63%. The probability of speaking english and long lifespan is 3%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.63/0.92 = -0.37
-0.37 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 83%. For people who speak english, the probability of long lifespan is 79%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.79
0.79 - 0.83 = -0.05
-0.05 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 88%. For people who do not speak english and with diabetes, the probability of long lifespan is 64%. For people who speak english and without diabetes, the probability of long lifespan is 94%. For people who speak english and with diabetes, the probability of long lifespan is 57%. For people who do not speak english and nonsmokers, the probability of having diabetes is 18%. For people who do not speak english and smokers, the probability of having diabetes is 53%. For people who speak english and nonsmokers, the probability of having diabetes is 41%. For people who speak english and smokers, the probability of having diabetes is 79%. The overall probability of smoker is 2%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.94
P(Y=1 | X=1, V3=1) = 0.57
P(V3=1 | X=0, V2=0) = 0.18
P(V3=1 | X=0, V2=1) = 0.53
P(V3=1 | X=1, V2=0) = 0.41
P(V3=1 | X=1, V2=1) = 0.79
P(V2=1) = 0.02
0.02 * 0.64 * (0.79 - 0.41)+ 0.98 * 0.64 * (0.53 - 0.18)= -0.05
-0.05 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 88%. For people who do not speak english and with diabetes, the probability of long lifespan is 64%. For people who speak english and without diabetes, the probability of long lifespan is 94%. For people who speak english and with diabetes, the probability of long lifespan is 57%. For people who do not speak english and nonsmokers, the probability of having diabetes is 18%. For people who do not speak english and smokers, the probability of having diabetes is 53%. For people who speak english and nonsmokers, the probability of having diabetes is 41%. For people who speak english and smokers, the probability of having diabetes is 79%. The overall probability of smoker is 2%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.94
P(Y=1 | X=1, V3=1) = 0.57
P(V3=1 | X=0, V2=0) = 0.18
P(V3=1 | X=0, V2=1) = 0.53
P(V3=1 | X=1, V2=0) = 0.41
P(V3=1 | X=1, V2=1) = 0.79
P(V2=1) = 0.02
0.02 * (0.57 - 0.94) * 0.53 + 0.98 * (0.64 - 0.88) * 0.41 = 0.03
0.03 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 19%. For people who do not speak english, the probability of long lifespan is 83%. For people who speak english, the probability of long lifespan is 79%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.79
0.19*0.79 - 0.81*0.83 = 0.83
0.83 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8732,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 19%. The probability of not speaking english and long lifespan is 68%. The probability of speaking english and long lifespan is 15%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.68
P(Y=1, X=1=1) = 0.15
0.15/0.19 - 0.68/0.81 = -0.05
-0.05 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8735,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 80%. For people who do not speak english and with diabetes, the probability of long lifespan is 50%. For people who speak english and without diabetes, the probability of long lifespan is 54%. For people who speak english and with diabetes, the probability of long lifespan is 22%. For people who do not speak english and nonsmokers, the probability of having diabetes is 14%. For people who do not speak english and smokers, the probability of having diabetes is 40%. For people who speak english and nonsmokers, the probability of having diabetes is 39%. For people who speak english and smokers, the probability of having diabetes is 69%. The overall probability of smoker is 17%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.14
P(V3=1 | X=0, V2=1) = 0.40
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.69
P(V2=1) = 0.17
0.17 * 0.50 * (0.69 - 0.39)+ 0.83 * 0.50 * (0.40 - 0.14)= -0.06
-0.06 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8744,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 20%. For people who do not speak english, the probability of long lifespan is 74%. For people who speak english, the probability of long lifespan is 40%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.40
0.20*0.40 - 0.80*0.74 = 0.68
0.68 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 20%. For people who do not speak english, the probability of long lifespan is 74%. For people who speak english, the probability of long lifespan is 40%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.40
0.20*0.40 - 0.80*0.74 = 0.68
0.68 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 38%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.38
0.38 - 0.70 = -0.32
-0.32 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 38%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.38
0.38 - 0.70 = -0.32
-0.32 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8753,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 38%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.38
0.38 - 0.70 = -0.32
-0.32 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 82%. For people who do not speak english and with diabetes, the probability of long lifespan is 58%. For people who speak english and without diabetes, the probability of long lifespan is 57%. For people who speak english and with diabetes, the probability of long lifespan is 37%. For people who do not speak english and nonsmokers, the probability of having diabetes is 49%. For people who do not speak english and smokers, the probability of having diabetes is 57%. For people who speak english and nonsmokers, the probability of having diabetes is 96%. For people who speak english and smokers, the probability of having diabetes is 87%. The overall probability of smoker is 10%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.49
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.96
P(V3=1 | X=1, V2=1) = 0.87
P(V2=1) = 0.10
0.10 * 0.58 * (0.87 - 0.96)+ 0.90 * 0.58 * (0.57 - 0.49)= -0.11
-0.11 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 13%. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 38%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.38
0.13*0.38 - 0.87*0.70 = 0.66
0.66 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 13%. The probability of not speaking english and long lifespan is 61%. The probability of speaking english and long lifespan is 5%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.05
0.05/0.13 - 0.61/0.87 = -0.32
-0.32 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how ability to speak english correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
8768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 80%. For people who do not speak english and with diabetes, the probability of long lifespan is 55%. For people who speak english and without diabetes, the probability of long lifespan is 59%. For people who speak english and with diabetes, the probability of long lifespan is 30%. For people who do not speak english and nonsmokers, the probability of having diabetes is 34%. For people who do not speak english and smokers, the probability of having diabetes is 47%. For people who speak english and nonsmokers, the probability of having diabetes is 73%. For people who speak english and smokers, the probability of having diabetes is 81%. The overall probability of smoker is 50%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.34
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.73
P(V3=1 | X=1, V2=1) = 0.81
P(V2=1) = 0.50
0.50 * 0.55 * (0.81 - 0.73)+ 0.50 * 0.55 * (0.47 - 0.34)= -0.08
-0.08 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 80%. For people who do not speak english and with diabetes, the probability of long lifespan is 55%. For people who speak english and without diabetes, the probability of long lifespan is 59%. For people who speak english and with diabetes, the probability of long lifespan is 30%. For people who do not speak english and nonsmokers, the probability of having diabetes is 34%. For people who do not speak english and smokers, the probability of having diabetes is 47%. For people who speak english and nonsmokers, the probability of having diabetes is 73%. For people who speak english and smokers, the probability of having diabetes is 81%. The overall probability of smoker is 50%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.34
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.73
P(V3=1 | X=1, V2=1) = 0.81
P(V2=1) = 0.50
0.50 * (0.30 - 0.59) * 0.47 + 0.50 * (0.55 - 0.80) * 0.73 = -0.23
-0.23 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 20%. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 37%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.37
0.20*0.37 - 0.80*0.70 = 0.64
0.64 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 71%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.71
0.71 - 0.70 = 0.01
0.01 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 70%. For people who speak english, the probability of long lifespan is 71%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.71
0.71 - 0.70 = 0.01
0.01 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 79%. For people who do not speak english and with diabetes, the probability of long lifespan is 29%. For people who speak english and without diabetes, the probability of long lifespan is 87%. For people who speak english and with diabetes, the probability of long lifespan is 49%. For people who do not speak english and nonsmokers, the probability of having diabetes is 15%. For people who do not speak english and smokers, the probability of having diabetes is 46%. For people who speak english and nonsmokers, the probability of having diabetes is 39%. For people who speak english and smokers, the probability of having diabetes is 73%. The overall probability of smoker is 11%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.15
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.73
P(V2=1) = 0.11
0.11 * 0.29 * (0.73 - 0.39)+ 0.89 * 0.29 * (0.46 - 0.15)= -0.11
-0.11 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 16%. The probability of not speaking english and long lifespan is 59%. The probability of speaking english and long lifespan is 11%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.11
0.11/0.16 - 0.59/0.84 = 0.01
0.01 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 16%. The probability of not speaking english and long lifespan is 59%. The probability of speaking english and long lifespan is 11%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.11
0.11/0.16 - 0.59/0.84 = 0.01
0.01 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
8792,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 81%. For people who speak english, the probability of long lifespan is 49%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.49
0.49 - 0.81 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 81%. For people who speak english, the probability of long lifespan is 49%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.49
0.49 - 0.81 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 81%. For people who speak english, the probability of long lifespan is 49%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.49
0.49 - 0.81 = -0.33
-0.33 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 87%. For people who do not speak english and with diabetes, the probability of long lifespan is 59%. For people who speak english and without diabetes, the probability of long lifespan is 66%. For people who speak english and with diabetes, the probability of long lifespan is 40%. For people who do not speak english and nonsmokers, the probability of having diabetes is 18%. For people who do not speak english and smokers, the probability of having diabetes is 43%. For people who speak english and nonsmokers, the probability of having diabetes is 66%. For people who speak english and smokers, the probability of having diabetes is 71%. The overall probability of smoker is 15%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.87
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.18
P(V3=1 | X=0, V2=1) = 0.43
P(V3=1 | X=1, V2=0) = 0.66
P(V3=1 | X=1, V2=1) = 0.71
P(V2=1) = 0.15
0.15 * 0.59 * (0.71 - 0.66)+ 0.85 * 0.59 * (0.43 - 0.18)= -0.11
-0.11 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
8800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of speaking english is 9%. For people who do not speak english, the probability of long lifespan is 81%. For people who speak english, the probability of long lifespan is 49%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.49
0.09*0.49 - 0.91*0.81 = 0.79
0.79 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
8807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 64%. For people who speak english, the probability of long lifespan is 52%.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.52
0.52 - 0.64 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english, the probability of long lifespan is 64%. For people who speak english, the probability of long lifespan is 52%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.52
0.52 - 0.64 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not speak english and without diabetes, the probability of long lifespan is 73%. For people who do not speak english and with diabetes, the probability of long lifespan is 26%. For people who speak english and without diabetes, the probability of long lifespan is 70%. For people who speak english and with diabetes, the probability of long lifespan is 34%. For people who do not speak english and nonsmokers, the probability of having diabetes is 17%. For people who do not speak english and smokers, the probability of having diabetes is 67%. For people who speak english and nonsmokers, the probability of having diabetes is 48%. For people who speak english and smokers, the probability of having diabetes is 97%. The overall probability of smoker is 5%.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.73
P(Y=1 | X=0, V3=1) = 0.26
P(Y=1 | X=1, V3=0) = 0.70
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.17
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.48
P(V3=1 | X=1, V2=1) = 0.97
P(V2=1) = 0.05
0.05 * (0.34 - 0.70) * 0.67 + 0.95 * (0.26 - 0.73) * 0.48 = -0.01
-0.01 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
8821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 73%. For patients consuming citrus, the probability of curly hair is 44%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.44
0.44 - 0.73 = -0.28
-0.28 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 73%. For patients consuming citrus, the probability of curly hair is 44%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.44
0.44 - 0.73 = -0.28
-0.28 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 73%. For patients consuming citrus, the probability of curly hair is 44%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.44
0.44 - 0.73 = -0.28
-0.28 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 95%. For patients not consuming citrus, the probability of curly hair is 73%. For patients consuming citrus, the probability of curly hair is 44%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.44
0.95*0.44 - 0.05*0.73 = 0.46
0.46 > 0",chain,orange_scurvy,1,marginal,P(Y)
8829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 95%. The probability of absence of citrus and curly hair is 3%. The probability of citrus intake and curly hair is 42%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.42
0.42/0.95 - 0.03/0.05 = -0.28
-0.28 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8831,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 58%. For patients consuming citrus, the probability of curly hair is 40%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.40
0.40 - 0.58 = -0.18
-0.18 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8835,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 58%. For patients consuming citrus, the probability of curly hair is 40%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.40
0.40 - 0.58 = -0.18
-0.18 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 53%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.53
0.53 - 0.68 = -0.15
-0.15 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 53%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.53
0.53 - 0.68 = -0.15
-0.15 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8848,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 53%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.53
0.53 - 0.68 = -0.15
-0.15 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 53%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.53
0.53 - 0.68 = -0.15
-0.15 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 84%. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 53%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.53
0.84*0.53 - 0.16*0.68 = 0.55
0.55 > 0",chain,orange_scurvy,1,marginal,P(Y)
8852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 84%. The probability of absence of citrus and curly hair is 11%. The probability of citrus intake and curly hair is 45%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.45
0.45/0.84 - 0.11/0.16 = -0.15
-0.15 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8853,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 84%. The probability of absence of citrus and curly hair is 11%. The probability of citrus intake and curly hair is 45%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.45
0.45/0.84 - 0.11/0.16 = -0.15
-0.15 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 89%. For patients consuming citrus, the probability of curly hair is 52%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.52
0.52 - 0.89 = -0.37
-0.37 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 89%. For patients consuming citrus, the probability of curly hair is 52%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.52
0.52 - 0.89 = -0.37
-0.37 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8862,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 90%. For patients not consuming citrus, the probability of curly hair is 89%. For patients consuming citrus, the probability of curly hair is 52%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.52
0.90*0.52 - 0.10*0.89 = 0.56
0.56 > 0",chain,orange_scurvy,1,marginal,P(Y)
8863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 90%. For patients not consuming citrus, the probability of curly hair is 89%. For patients consuming citrus, the probability of curly hair is 52%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.52
0.90*0.52 - 0.10*0.89 = 0.56
0.56 > 0",chain,orange_scurvy,1,marginal,P(Y)
8865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 90%. The probability of absence of citrus and curly hair is 9%. The probability of citrus intake and curly hair is 47%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.47
0.47/0.90 - 0.09/0.10 = -0.37
-0.37 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8866,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 63%. For patients consuming citrus, the probability of curly hair is 41%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.41
0.41 - 0.63 = -0.22
-0.22 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 63%. For patients consuming citrus, the probability of curly hair is 41%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.41
0.41 - 0.63 = -0.22
-0.22 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8874,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 92%. For patients not consuming citrus, the probability of curly hair is 63%. For patients consuming citrus, the probability of curly hair is 41%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.41
0.92*0.41 - 0.08*0.63 = 0.43
0.43 > 0",chain,orange_scurvy,1,marginal,P(Y)
8875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 92%. For patients not consuming citrus, the probability of curly hair is 63%. For patients consuming citrus, the probability of curly hair is 41%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.41
0.92*0.41 - 0.08*0.63 = 0.43
0.43 > 0",chain,orange_scurvy,1,marginal,P(Y)
8876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 92%. The probability of absence of citrus and curly hair is 5%. The probability of citrus intake and curly hair is 38%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.38
0.38/0.92 - 0.05/0.08 = -0.22
-0.22 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 41%. For patients consuming citrus, the probability of curly hair is 25%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.25
0.25 - 0.41 = -0.17
-0.17 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 41%. For patients consuming citrus, the probability of curly hair is 25%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.25
0.25 - 0.41 = -0.17
-0.17 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 41%. For patients consuming citrus, the probability of curly hair is 25%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.25
0.25 - 0.41 = -0.17
-0.17 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 82%. For patients not consuming citrus, the probability of curly hair is 41%. For patients consuming citrus, the probability of curly hair is 25%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.25
0.82*0.25 - 0.18*0.41 = 0.28
0.28 > 0",chain,orange_scurvy,1,marginal,P(Y)
8887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 82%. For patients not consuming citrus, the probability of curly hair is 41%. For patients consuming citrus, the probability of curly hair is 25%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.25
0.82*0.25 - 0.18*0.41 = 0.28
0.28 > 0",chain,orange_scurvy,1,marginal,P(Y)
8888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 82%. The probability of absence of citrus and curly hair is 7%. The probability of citrus intake and curly hair is 20%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.20
0.20/0.82 - 0.07/0.18 = -0.17
-0.17 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 38%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.38
0.38 - 0.61 = -0.23
-0.23 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 38%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.38
0.38 - 0.61 = -0.23
-0.23 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8900,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 97%. The probability of absence of citrus and curly hair is 2%. The probability of citrus intake and curly hair is 37%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.37
0.37/0.97 - 0.02/0.03 = -0.23
-0.23 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8901,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 97%. The probability of absence of citrus and curly hair is 2%. The probability of citrus intake and curly hair is 37%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.37
0.37/0.97 - 0.02/0.03 = -0.23
-0.23 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 60%. For patients consuming citrus, the probability of curly hair is 42%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.42
0.42 - 0.60 = -0.17
-0.17 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 60%. For patients consuming citrus, the probability of curly hair is 42%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.42
0.42 - 0.60 = -0.17
-0.17 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 60%. For patients consuming citrus, the probability of curly hair is 42%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.42
0.42 - 0.60 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 60%. For patients consuming citrus, the probability of curly hair is 42%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.42
0.42 - 0.60 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 84%. The probability of absence of citrus and curly hair is 10%. The probability of citrus intake and curly hair is 36%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.36
0.36/0.84 - 0.10/0.16 = -0.17
-0.17 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8913,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 84%. The probability of absence of citrus and curly hair is 10%. The probability of citrus intake and curly hair is 36%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.36
0.36/0.84 - 0.10/0.16 = -0.17
-0.17 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8916,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 13%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.13
0.13 - 0.33 = -0.20
-0.20 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 13%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.13
0.13 - 0.33 = -0.20
-0.20 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 13%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.13
0.13 - 0.33 = -0.20
-0.20 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 13%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.13
0.13 - 0.33 = -0.20
-0.20 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 13%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.13
0.13 - 0.33 = -0.20
-0.20 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 93%. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 13%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.13
0.93*0.13 - 0.07*0.33 = 0.14
0.14 > 0",chain,orange_scurvy,1,marginal,P(Y)
8925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 93%. The probability of absence of citrus and curly hair is 2%. The probability of citrus intake and curly hair is 12%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.12
0.12/0.93 - 0.02/0.07 = -0.20
-0.20 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8932,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 66%. For patients consuming citrus, the probability of curly hair is 30%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.30
0.30 - 0.66 = -0.37
-0.37 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 90%. The probability of absence of citrus and curly hair is 7%. The probability of citrus intake and curly hair is 27%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.27
0.27/0.90 - 0.07/0.10 = -0.37
-0.37 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 52%. For patients consuming citrus, the probability of curly hair is 33%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.33
0.33 - 0.52 = -0.18
-0.18 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 52%. For patients consuming citrus, the probability of curly hair is 33%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.33
0.33 - 0.52 = -0.18
-0.18 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 52%. For patients consuming citrus, the probability of curly hair is 33%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.33
0.33 - 0.52 = -0.18
-0.18 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 93%. The probability of absence of citrus and curly hair is 3%. The probability of citrus intake and curly hair is 31%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.31
0.31/0.93 - 0.03/0.07 = -0.18
-0.18 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 93%. The probability of absence of citrus and curly hair is 3%. The probability of citrus intake and curly hair is 31%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.31
0.31/0.93 - 0.03/0.07 = -0.18
-0.18 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 75%. For patients consuming citrus, the probability of curly hair is 40%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.40
0.40 - 0.75 = -0.36
-0.36 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 91%. For patients not consuming citrus, the probability of curly hair is 75%. For patients consuming citrus, the probability of curly hair is 40%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.40
0.91*0.40 - 0.09*0.75 = 0.43
0.43 > 0",chain,orange_scurvy,1,marginal,P(Y)
8959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 91%. For patients not consuming citrus, the probability of curly hair is 75%. For patients consuming citrus, the probability of curly hair is 40%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.40
0.91*0.40 - 0.09*0.75 = 0.43
0.43 > 0",chain,orange_scurvy,1,marginal,P(Y)
8960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 91%. The probability of absence of citrus and curly hair is 7%. The probability of citrus intake and curly hair is 36%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.36
0.36/0.91 - 0.07/0.09 = -0.36
-0.36 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 52%. For patients consuming citrus, the probability of curly hair is 27%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.27
0.27 - 0.52 = -0.25
-0.25 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 83%. For patients not consuming citrus, the probability of curly hair is 52%. For patients consuming citrus, the probability of curly hair is 27%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.27
0.83*0.27 - 0.17*0.52 = 0.31
0.31 > 0",chain,orange_scurvy,1,marginal,P(Y)
8973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 83%. The probability of absence of citrus and curly hair is 9%. The probability of citrus intake and curly hair is 22%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.22
0.22/0.83 - 0.09/0.17 = -0.25
-0.25 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
8977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 86%. For patients consuming citrus, the probability of curly hair is 59%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.59
0.59 - 0.86 = -0.28
-0.28 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
8978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 86%. For patients consuming citrus, the probability of curly hair is 59%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.59
0.59 - 0.86 = -0.28
-0.28 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 86%. For patients consuming citrus, the probability of curly hair is 59%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.59
0.59 - 0.86 = -0.28
-0.28 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
8981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 86%. For patients consuming citrus, the probability of curly hair is 59%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.59
0.59 - 0.86 = -0.28
-0.28 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
8992,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 53%. For patients consuming citrus, the probability of curly hair is 42%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.42
0.42 - 0.53 = -0.11
-0.11 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
8996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 93%. The probability of absence of citrus and curly hair is 4%. The probability of citrus intake and curly hair is 39%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.39
0.39/0.93 - 0.04/0.07 = -0.11
-0.11 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 55%. For patients consuming citrus, the probability of curly hair is 36%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.36
0.36 - 0.55 = -0.18
-0.18 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 55%. For patients consuming citrus, the probability of curly hair is 36%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.36
0.36 - 0.55 = -0.18
-0.18 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 97%. For patients not consuming citrus, the probability of curly hair is 55%. For patients consuming citrus, the probability of curly hair is 36%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.36
0.97*0.36 - 0.03*0.55 = 0.37
0.37 > 0",chain,orange_scurvy,1,marginal,P(Y)
9010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 53%. For patients consuming citrus, the probability of curly hair is 23%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.23
0.23 - 0.53 = -0.31
-0.31 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 89%. For patients not consuming citrus, the probability of curly hair is 53%. For patients consuming citrus, the probability of curly hair is 23%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.23
0.89*0.23 - 0.11*0.53 = 0.26
0.26 > 0",chain,orange_scurvy,1,marginal,P(Y)
9019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 89%. For patients not consuming citrus, the probability of curly hair is 53%. For patients consuming citrus, the probability of curly hair is 23%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.23
0.89*0.23 - 0.11*0.53 = 0.26
0.26 > 0",chain,orange_scurvy,1,marginal,P(Y)
9021,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 89%. The probability of absence of citrus and curly hair is 6%. The probability of citrus intake and curly hair is 20%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.20
0.20/0.89 - 0.06/0.11 = -0.31
-0.31 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 27%. For patients consuming citrus, the probability of curly hair is 16%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.16
0.16 - 0.27 = -0.11
-0.11 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 27%. For patients consuming citrus, the probability of curly hair is 16%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.16
0.16 - 0.27 = -0.11
-0.11 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 97%. For patients not consuming citrus, the probability of curly hair is 27%. For patients consuming citrus, the probability of curly hair is 16%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.16
0.97*0.16 - 0.03*0.27 = 0.17
0.17 > 0",chain,orange_scurvy,1,marginal,P(Y)
9033,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 97%. The probability of absence of citrus and curly hair is 1%. The probability of citrus intake and curly hair is 16%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.16
0.16/0.97 - 0.01/0.03 = -0.11
-0.11 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9036,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 54%. For patients consuming citrus, the probability of curly hair is 24%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.24
0.24 - 0.54 = -0.30
-0.30 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 54%. For patients consuming citrus, the probability of curly hair is 24%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.24
0.24 - 0.54 = -0.30
-0.30 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 54%. For patients consuming citrus, the probability of curly hair is 24%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.24
0.24 - 0.54 = -0.30
-0.30 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 99%. For patients not consuming citrus, the probability of curly hair is 54%. For patients consuming citrus, the probability of curly hair is 24%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.24
0.99*0.24 - 0.01*0.54 = 0.24
0.24 > 0",chain,orange_scurvy,1,marginal,P(Y)
9045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 99%. The probability of absence of citrus and curly hair is 1%. The probability of citrus intake and curly hair is 24%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.24
0.24/0.99 - 0.01/0.01 = -0.30
-0.30 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 83%. For patients consuming citrus, the probability of curly hair is 56%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.56
0.56 - 0.83 = -0.27
-0.27 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 83%. For patients consuming citrus, the probability of curly hair is 56%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.56
0.56 - 0.83 = -0.27
-0.27 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9052,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 83%. For patients consuming citrus, the probability of curly hair is 56%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.56
0.56 - 0.83 = -0.27
-0.27 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 91%. For patients not consuming citrus, the probability of curly hair is 83%. For patients consuming citrus, the probability of curly hair is 56%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.56
0.91*0.56 - 0.09*0.83 = 0.59
0.59 > 0",chain,orange_scurvy,1,marginal,P(Y)
9055,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 91%. For patients not consuming citrus, the probability of curly hair is 83%. For patients consuming citrus, the probability of curly hair is 56%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.56
0.91*0.56 - 0.09*0.83 = 0.59
0.59 > 0",chain,orange_scurvy,1,marginal,P(Y)
9056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 91%. The probability of absence of citrus and curly hair is 8%. The probability of citrus intake and curly hair is 51%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.51
0.51/0.91 - 0.08/0.09 = -0.27
-0.27 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 91%. The probability of absence of citrus and curly hair is 8%. The probability of citrus intake and curly hair is 51%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.51
0.51/0.91 - 0.08/0.09 = -0.27
-0.27 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9058,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 82%. For patients consuming citrus, the probability of curly hair is 37%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.37
0.37 - 0.82 = -0.46
-0.46 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 82%. For patients consuming citrus, the probability of curly hair is 37%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.37
0.37 - 0.82 = -0.46
-0.46 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 86%. For patients not consuming citrus, the probability of curly hair is 82%. For patients consuming citrus, the probability of curly hair is 37%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.37
0.86*0.37 - 0.14*0.82 = 0.43
0.43 > 0",chain,orange_scurvy,1,marginal,P(Y)
9067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 86%. For patients not consuming citrus, the probability of curly hair is 82%. For patients consuming citrus, the probability of curly hair is 37%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.37
0.86*0.37 - 0.14*0.82 = 0.43
0.43 > 0",chain,orange_scurvy,1,marginal,P(Y)
9069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 86%. The probability of absence of citrus and curly hair is 11%. The probability of citrus intake and curly hair is 32%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.86
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.32
0.32/0.86 - 0.11/0.14 = -0.46
-0.46 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 15%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.15
0.15 - 0.47 = -0.32
-0.32 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 15%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.15
0.15 - 0.47 = -0.32
-0.32 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9074,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 15%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.15
0.15 - 0.47 = -0.32
-0.32 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 15%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.15
0.15 - 0.47 = -0.32
-0.32 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 84%. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 15%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.15
0.84*0.15 - 0.16*0.47 = 0.21
0.21 > 0",chain,orange_scurvy,1,marginal,P(Y)
9079,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 84%. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 15%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.15
0.84*0.15 - 0.16*0.47 = 0.21
0.21 > 0",chain,orange_scurvy,1,marginal,P(Y)
9081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 84%. The probability of absence of citrus and curly hair is 8%. The probability of citrus intake and curly hair is 13%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.13
0.13/0.84 - 0.08/0.16 = -0.32
-0.32 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 82%. For patients consuming citrus, the probability of curly hair is 65%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.65
0.65 - 0.82 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 82%. For patients consuming citrus, the probability of curly hair is 65%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.65
0.65 - 0.82 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 30%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.30
0.30 - 0.61 = -0.31
-0.31 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 30%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.30
0.30 - 0.61 = -0.31
-0.31 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 97%. The probability of absence of citrus and curly hair is 2%. The probability of citrus intake and curly hair is 30%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.30
0.30/0.97 - 0.02/0.03 = -0.31
-0.31 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9111,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 74%. For patients consuming citrus, the probability of curly hair is 48%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.48
0.48 - 0.74 = -0.26
-0.26 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 74%. For patients consuming citrus, the probability of curly hair is 48%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.48
0.48 - 0.74 = -0.26
-0.26 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 81%. The probability of absence of citrus and curly hair is 14%. The probability of citrus intake and curly hair is 39%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.39
0.39/0.81 - 0.14/0.19 = -0.26
-0.26 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 72%. For patients consuming citrus, the probability of curly hair is 34%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.34
0.34 - 0.72 = -0.38
-0.38 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 90%. For patients not consuming citrus, the probability of curly hair is 72%. For patients consuming citrus, the probability of curly hair is 34%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.34
0.90*0.34 - 0.10*0.72 = 0.38
0.38 > 0",chain,orange_scurvy,1,marginal,P(Y)
9128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 90%. The probability of absence of citrus and curly hair is 7%. The probability of citrus intake and curly hair is 30%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.30
0.30/0.90 - 0.07/0.10 = -0.38
-0.38 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 14%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.14
0.14 - 0.33 = -0.19
-0.19 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 14%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.14
0.14 - 0.33 = -0.19
-0.19 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 14%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.14
0.14 - 0.33 = -0.19
-0.19 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 14%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.14
0.14 - 0.33 = -0.19
-0.19 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 99%. The probability of absence of citrus and curly hair is 0%. The probability of citrus intake and curly hair is 14%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.14
0.14/0.99 - 0.00/0.01 = -0.19
-0.19 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 99%. The probability of absence of citrus and curly hair is 0%. The probability of citrus intake and curly hair is 14%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.14
0.14/0.99 - 0.00/0.01 = -0.19
-0.19 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
9142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9143,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
9146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 30%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.30
0.30 - 0.49 = -0.19
-0.19 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 30%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.30
0.30 - 0.49 = -0.19
-0.19 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9150,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 95%. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 30%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.30
0.95*0.30 - 0.05*0.49 = 0.31
0.31 > 0",chain,orange_scurvy,1,marginal,P(Y)
9151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 95%. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 30%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.30
0.95*0.30 - 0.05*0.49 = 0.31
0.31 > 0",chain,orange_scurvy,1,marginal,P(Y)
9157,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 51%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.51
0.51 - 0.68 = -0.17
-0.17 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 51%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.51
0.51 - 0.68 = -0.17
-0.17 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 51%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.51
0.51 - 0.68 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9163,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 94%. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 51%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.51
0.94*0.51 - 0.06*0.68 = 0.52
0.52 > 0",chain,orange_scurvy,1,marginal,P(Y)
9168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 59%. For patients consuming citrus, the probability of curly hair is 47%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.47
0.47 - 0.59 = -0.12
-0.12 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9173,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 59%. For patients consuming citrus, the probability of curly hair is 47%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.47
0.47 - 0.59 = -0.12
-0.12 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
9180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 61%. For farms with increased crop yield per acre, the probability of high rainfall is 53%. For farms with reduced crop yield per acre, the probability of increased supply is 59%. For farms with increased crop yield per acre, the probability of increased supply is 89%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.53
P(X=1 | V2=0) = 0.59
P(X=1 | V2=1) = 0.89
(0.53 - 0.61) / (0.89 - 0.59) = -0.28
-0.28 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 61%. For farms with increased crop yield per acre, the probability of high rainfall is 53%. For farms with reduced crop yield per acre, the probability of increased supply is 59%. For farms with increased crop yield per acre, the probability of increased supply is 89%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.53
P(X=1 | V2=0) = 0.59
P(X=1 | V2=1) = 0.89
(0.53 - 0.61) / (0.89 - 0.59) = -0.28
-0.28 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 71%. For situations with reduced supply, the probability of high rainfall is 76%. For situations with increased supply, the probability of high rainfall is 51%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.51
0.71*0.51 - 0.29*0.76 = 0.58
0.58 > 0",IV,price,1,marginal,P(Y)
9184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 71%. The probability of reduced supply and high rainfall is 22%. The probability of increased supply and high rainfall is 36%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.71
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.36
0.36/0.71 - 0.22/0.29 = -0.25
-0.25 < 0",IV,price,1,correlation,P(Y | X)
9189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 55%. For farms with increased crop yield per acre, the probability of high rainfall is 44%. For farms with reduced crop yield per acre, the probability of increased supply is 7%. For farms with increased crop yield per acre, the probability of increased supply is 48%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.55
P(Y=1 | V2=1) = 0.44
P(X=1 | V2=0) = 0.07
P(X=1 | V2=1) = 0.48
(0.44 - 0.55) / (0.48 - 0.07) = -0.26
-0.26 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 30%. The probability of reduced supply and high rainfall is 40%. The probability of increased supply and high rainfall is 9%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.09
0.09/0.30 - 0.40/0.70 = -0.25
-0.25 < 0",IV,price,1,correlation,P(Y | X)
9194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9195,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 51%. For situations with reduced supply, the probability of high rainfall is 68%. For situations with increased supply, the probability of high rainfall is 38%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.38
0.51*0.38 - 0.49*0.68 = 0.53
0.53 > 0",IV,price,1,marginal,P(Y)
9204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 52%. For farms with increased crop yield per acre, the probability of high rainfall is 35%. For farms with reduced crop yield per acre, the probability of increased supply is 24%. For farms with increased crop yield per acre, the probability of increased supply is 66%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.35
P(X=1 | V2=0) = 0.24
P(X=1 | V2=1) = 0.66
(0.35 - 0.52) / (0.66 - 0.24) = -0.40
-0.40 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 52%. For farms with increased crop yield per acre, the probability of high rainfall is 35%. For farms with reduced crop yield per acre, the probability of increased supply is 24%. For farms with increased crop yield per acre, the probability of increased supply is 66%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.35
P(X=1 | V2=0) = 0.24
P(X=1 | V2=1) = 0.66
(0.35 - 0.52) / (0.66 - 0.24) = -0.40
-0.40 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 46%. For situations with reduced supply, the probability of high rainfall is 59%. For situations with increased supply, the probability of high rainfall is 23%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.23
0.46*0.23 - 0.54*0.59 = 0.43
0.43 > 0",IV,price,1,marginal,P(Y)
9210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9211,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 42%. The probability of reduced supply and high rainfall is 46%. The probability of increased supply and high rainfall is 21%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.21
0.21/0.42 - 0.46/0.58 = -0.31
-0.31 < 0",IV,price,1,correlation,P(Y | X)
9218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 54%. The probability of reduced supply and high rainfall is 32%. The probability of increased supply and high rainfall is 18%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.18
0.18/0.54 - 0.32/0.46 = -0.37
-0.37 < 0",IV,price,1,correlation,P(Y | X)
9225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 54%. The probability of reduced supply and high rainfall is 32%. The probability of increased supply and high rainfall is 18%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.18
0.18/0.54 - 0.32/0.46 = -0.37
-0.37 < 0",IV,price,1,correlation,P(Y | X)
9228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 70%. For farms with increased crop yield per acre, the probability of high rainfall is 54%. For farms with reduced crop yield per acre, the probability of increased supply is 38%. For farms with increased crop yield per acre, the probability of increased supply is 72%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.70
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.38
P(X=1 | V2=1) = 0.72
(0.54 - 0.70) / (0.72 - 0.38) = -0.47
-0.47 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 70%. For farms with increased crop yield per acre, the probability of high rainfall is 54%. For farms with reduced crop yield per acre, the probability of increased supply is 38%. For farms with increased crop yield per acre, the probability of increased supply is 72%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.70
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.38
P(X=1 | V2=1) = 0.72
(0.54 - 0.70) / (0.72 - 0.38) = -0.47
-0.47 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 53%. For situations with reduced supply, the probability of high rainfall is 85%. For situations with increased supply, the probability of high rainfall is 42%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.42
0.53*0.42 - 0.47*0.85 = 0.63
0.63 > 0",IV,price,1,marginal,P(Y)
9237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 57%. For farms with increased crop yield per acre, the probability of high rainfall is 51%. For farms with reduced crop yield per acre, the probability of increased supply is 37%. For farms with increased crop yield per acre, the probability of increased supply is 67%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.57
P(Y=1 | V2=1) = 0.51
P(X=1 | V2=0) = 0.37
P(X=1 | V2=1) = 0.67
(0.51 - 0.57) / (0.67 - 0.37) = -0.22
-0.22 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 52%. For situations with reduced supply, the probability of high rainfall is 65%. For situations with increased supply, the probability of high rainfall is 44%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.44
0.52*0.44 - 0.48*0.65 = 0.54
0.54 > 0",IV,price,1,marginal,P(Y)
9241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 52%. The probability of reduced supply and high rainfall is 31%. The probability of increased supply and high rainfall is 23%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.23
0.23/0.52 - 0.31/0.48 = -0.22
-0.22 < 0",IV,price,1,correlation,P(Y | X)
9242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 63%. For farms with increased crop yield per acre, the probability of high rainfall is 55%. For farms with reduced crop yield per acre, the probability of increased supply is 48%. For farms with increased crop yield per acre, the probability of increased supply is 78%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.63
P(Y=1 | V2=1) = 0.55
P(X=1 | V2=0) = 0.48
P(X=1 | V2=1) = 0.78
(0.55 - 0.63) / (0.78 - 0.48) = -0.27
-0.27 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 64%. For situations with reduced supply, the probability of high rainfall is 76%. For situations with increased supply, the probability of high rainfall is 49%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.64
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.49
0.64*0.49 - 0.36*0.76 = 0.59
0.59 > 0",IV,price,1,marginal,P(Y)
9252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 43%. For farms with increased crop yield per acre, the probability of high rainfall is 36%. For farms with reduced crop yield per acre, the probability of increased supply is 52%. For farms with increased crop yield per acre, the probability of increased supply is 82%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.43
P(Y=1 | V2=1) = 0.36
P(X=1 | V2=0) = 0.52
P(X=1 | V2=1) = 0.82
(0.36 - 0.43) / (0.82 - 0.52) = -0.24
-0.24 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 66%. For situations with reduced supply, the probability of high rainfall is 56%. For situations with increased supply, the probability of high rainfall is 31%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.31
0.66*0.31 - 0.34*0.56 = 0.40
0.40 > 0",IV,price,1,marginal,P(Y)
9257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 66%. The probability of reduced supply and high rainfall is 19%. The probability of increased supply and high rainfall is 20%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.20
0.20/0.66 - 0.19/0.34 = -0.25
-0.25 < 0",IV,price,1,correlation,P(Y | X)
9259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 53%. For farms with increased crop yield per acre, the probability of high rainfall is 47%. For farms with reduced crop yield per acre, the probability of increased supply is 49%. For farms with increased crop yield per acre, the probability of increased supply is 72%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.53
P(Y=1 | V2=1) = 0.47
P(X=1 | V2=0) = 0.49
P(X=1 | V2=1) = 0.72
(0.47 - 0.53) / (0.72 - 0.49) = -0.26
-0.26 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9262,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 60%. For situations with reduced supply, the probability of high rainfall is 63%. For situations with increased supply, the probability of high rainfall is 40%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.40
0.60*0.40 - 0.40*0.63 = 0.50
0.50 > 0",IV,price,1,marginal,P(Y)
9264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 60%. The probability of reduced supply and high rainfall is 25%. The probability of increased supply and high rainfall is 24%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.24
0.24/0.60 - 0.25/0.40 = -0.23
-0.23 < 0",IV,price,1,correlation,P(Y | X)
9265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 60%. The probability of reduced supply and high rainfall is 25%. The probability of increased supply and high rainfall is 24%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.24
0.24/0.60 - 0.25/0.40 = -0.23
-0.23 < 0",IV,price,1,correlation,P(Y | X)
9267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 40%. For farms with increased crop yield per acre, the probability of high rainfall is 26%. For farms with reduced crop yield per acre, the probability of increased supply is 38%. For farms with increased crop yield per acre, the probability of increased supply is 72%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.40
P(Y=1 | V2=1) = 0.26
P(X=1 | V2=0) = 0.38
P(X=1 | V2=1) = 0.72
(0.26 - 0.40) / (0.72 - 0.38) = -0.42
-0.42 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 40%. For farms with increased crop yield per acre, the probability of high rainfall is 26%. For farms with reduced crop yield per acre, the probability of increased supply is 38%. For farms with increased crop yield per acre, the probability of increased supply is 72%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.40
P(Y=1 | V2=1) = 0.26
P(X=1 | V2=0) = 0.38
P(X=1 | V2=1) = 0.72
(0.26 - 0.40) / (0.72 - 0.38) = -0.42
-0.42 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. For situations with reduced supply, the probability of high rainfall is 55%. For situations with increased supply, the probability of high rainfall is 15%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.15
0.56*0.15 - 0.44*0.55 = 0.33
0.33 > 0",IV,price,1,marginal,P(Y)
9272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. The probability of reduced supply and high rainfall is 24%. The probability of increased supply and high rainfall is 8%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.08
0.08/0.56 - 0.24/0.44 = -0.40
-0.40 < 0",IV,price,1,correlation,P(Y | X)
9273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. The probability of reduced supply and high rainfall is 24%. The probability of increased supply and high rainfall is 8%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.08
0.08/0.56 - 0.24/0.44 = -0.40
-0.40 < 0",IV,price,1,correlation,P(Y | X)
9275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 64%. For farms with increased crop yield per acre, the probability of high rainfall is 54%. For farms with reduced crop yield per acre, the probability of increased supply is 46%. For farms with increased crop yield per acre, the probability of increased supply is 75%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.64
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.46
P(X=1 | V2=1) = 0.75
(0.54 - 0.64) / (0.75 - 0.46) = -0.33
-0.33 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9278,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 61%. For situations with reduced supply, the probability of high rainfall is 77%. For situations with increased supply, the probability of high rainfall is 46%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.46
0.61*0.46 - 0.39*0.77 = 0.59
0.59 > 0",IV,price,1,marginal,P(Y)
9279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 61%. For situations with reduced supply, the probability of high rainfall is 77%. For situations with increased supply, the probability of high rainfall is 46%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.46
0.61*0.46 - 0.39*0.77 = 0.59
0.59 > 0",IV,price,1,marginal,P(Y)
9281,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 61%. The probability of reduced supply and high rainfall is 30%. The probability of increased supply and high rainfall is 28%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.61
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.28
0.28/0.61 - 0.30/0.39 = -0.31
-0.31 < 0",IV,price,1,correlation,P(Y | X)
9284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 59%. For farms with increased crop yield per acre, the probability of high rainfall is 50%. For farms with reduced crop yield per acre, the probability of increased supply is 41%. For farms with increased crop yield per acre, the probability of increased supply is 79%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.41
P(X=1 | V2=1) = 0.79
(0.50 - 0.59) / (0.79 - 0.41) = -0.24
-0.24 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 59%. For situations with reduced supply, the probability of high rainfall is 66%. For situations with increased supply, the probability of high rainfall is 46%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.46
0.59*0.46 - 0.41*0.66 = 0.55
0.55 > 0",IV,price,1,marginal,P(Y)
9290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 59%. For farms with increased crop yield per acre, the probability of high rainfall is 48%. For farms with reduced crop yield per acre, the probability of increased supply is 48%. For farms with increased crop yield per acre, the probability of increased supply is 92%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.48
P(X=1 | V2=0) = 0.48
P(X=1 | V2=1) = 0.92
(0.48 - 0.59) / (0.92 - 0.48) = -0.23
-0.23 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 59%. For farms with increased crop yield per acre, the probability of high rainfall is 48%. For farms with reduced crop yield per acre, the probability of increased supply is 48%. For farms with increased crop yield per acre, the probability of increased supply is 92%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.48
P(X=1 | V2=0) = 0.48
P(X=1 | V2=1) = 0.92
(0.48 - 0.59) / (0.92 - 0.48) = -0.23
-0.23 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 69%. For situations with reduced supply, the probability of high rainfall is 68%. For situations with increased supply, the probability of high rainfall is 48%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.69
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.48
0.69*0.48 - 0.31*0.68 = 0.54
0.54 > 0",IV,price,1,marginal,P(Y)
9299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9310,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. For situations with reduced supply, the probability of high rainfall is 71%. For situations with increased supply, the probability of high rainfall is 41%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.41
0.56*0.41 - 0.44*0.71 = 0.54
0.54 > 0",IV,price,1,marginal,P(Y)
9311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. For situations with reduced supply, the probability of high rainfall is 71%. For situations with increased supply, the probability of high rainfall is 41%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.41
0.56*0.41 - 0.44*0.71 = 0.54
0.54 > 0",IV,price,1,marginal,P(Y)
9312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. The probability of reduced supply and high rainfall is 32%. The probability of increased supply and high rainfall is 23%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.23
0.23/0.56 - 0.32/0.44 = -0.30
-0.30 < 0",IV,price,1,correlation,P(Y | X)
9313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. The probability of reduced supply and high rainfall is 32%. The probability of increased supply and high rainfall is 23%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.23
0.23/0.56 - 0.32/0.44 = -0.30
-0.30 < 0",IV,price,1,correlation,P(Y | X)
9318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 23%. For situations with reduced supply, the probability of high rainfall is 71%. For situations with increased supply, the probability of high rainfall is 44%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.44
0.23*0.44 - 0.77*0.71 = 0.65
0.65 > 0",IV,price,1,marginal,P(Y)
9321,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 23%. The probability of reduced supply and high rainfall is 54%. The probability of increased supply and high rainfall is 10%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.23
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.10
0.10/0.23 - 0.54/0.77 = -0.27
-0.27 < 0",IV,price,1,correlation,P(Y | X)
9322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9323,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. For situations with reduced supply, the probability of high rainfall is 81%. For situations with increased supply, the probability of high rainfall is 37%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.37
0.56*0.37 - 0.44*0.81 = 0.57
0.57 > 0",IV,price,1,marginal,P(Y)
9327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 56%. For situations with reduced supply, the probability of high rainfall is 81%. For situations with increased supply, the probability of high rainfall is 37%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.37
0.56*0.37 - 0.44*0.81 = 0.57
0.57 > 0",IV,price,1,marginal,P(Y)
9330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 31%. The probability of reduced supply and high rainfall is 32%. The probability of increased supply and high rainfall is 8%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.08
0.08/0.31 - 0.32/0.69 = -0.20
-0.20 < 0",IV,price,1,correlation,P(Y | X)
9346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 42%. The probability of reduced supply and high rainfall is 42%. The probability of increased supply and high rainfall is 22%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.22
0.22/0.42 - 0.42/0.58 = -0.22
-0.22 < 0",IV,price,1,correlation,P(Y | X)
9353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 42%. The probability of reduced supply and high rainfall is 42%. The probability of increased supply and high rainfall is 22%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.22
0.22/0.42 - 0.42/0.58 = -0.22
-0.22 < 0",IV,price,1,correlation,P(Y | X)
9354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 49%. The probability of reduced supply and high rainfall is 46%. The probability of increased supply and high rainfall is 35%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.35
0.35/0.49 - 0.46/0.51 = -0.19
-0.19 < 0",IV,price,1,correlation,P(Y | X)
9372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 91%. For farms with increased crop yield per acre, the probability of high rainfall is 82%. For farms with reduced crop yield per acre, the probability of increased supply is 26%. For farms with increased crop yield per acre, the probability of increased supply is 70%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.91
P(Y=1 | V2=1) = 0.82
P(X=1 | V2=0) = 0.26
P(X=1 | V2=1) = 0.70
(0.82 - 0.91) / (0.70 - 0.26) = -0.20
-0.20 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 71%. For situations with reduced supply, the probability of high rainfall is 86%. For situations with increased supply, the probability of high rainfall is 43%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.43
0.71*0.43 - 0.29*0.86 = 0.56
0.56 > 0",IV,price,1,marginal,P(Y)
9390,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 73%. For situations with reduced supply, the probability of high rainfall is 88%. For situations with increased supply, the probability of high rainfall is 59%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.73
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.59
0.73*0.59 - 0.27*0.88 = 0.67
0.67 > 0",IV,price,1,marginal,P(Y)
9391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 73%. For situations with reduced supply, the probability of high rainfall is 88%. For situations with increased supply, the probability of high rainfall is 59%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.73
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.59
0.73*0.59 - 0.27*0.88 = 0.67
0.67 > 0",IV,price,1,marginal,P(Y)
9392,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 73%. The probability of reduced supply and high rainfall is 24%. The probability of increased supply and high rainfall is 43%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.43
0.43/0.73 - 0.24/0.27 = -0.29
-0.29 < 0",IV,price,1,correlation,P(Y | X)
9393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 73%. The probability of reduced supply and high rainfall is 24%. The probability of increased supply and high rainfall is 43%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.43
0.43/0.73 - 0.24/0.27 = -0.29
-0.29 < 0",IV,price,1,correlation,P(Y | X)
9394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 51%. For situations with reduced supply, the probability of high rainfall is 62%. For situations with increased supply, the probability of high rainfall is 29%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.29
0.51*0.29 - 0.49*0.62 = 0.45
0.45 > 0",IV,price,1,marginal,P(Y)
9400,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 51%. The probability of reduced supply and high rainfall is 30%. The probability of increased supply and high rainfall is 15%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.15
0.15/0.51 - 0.30/0.49 = -0.32
-0.32 < 0",IV,price,1,correlation,P(Y | X)
9402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look at how supply correlates with rainfall case by case according to demand. Method 2: We look directly at how supply correlates with rainfall in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 46%. For situations with reduced supply, the probability of high rainfall is 66%. For situations with increased supply, the probability of high rainfall is 36%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.36
0.46*0.36 - 0.54*0.66 = 0.53
0.53 > 0",IV,price,1,marginal,P(Y)
9409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 46%. The probability of reduced supply and high rainfall is 36%. The probability of increased supply and high rainfall is 17%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.17
0.17/0.46 - 0.36/0.54 = -0.30
-0.30 < 0",IV,price,1,correlation,P(Y | X)
9410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 54%. For farms with increased crop yield per acre, the probability of high rainfall is 47%. For farms with reduced crop yield per acre, the probability of increased supply is 41%. For farms with increased crop yield per acre, the probability of increased supply is 64%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.47
P(X=1 | V2=0) = 0.41
P(X=1 | V2=1) = 0.64
(0.47 - 0.54) / (0.64 - 0.41) = -0.31
-0.31 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. For farms with reduced crop yield per acre, the probability of high rainfall is 54%. For farms with increased crop yield per acre, the probability of high rainfall is 47%. For farms with reduced crop yield per acre, the probability of increased supply is 41%. For farms with increased crop yield per acre, the probability of increased supply is 64%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.47
P(X=1 | V2=0) = 0.41
P(X=1 | V2=1) = 0.64
(0.47 - 0.54) / (0.64 - 0.41) = -0.31
-0.31 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 50%. For situations with reduced supply, the probability of high rainfall is 66%. For situations with increased supply, the probability of high rainfall is 37%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.37
0.50*0.37 - 0.50*0.66 = 0.51
0.51 > 0",IV,price,1,marginal,P(Y)
9416,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 50%. The probability of reduced supply and high rainfall is 33%. The probability of increased supply and high rainfall is 19%.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.19
0.19/0.50 - 0.33/0.50 = -0.30
-0.30 < 0",IV,price,1,correlation,P(Y | X)
9417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. The overall probability of increased supply is 50%. The probability of reduced supply and high rainfall is 33%. The probability of increased supply and high rainfall is 19%.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.19
0.19/0.50 - 0.33/0.50 = -0.30
-0.30 < 0",IV,price,1,correlation,P(Y | X)
9418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. Method 1: We look directly at how supply correlates with rainfall in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
9420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 25%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 43%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.43
0.57 * (0.25 - 0.04) + 0.43 * (0.97 - 0.76) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9424,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 57%. For patients who do not have a brother, the probability of recovery is 64%. For patients who have a brother, the probability of recovery is 34%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.34
0.57*0.34 - 0.43*0.64 = 0.47
0.47 > 0",confounding,simpson_drug,1,marginal,P(Y)
9427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 57%. The probability of not having a brother and recovery is 27%. The probability of having a brother and recovery is 20%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.20
0.20/0.57 - 0.27/0.43 = -0.29
-0.29 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 14%. For patients who are not male and have a brother, the probability of recovery is 25%. For patients who are male and do not have a brother, the probability of recovery is 72%. For patients who are male and have a brother, the probability of recovery is 90%. The overall probability of male gender is 41%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.14
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.72
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.41
0.59 * (0.25 - 0.14) + 0.41 * (0.90 - 0.72) = 0.14
0.14 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 60%. The probability of not having a brother and recovery is 27%. The probability of having a brother and recovery is 18%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.18
0.18/0.60 - 0.27/0.40 = -0.37
-0.37 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 60%. The probability of not having a brother and recovery is 27%. The probability of having a brother and recovery is 18%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.18
0.18/0.60 - 0.27/0.40 = -0.37
-0.37 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 46%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.46
0.54 * (0.24 - 0.04) + 0.46 * (0.97 - 0.76) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 46%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.46
0.54 * (0.24 - 0.04) + 0.46 * (0.97 - 0.76) = 0.20
0.20 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 46%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.46
0.54 * (0.24 - 0.04) + 0.46 * (0.97 - 0.76) = 0.20
0.20 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9445,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 54%. For patients who do not have a brother, the probability of recovery is 62%. For patients who have a brother, the probability of recovery is 36%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.36
0.54*0.36 - 0.46*0.62 = 0.48
0.48 > 0",confounding,simpson_drug,1,marginal,P(Y)
9446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 54%. The probability of not having a brother and recovery is 29%. The probability of having a brother and recovery is 20%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.20
0.20/0.54 - 0.29/0.46 = -0.26
-0.26 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 54%. The probability of not having a brother and recovery is 29%. The probability of having a brother and recovery is 20%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.20
0.20/0.54 - 0.29/0.46 = -0.26
-0.26 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 52%. For patients who do not have a brother, the probability of recovery is 72%. For patients who have a brother, the probability of recovery is 29%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.29
0.52*0.29 - 0.48*0.72 = 0.49
0.49 > 0",confounding,simpson_drug,1,marginal,P(Y)
9456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 52%. The probability of not having a brother and recovery is 35%. The probability of having a brother and recovery is 15%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.15
0.15/0.52 - 0.35/0.48 = -0.43
-0.43 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 3%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 74%. For patients who are male and have a brother, the probability of recovery is 96%. The overall probability of male gender is 53%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.74
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.53
0.47 * (0.24 - 0.03) + 0.53 * (0.96 - 0.74) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 3%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 74%. For patients who are male and have a brother, the probability of recovery is 96%. The overall probability of male gender is 53%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.74
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.53
0.47 * (0.24 - 0.03) + 0.53 * (0.96 - 0.74) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9465,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 41%. For patients who do not have a brother, the probability of recovery is 63%. For patients who have a brother, the probability of recovery is 30%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.30
0.41*0.30 - 0.59*0.63 = 0.50
0.50 > 0",confounding,simpson_drug,1,marginal,P(Y)
9466,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 41%. The probability of not having a brother and recovery is 37%. The probability of having a brother and recovery is 12%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.12
0.12/0.41 - 0.37/0.59 = -0.32
-0.32 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 21%. For patients who are not male and have a brother, the probability of recovery is 35%. For patients who are male and do not have a brother, the probability of recovery is 85%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 44%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.21
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.44
0.56 * (0.35 - 0.21) + 0.44 * (0.99 - 0.85) = 0.14
0.14 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 21%. For patients who are not male and have a brother, the probability of recovery is 35%. For patients who are male and do not have a brother, the probability of recovery is 85%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 44%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.21
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.44
0.56 * (0.35 - 0.21) + 0.44 * (0.99 - 0.85) = 0.14
0.14 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 5%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 77%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 52%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.52
0.48 * (0.26 - 0.05) + 0.52 * (0.98 - 0.77) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 5%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 77%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 52%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.52
0.48 * (0.26 - 0.05) + 0.52 * (0.98 - 0.77) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 48%. For patients who do not have a brother, the probability of recovery is 66%. For patients who have a brother, the probability of recovery is 39%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.39
0.48*0.39 - 0.52*0.66 = 0.53
0.53 > 0",confounding,simpson_drug,1,marginal,P(Y)
9494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 56%. For patients who do not have a brother, the probability of recovery is 66%. For patients who have a brother, the probability of recovery is 28%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.28
0.56*0.28 - 0.44*0.66 = 0.45
0.45 > 0",confounding,simpson_drug,1,marginal,P(Y)
9495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 56%. For patients who do not have a brother, the probability of recovery is 66%. For patients who have a brother, the probability of recovery is 28%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.28
0.56*0.28 - 0.44*0.66 = 0.45
0.45 > 0",confounding,simpson_drug,1,marginal,P(Y)
9500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 25%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 59%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.59
0.41 * (0.25 - 0.04) + 0.59 * (0.98 - 0.76) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 25%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 59%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.59
0.41 * (0.25 - 0.04) + 0.59 * (0.98 - 0.76) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 25%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 59%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.59
0.41 * (0.25 - 0.04) + 0.59 * (0.98 - 0.76) = 0.21
0.21 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 19%. For patients who are not male and have a brother, the probability of recovery is 35%. For patients who are male and do not have a brother, the probability of recovery is 81%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 58%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.19
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.58
0.42 * (0.35 - 0.19) + 0.58 * (0.98 - 0.81) = 0.17
0.17 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 19%. For patients who are not male and have a brother, the probability of recovery is 35%. For patients who are male and do not have a brother, the probability of recovery is 81%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 58%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.19
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.58
0.42 * (0.35 - 0.19) + 0.58 * (0.98 - 0.81) = 0.17
0.17 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 44%. The probability of not having a brother and recovery is 44%. The probability of having a brother and recovery is 18%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.18
0.18/0.44 - 0.44/0.56 = -0.37
-0.37 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 5%. For patients who are not male and have a brother, the probability of recovery is 25%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 48%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.48
0.52 * (0.25 - 0.05) + 0.48 * (0.97 - 0.76) = 0.20
0.20 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 8%. For patients who are not male and have a brother, the probability of recovery is 22%. For patients who are male and do not have a brother, the probability of recovery is 71%. For patients who are male and have a brother, the probability of recovery is 84%. The overall probability of male gender is 47%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.84
P(V1=1) = 0.47
0.53 * (0.22 - 0.08) + 0.47 * (0.84 - 0.71) = 0.14
0.14 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 8%. For patients who are not male and have a brother, the probability of recovery is 22%. For patients who are male and do not have a brother, the probability of recovery is 71%. For patients who are male and have a brother, the probability of recovery is 84%. The overall probability of male gender is 47%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.84
P(V1=1) = 0.47
0.53 * (0.22 - 0.08) + 0.47 * (0.84 - 0.71) = 0.14
0.14 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9533,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 8%. For patients who are not male and have a brother, the probability of recovery is 22%. For patients who are male and do not have a brother, the probability of recovery is 71%. For patients who are male and have a brother, the probability of recovery is 84%. The overall probability of male gender is 47%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.84
P(V1=1) = 0.47
0.53 * (0.22 - 0.08) + 0.47 * (0.84 - 0.71) = 0.14
0.14 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 50%. For patients who do not have a brother, the probability of recovery is 66%. For patients who have a brother, the probability of recovery is 23%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.23
0.50*0.23 - 0.50*0.66 = 0.44
0.44 > 0",confounding,simpson_drug,1,marginal,P(Y)
9536,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 50%. The probability of not having a brother and recovery is 33%. The probability of having a brother and recovery is 12%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.12
0.12/0.50 - 0.33/0.50 = -0.43
-0.43 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 1%. For patients who are not male and have a brother, the probability of recovery is 21%. For patients who are male and do not have a brother, the probability of recovery is 71%. For patients who are male and have a brother, the probability of recovery is 94%. The overall probability of male gender is 50%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.01
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.50
0.50 * (0.21 - 0.01) + 0.50 * (0.94 - 0.71) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 45%. For patients who do not have a brother, the probability of recovery is 60%. For patients who have a brother, the probability of recovery is 26%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.26
0.45*0.26 - 0.55*0.60 = 0.45
0.45 > 0",confounding,simpson_drug,1,marginal,P(Y)
9551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 15%. For patients who are not male and have a brother, the probability of recovery is 28%. For patients who are male and do not have a brother, the probability of recovery is 77%. For patients who are male and have a brother, the probability of recovery is 87%. The overall probability of male gender is 59%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.15
P(Y=1 | V1=0, X=1) = 0.28
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.87
P(V1=1) = 0.59
0.41 * (0.28 - 0.15) + 0.59 * (0.87 - 0.77) = 0.12
0.12 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 15%. For patients who are not male and have a brother, the probability of recovery is 28%. For patients who are male and do not have a brother, the probability of recovery is 77%. For patients who are male and have a brother, the probability of recovery is 87%. The overall probability of male gender is 59%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.15
P(Y=1 | V1=0, X=1) = 0.28
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.87
P(V1=1) = 0.59
0.41 * (0.28 - 0.15) + 0.59 * (0.87 - 0.77) = 0.13
0.13 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 15%. For patients who are not male and have a brother, the probability of recovery is 28%. For patients who are male and do not have a brother, the probability of recovery is 77%. For patients who are male and have a brother, the probability of recovery is 87%. The overall probability of male gender is 59%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.15
P(Y=1 | V1=0, X=1) = 0.28
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.87
P(V1=1) = 0.59
0.41 * (0.28 - 0.15) + 0.59 * (0.87 - 0.77) = 0.13
0.13 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 42%. For patients who do not have a brother, the probability of recovery is 72%. For patients who have a brother, the probability of recovery is 34%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.34
0.42*0.34 - 0.58*0.72 = 0.56
0.56 > 0",confounding,simpson_drug,1,marginal,P(Y)
9557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 42%. The probability of not having a brother and recovery is 42%. The probability of having a brother and recovery is 14%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.14
0.14/0.42 - 0.42/0.58 = -0.38
-0.38 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9558,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 6%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 78%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 53%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.53
0.47 * (0.26 - 0.06) + 0.53 * (0.99 - 0.78) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 6%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 78%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 53%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.53
0.47 * (0.26 - 0.06) + 0.53 * (0.99 - 0.78) = 0.21
0.21 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 6%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 78%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 53%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.53
0.47 * (0.26 - 0.06) + 0.53 * (0.99 - 0.78) = 0.21
0.21 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 51%. For patients who do not have a brother, the probability of recovery is 65%. For patients who have a brother, the probability of recovery is 45%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.45
0.51*0.45 - 0.49*0.65 = 0.55
0.55 > 0",confounding,simpson_drug,1,marginal,P(Y)
9566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 51%. The probability of not having a brother and recovery is 32%. The probability of having a brother and recovery is 23%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.23
0.23/0.51 - 0.32/0.49 = -0.19
-0.19 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 51%. The probability of not having a brother and recovery is 32%. The probability of having a brother and recovery is 23%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.23
0.23/0.51 - 0.32/0.49 = -0.19
-0.19 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 18%. For patients who are not male and have a brother, the probability of recovery is 31%. For patients who are male and do not have a brother, the probability of recovery is 84%. For patients who are male and have a brother, the probability of recovery is 96%. The overall probability of male gender is 56%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.18
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.56
0.44 * (0.31 - 0.18) + 0.56 * (0.96 - 0.84) = 0.13
0.13 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 41%. For patients who do not have a brother, the probability of recovery is 78%. For patients who have a brother, the probability of recovery is 33%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.33
0.41*0.33 - 0.59*0.78 = 0.60
0.60 > 0",confounding,simpson_drug,1,marginal,P(Y)
9576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 41%. The probability of not having a brother and recovery is 46%. The probability of having a brother and recovery is 14%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.14
0.14/0.41 - 0.46/0.59 = -0.45
-0.45 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 41%. The probability of not having a brother and recovery is 46%. The probability of having a brother and recovery is 14%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.14
0.14/0.41 - 0.46/0.59 = -0.45
-0.45 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9580,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 25%. For patients who are male and do not have a brother, the probability of recovery is 78%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 53%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.53
0.47 * (0.25 - 0.04) + 0.53 * (0.99 - 0.78) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 25%. For patients who are male and do not have a brother, the probability of recovery is 78%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 53%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.53
0.47 * (0.25 - 0.04) + 0.53 * (0.99 - 0.78) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 6%. For patients who are not male and have a brother, the probability of recovery is 20%. For patients who are male and do not have a brother, the probability of recovery is 71%. For patients who are male and have a brother, the probability of recovery is 88%. The overall probability of male gender is 60%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.88
P(V1=1) = 0.60
0.40 * (0.20 - 0.06) + 0.60 * (0.88 - 0.71) = 0.16
0.16 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 6%. For patients who are not male and have a brother, the probability of recovery is 20%. For patients who are male and do not have a brother, the probability of recovery is 71%. For patients who are male and have a brother, the probability of recovery is 88%. The overall probability of male gender is 60%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.88
P(V1=1) = 0.60
0.40 * (0.20 - 0.06) + 0.60 * (0.88 - 0.71) = 0.14
0.14 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9604,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 52%. For patients who do not have a brother, the probability of recovery is 64%. For patients who have a brother, the probability of recovery is 29%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.29
0.52*0.29 - 0.48*0.64 = 0.46
0.46 > 0",confounding,simpson_drug,1,marginal,P(Y)
9605,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 52%. For patients who do not have a brother, the probability of recovery is 64%. For patients who have a brother, the probability of recovery is 29%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.29
0.52*0.29 - 0.48*0.64 = 0.46
0.46 > 0",confounding,simpson_drug,1,marginal,P(Y)
9606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 52%. The probability of not having a brother and recovery is 30%. The probability of having a brother and recovery is 15%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.15
0.15/0.52 - 0.30/0.48 = -0.34
-0.34 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 49%. The probability of not having a brother and recovery is 42%. The probability of having a brother and recovery is 21%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.21
0.21/0.49 - 0.42/0.51 = -0.39
-0.39 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9620,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 6%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 78%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 47%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.47
0.53 * (0.26 - 0.06) + 0.47 * (0.98 - 0.78) = 0.20
0.20 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 6%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 78%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 47%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.47
0.53 * (0.26 - 0.06) + 0.47 * (0.98 - 0.78) = 0.20
0.20 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 6%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 78%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 47%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.47
0.53 * (0.26 - 0.06) + 0.47 * (0.98 - 0.78) = 0.20
0.20 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 64%. The probability of not having a brother and recovery is 27%. The probability of having a brother and recovery is 25%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.25
0.25/0.64 - 0.27/0.36 = -0.35
-0.35 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 64%. The probability of not having a brother and recovery is 27%. The probability of having a brother and recovery is 25%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.25
0.25/0.64 - 0.27/0.36 = -0.35
-0.35 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 59%. For patients who do not have a brother, the probability of recovery is 65%. For patients who have a brother, the probability of recovery is 26%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.26
0.59*0.26 - 0.41*0.65 = 0.43
0.43 > 0",confounding,simpson_drug,1,marginal,P(Y)
9636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 59%. The probability of not having a brother and recovery is 27%. The probability of having a brother and recovery is 15%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.15
0.15/0.59 - 0.27/0.41 = -0.39
-0.39 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9640,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 0%. For patients who are not male and have a brother, the probability of recovery is 22%. For patients who are male and do not have a brother, the probability of recovery is 73%. For patients who are male and have a brother, the probability of recovery is 94%. The overall probability of male gender is 46%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.73
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.46
0.54 * (0.22 - 0.00) + 0.46 * (0.94 - 0.73) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 0%. For patients who are not male and have a brother, the probability of recovery is 22%. For patients who are male and do not have a brother, the probability of recovery is 73%. For patients who are male and have a brother, the probability of recovery is 94%. The overall probability of male gender is 46%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.73
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.46
0.54 * (0.22 - 0.00) + 0.46 * (0.94 - 0.73) = 0.21
0.21 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 45%. For patients who do not have a brother, the probability of recovery is 61%. For patients who have a brother, the probability of recovery is 22%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.22
0.45*0.22 - 0.55*0.61 = 0.43
0.43 > 0",confounding,simpson_drug,1,marginal,P(Y)
9650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 24%. For patients who are not male and have a brother, the probability of recovery is 41%. For patients who are male and do not have a brother, the probability of recovery is 87%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 42%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.24
P(Y=1 | V1=0, X=1) = 0.41
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.42
0.58 * (0.41 - 0.24) + 0.42 * (0.97 - 0.87) = 0.14
0.14 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9652,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 24%. For patients who are not male and have a brother, the probability of recovery is 41%. For patients who are male and do not have a brother, the probability of recovery is 87%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 42%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.24
P(Y=1 | V1=0, X=1) = 0.41
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.42
0.58 * (0.41 - 0.24) + 0.42 * (0.97 - 0.87) = 0.17
0.17 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9654,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 58%. For patients who do not have a brother, the probability of recovery is 82%. For patients who have a brother, the probability of recovery is 44%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.44
0.58*0.44 - 0.42*0.82 = 0.59
0.59 > 0",confounding,simpson_drug,1,marginal,P(Y)
9657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 58%. The probability of not having a brother and recovery is 34%. The probability of having a brother and recovery is 26%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.26
0.26/0.58 - 0.34/0.42 = -0.38
-0.38 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 4%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 77%. For patients who are male and have a brother, the probability of recovery is 98%. The overall probability of male gender is 56%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.56
0.44 * (0.26 - 0.04) + 0.56 * (0.98 - 0.77) = 0.22
0.22 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 50%. For patients who do not have a brother, the probability of recovery is 74%. For patients who have a brother, the probability of recovery is 36%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.36
0.50*0.36 - 0.50*0.74 = 0.55
0.55 > 0",confounding,simpson_drug,1,marginal,P(Y)
9665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 50%. For patients who do not have a brother, the probability of recovery is 74%. For patients who have a brother, the probability of recovery is 36%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.36
0.50*0.36 - 0.50*0.74 = 0.55
0.55 > 0",confounding,simpson_drug,1,marginal,P(Y)
9669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9670,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 8%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 84%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 53%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.53
0.47 * (0.26 - 0.08) + 0.53 * (0.99 - 0.84) = 0.16
0.16 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 8%. For patients who are not male and have a brother, the probability of recovery is 26%. For patients who are male and do not have a brother, the probability of recovery is 84%. For patients who are male and have a brother, the probability of recovery is 99%. The overall probability of male gender is 53%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.53
0.47 * (0.26 - 0.08) + 0.53 * (0.99 - 0.84) = 0.16
0.16 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 49%. The probability of not having a brother and recovery is 40%. The probability of having a brother and recovery is 17%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.17
0.17/0.49 - 0.40/0.51 = -0.45
-0.45 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 49%. The probability of not having a brother and recovery is 40%. The probability of having a brother and recovery is 17%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.17
0.17/0.49 - 0.40/0.51 = -0.45
-0.45 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 3%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 75%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 50%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.75
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.50
0.50 * (0.24 - 0.03) + 0.50 * (0.97 - 0.75) = 0.21
0.21 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 3%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 75%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 50%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.75
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.50
0.50 * (0.24 - 0.03) + 0.50 * (0.97 - 0.75) = 0.21
0.21 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 46%. For patients who do not have a brother, the probability of recovery is 62%. For patients who have a brother, the probability of recovery is 34%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.34
0.46*0.34 - 0.54*0.62 = 0.49
0.49 > 0",confounding,simpson_drug,1,marginal,P(Y)
9686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 46%. The probability of not having a brother and recovery is 33%. The probability of having a brother and recovery is 16%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.16
0.16/0.46 - 0.33/0.54 = -0.28
-0.28 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 2%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 74%. For patients who are male and have a brother, the probability of recovery is 93%. The overall probability of male gender is 56%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.74
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.56
0.44 * (0.24 - 0.02) + 0.56 * (0.93 - 0.74) = 0.20
0.20 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9692,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 2%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 74%. For patients who are male and have a brother, the probability of recovery is 93%. The overall probability of male gender is 56%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.74
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.56
0.44 * (0.24 - 0.02) + 0.56 * (0.93 - 0.74) = 0.22
0.22 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9693,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 2%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 74%. For patients who are male and have a brother, the probability of recovery is 93%. The overall probability of male gender is 56%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.74
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.56
0.44 * (0.24 - 0.02) + 0.56 * (0.93 - 0.74) = 0.22
0.22 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 41%. For patients who do not have a brother, the probability of recovery is 71%. For patients who have a brother, the probability of recovery is 24%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.24
0.41*0.24 - 0.59*0.71 = 0.51
0.51 > 0",confounding,simpson_drug,1,marginal,P(Y)
9695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 41%. For patients who do not have a brother, the probability of recovery is 71%. For patients who have a brother, the probability of recovery is 24%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.24
0.41*0.24 - 0.59*0.71 = 0.51
0.51 > 0",confounding,simpson_drug,1,marginal,P(Y)
9697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 41%. The probability of not having a brother and recovery is 42%. The probability of having a brother and recovery is 10%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.10
0.10/0.41 - 0.42/0.59 = -0.47
-0.47 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look directly at how having a brother correlates with recovery in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. Method 1: We look at how having a brother correlates with recovery case by case according to gender. Method 2: We look directly at how having a brother correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
9702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 1%. For patients who are not male and have a brother, the probability of recovery is 21%. For patients who are male and do not have a brother, the probability of recovery is 71%. For patients who are male and have a brother, the probability of recovery is 90%. The overall probability of male gender is 50%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.01
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.50
0.50 * (0.21 - 0.01) + 0.50 * (0.90 - 0.71) = 0.20
0.20 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9703,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 1%. For patients who are not male and have a brother, the probability of recovery is 21%. For patients who are male and do not have a brother, the probability of recovery is 71%. For patients who are male and have a brother, the probability of recovery is 90%. The overall probability of male gender is 50%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.01
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.50
0.50 * (0.21 - 0.01) + 0.50 * (0.90 - 0.71) = 0.20
0.20 > 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 51%. The probability of not having a brother and recovery is 32%. The probability of having a brother and recovery is 14%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.14
0.14/0.51 - 0.32/0.49 = -0.39
-0.39 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 51%. The probability of not having a brother and recovery is 32%. The probability of having a brother and recovery is 14%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.14
0.14/0.51 - 0.32/0.49 = -0.39
-0.39 < 0",confounding,simpson_drug,1,correlation,P(Y | X)
9710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 2%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 51%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.51
0.49 * (0.24 - 0.02) + 0.51 * (0.97 - 0.76) = 0.22
0.22 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. For patients who are not male and do not have a brother, the probability of recovery is 2%. For patients who are not male and have a brother, the probability of recovery is 24%. For patients who are male and do not have a brother, the probability of recovery is 76%. For patients who are male and have a brother, the probability of recovery is 97%. The overall probability of male gender is 51%.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.51
0.49 * (0.24 - 0.02) + 0.51 * (0.97 - 0.76) = 0.22
0.22 > 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. The overall probability of having a brother is 45%. For patients who do not have a brother, the probability of recovery is 61%. For patients who have a brother, the probability of recovery is 36%.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.36
0.45*0.36 - 0.55*0.61 = 0.49
0.49 > 0",confounding,simpson_drug,1,marginal,P(Y)
9721,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 15%. For patients who are young and pay a high hospital bill, the probability of freckles is 23%. For patients who are old and pay a low hospital bill, the probability of freckles is 85%. For patients who are old and pay a high hospital bill, the probability of freckles is 92%. The overall probability of old age is 49%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.15
P(Y=1 | V1=0, X=1) = 0.23
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.49
0.51 * (0.23 - 0.15) + 0.49 * (0.92 - 0.85) = 0.08
0.08 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. For patients who pay a low hospital bill, the probability of freckles is 76%. For people who pay a high hospital bill, the probability of freckles is 33%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.33
0.51*0.33 - 0.49*0.76 = 0.54
0.54 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. The probability of low hospital bill and freckles is 37%. The probability of high hospital bill and freckles is 17%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.17
0.17/0.51 - 0.37/0.49 = -0.44
-0.44 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. The probability of low hospital bill and freckles is 37%. The probability of high hospital bill and freckles is 17%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.17
0.17/0.51 - 0.37/0.49 = -0.44
-0.44 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9732,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 3%. For patients who are young and pay a high hospital bill, the probability of freckles is 13%. For patients who are old and pay a low hospital bill, the probability of freckles is 79%. For patients who are old and pay a high hospital bill, the probability of freckles is 93%. The overall probability of old age is 44%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.13
P(Y=1 | V1=1, X=0) = 0.79
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.44
0.56 * (0.13 - 0.03) + 0.44 * (0.93 - 0.79) = 0.11
0.11 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 45%. For patients who pay a low hospital bill, the probability of freckles is 58%. For people who pay a high hospital bill, the probability of freckles is 18%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.18
0.45*0.18 - 0.55*0.58 = 0.41
0.41 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 46%. The probability of low hospital bill and freckles is 34%. The probability of high hospital bill and freckles is 8%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.08
0.08/0.46 - 0.34/0.54 = -0.45
-0.45 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 46%. The probability of low hospital bill and freckles is 34%. The probability of high hospital bill and freckles is 8%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.08
0.08/0.46 - 0.34/0.54 = -0.45
-0.45 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9753,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 8%. For patients who are young and pay a high hospital bill, the probability of freckles is 19%. For patients who are old and pay a low hospital bill, the probability of freckles is 81%. For patients who are old and pay a high hospital bill, the probability of freckles is 92%. The overall probability of old age is 45%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.45
0.55 * (0.19 - 0.08) + 0.45 * (0.92 - 0.81) = 0.11
0.11 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 59%. For patients who pay a low hospital bill, the probability of freckles is 59%. For people who pay a high hospital bill, the probability of freckles is 38%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.38
0.59*0.38 - 0.41*0.59 = 0.47
0.47 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 59%. For patients who pay a low hospital bill, the probability of freckles is 59%. For people who pay a high hospital bill, the probability of freckles is 38%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.38
0.59*0.38 - 0.41*0.59 = 0.47
0.47 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 59%. The probability of low hospital bill and freckles is 24%. The probability of high hospital bill and freckles is 22%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.22
0.22/0.59 - 0.24/0.41 = -0.21
-0.21 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 17%. For patients who are young and pay a high hospital bill, the probability of freckles is 22%. For patients who are old and pay a low hospital bill, the probability of freckles is 81%. For patients who are old and pay a high hospital bill, the probability of freckles is 91%. The overall probability of old age is 42%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.17
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.42
0.58 * (0.22 - 0.17) + 0.42 * (0.91 - 0.81) = 0.07
0.07 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 53%. The probability of low hospital bill and freckles is 33%. The probability of high hospital bill and freckles is 14%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.14
0.14/0.53 - 0.33/0.47 = -0.43
-0.43 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 53%. The probability of low hospital bill and freckles is 33%. The probability of high hospital bill and freckles is 14%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.14
0.14/0.53 - 0.33/0.47 = -0.43
-0.43 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9770,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 12%. For patients who are young and pay a high hospital bill, the probability of freckles is 23%. For patients who are old and pay a low hospital bill, the probability of freckles is 87%. For patients who are old and pay a high hospital bill, the probability of freckles is 99%. The overall probability of old age is 45%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.12
P(Y=1 | V1=0, X=1) = 0.23
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.45
0.55 * (0.23 - 0.12) + 0.45 * (0.99 - 0.87) = 0.11
0.11 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 12%. For patients who are young and pay a high hospital bill, the probability of freckles is 23%. For patients who are old and pay a low hospital bill, the probability of freckles is 87%. For patients who are old and pay a high hospital bill, the probability of freckles is 99%. The overall probability of old age is 45%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.12
P(Y=1 | V1=0, X=1) = 0.23
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.45
0.55 * (0.23 - 0.12) + 0.45 * (0.99 - 0.87) = 0.11
0.11 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 48%. For patients who pay a low hospital bill, the probability of freckles is 68%. For people who pay a high hospital bill, the probability of freckles is 34%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.34
0.48*0.34 - 0.52*0.68 = 0.52
0.52 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 5%. For patients who are young and pay a high hospital bill, the probability of freckles is 11%. For patients who are old and pay a low hospital bill, the probability of freckles is 71%. For patients who are old and pay a high hospital bill, the probability of freckles is 83%. The overall probability of old age is 48%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.11
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.83
P(V1=1) = 0.48
0.52 * (0.11 - 0.05) + 0.48 * (0.83 - 0.71) = 0.09
0.09 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 5%. For patients who are young and pay a high hospital bill, the probability of freckles is 11%. For patients who are old and pay a low hospital bill, the probability of freckles is 71%. For patients who are old and pay a high hospital bill, the probability of freckles is 83%. The overall probability of old age is 48%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.11
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.83
P(V1=1) = 0.48
0.52 * (0.11 - 0.05) + 0.48 * (0.83 - 0.71) = 0.07
0.07 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. For patients who pay a low hospital bill, the probability of freckles is 61%. For people who pay a high hospital bill, the probability of freckles is 20%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.20
0.51*0.20 - 0.49*0.61 = 0.41
0.41 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. For patients who pay a low hospital bill, the probability of freckles is 61%. For people who pay a high hospital bill, the probability of freckles is 20%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.20
0.51*0.20 - 0.49*0.61 = 0.41
0.41 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. The probability of low hospital bill and freckles is 30%. The probability of high hospital bill and freckles is 10%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.10
0.10/0.51 - 0.30/0.49 = -0.41
-0.41 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9790,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 7%. For patients who are young and pay a high hospital bill, the probability of freckles is 17%. For patients who are old and pay a low hospital bill, the probability of freckles is 80%. For patients who are old and pay a high hospital bill, the probability of freckles is 92%. The overall probability of old age is 54%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.17
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.54
0.46 * (0.17 - 0.07) + 0.54 * (0.92 - 0.80) = 0.11
0.11 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. For patients who pay a low hospital bill, the probability of freckles is 72%. For people who pay a high hospital bill, the probability of freckles is 32%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.32
0.51*0.32 - 0.49*0.72 = 0.52
0.52 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 6%. For patients who are young and pay a high hospital bill, the probability of freckles is 16%. For patients who are old and pay a low hospital bill, the probability of freckles is 76%. For patients who are old and pay a high hospital bill, the probability of freckles is 82%. The overall probability of old age is 51%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.16
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.82
P(V1=1) = 0.51
0.49 * (0.16 - 0.06) + 0.51 * (0.82 - 0.76) = 0.08
0.08 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 47%. For patients who pay a low hospital bill, the probability of freckles is 68%. For people who pay a high hospital bill, the probability of freckles is 21%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.21
0.47*0.21 - 0.53*0.68 = 0.45
0.45 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 1%. For patients who are young and pay a high hospital bill, the probability of freckles is 14%. For patients who are old and pay a low hospital bill, the probability of freckles is 76%. For patients who are old and pay a high hospital bill, the probability of freckles is 88%. The overall probability of old age is 59%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.01
P(Y=1 | V1=0, X=1) = 0.14
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.88
P(V1=1) = 0.59
0.41 * (0.14 - 0.01) + 0.59 * (0.88 - 0.76) = 0.12
0.12 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 49%. The probability of low hospital bill and freckles is 34%. The probability of high hospital bill and freckles is 17%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.17
0.17/0.49 - 0.34/0.51 = -0.33
-0.33 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 9%. For patients who are young and pay a high hospital bill, the probability of freckles is 21%. For patients who are old and pay a low hospital bill, the probability of freckles is 78%. For patients who are old and pay a high hospital bill, the probability of freckles is 84%. The overall probability of old age is 51%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.09
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.84
P(V1=1) = 0.51
0.49 * (0.21 - 0.09) + 0.51 * (0.84 - 0.78) = 0.09
0.09 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 53%. The probability of low hospital bill and freckles is 34%. The probability of high hospital bill and freckles is 16%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.16
0.16/0.53 - 0.34/0.47 = -0.43
-0.43 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 6%. For patients who are young and pay a high hospital bill, the probability of freckles is 18%. For patients who are old and pay a low hospital bill, the probability of freckles is 81%. For patients who are old and pay a high hospital bill, the probability of freckles is 93%. The overall probability of old age is 46%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.46
0.54 * (0.18 - 0.06) + 0.46 * (0.93 - 0.81) = 0.12
0.12 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9833,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 6%. For patients who are young and pay a high hospital bill, the probability of freckles is 18%. For patients who are old and pay a low hospital bill, the probability of freckles is 81%. For patients who are old and pay a high hospital bill, the probability of freckles is 93%. The overall probability of old age is 46%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.46
0.54 * (0.18 - 0.06) + 0.46 * (0.93 - 0.81) = 0.12
0.12 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9835,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 56%. For patients who pay a low hospital bill, the probability of freckles is 67%. For people who pay a high hospital bill, the probability of freckles is 32%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.32
0.56*0.32 - 0.44*0.67 = 0.48
0.48 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 56%. The probability of low hospital bill and freckles is 30%. The probability of high hospital bill and freckles is 18%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.18
0.18/0.56 - 0.30/0.44 = -0.36
-0.36 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 56%. The probability of low hospital bill and freckles is 30%. The probability of high hospital bill and freckles is 18%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.18
0.18/0.56 - 0.30/0.44 = -0.36
-0.36 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9840,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 15%. For patients who are young and pay a high hospital bill, the probability of freckles is 21%. For patients who are old and pay a low hospital bill, the probability of freckles is 82%. For patients who are old and pay a high hospital bill, the probability of freckles is 90%. The overall probability of old age is 58%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.15
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.82
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.58
0.42 * (0.21 - 0.15) + 0.58 * (0.90 - 0.82) = 0.08
0.08 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 15%. For patients who are young and pay a high hospital bill, the probability of freckles is 21%. For patients who are old and pay a low hospital bill, the probability of freckles is 82%. For patients who are old and pay a high hospital bill, the probability of freckles is 90%. The overall probability of old age is 58%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.15
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.82
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.58
0.42 * (0.21 - 0.15) + 0.58 * (0.90 - 0.82) = 0.08
0.08 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 15%. For patients who are young and pay a high hospital bill, the probability of freckles is 21%. For patients who are old and pay a low hospital bill, the probability of freckles is 82%. For patients who are old and pay a high hospital bill, the probability of freckles is 90%. The overall probability of old age is 58%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.15
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.82
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.58
0.42 * (0.21 - 0.15) + 0.58 * (0.90 - 0.82) = 0.07
0.07 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9844,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 39%. For patients who pay a low hospital bill, the probability of freckles is 78%. For people who pay a high hospital bill, the probability of freckles is 21%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.21
0.39*0.21 - 0.61*0.78 = 0.57
0.57 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 39%. For patients who pay a low hospital bill, the probability of freckles is 78%. For people who pay a high hospital bill, the probability of freckles is 21%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.21
0.39*0.21 - 0.61*0.78 = 0.57
0.57 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 9%. For patients who are young and pay a high hospital bill, the probability of freckles is 22%. For patients who are old and pay a low hospital bill, the probability of freckles is 85%. For patients who are old and pay a high hospital bill, the probability of freckles is 97%. The overall probability of old age is 41%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.09
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.41
0.59 * (0.22 - 0.09) + 0.41 * (0.97 - 0.85) = 0.12
0.12 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 9%. For patients who are young and pay a high hospital bill, the probability of freckles is 22%. For patients who are old and pay a low hospital bill, the probability of freckles is 85%. For patients who are old and pay a high hospital bill, the probability of freckles is 97%. The overall probability of old age is 41%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.09
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.41
0.59 * (0.22 - 0.09) + 0.41 * (0.97 - 0.85) = 0.12
0.12 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 66%. For patients who pay a low hospital bill, the probability of freckles is 63%. For people who pay a high hospital bill, the probability of freckles is 41%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.41
0.66*0.41 - 0.34*0.63 = 0.48
0.48 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 66%. For patients who pay a low hospital bill, the probability of freckles is 63%. For people who pay a high hospital bill, the probability of freckles is 41%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.41
0.66*0.41 - 0.34*0.63 = 0.48
0.48 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 1%. For patients who are young and pay a high hospital bill, the probability of freckles is 10%. For patients who are old and pay a low hospital bill, the probability of freckles is 70%. For patients who are old and pay a high hospital bill, the probability of freckles is 75%. The overall probability of old age is 44%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.01
P(Y=1 | V1=0, X=1) = 0.10
P(Y=1 | V1=1, X=0) = 0.70
P(Y=1 | V1=1, X=1) = 0.75
P(V1=1) = 0.44
0.56 * (0.10 - 0.01) + 0.44 * (0.75 - 0.70) = 0.08
0.08 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9862,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 1%. For patients who are young and pay a high hospital bill, the probability of freckles is 10%. For patients who are old and pay a low hospital bill, the probability of freckles is 70%. For patients who are old and pay a high hospital bill, the probability of freckles is 75%. The overall probability of old age is 44%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.01
P(Y=1 | V1=0, X=1) = 0.10
P(Y=1 | V1=1, X=0) = 0.70
P(Y=1 | V1=1, X=1) = 0.75
P(V1=1) = 0.44
0.56 * (0.10 - 0.01) + 0.44 * (0.75 - 0.70) = 0.09
0.09 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 56%. For patients who pay a low hospital bill, the probability of freckles is 62%. For people who pay a high hospital bill, the probability of freckles is 16%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.16
0.56*0.16 - 0.44*0.62 = 0.35
0.35 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9866,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 56%. The probability of low hospital bill and freckles is 27%. The probability of high hospital bill and freckles is 9%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.09
0.09/0.56 - 0.27/0.44 = -0.46
-0.46 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 52%. For patients who pay a low hospital bill, the probability of freckles is 66%. For people who pay a high hospital bill, the probability of freckles is 38%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.38
0.52*0.38 - 0.48*0.66 = 0.52
0.52 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 8%. For patients who are young and pay a high hospital bill, the probability of freckles is 17%. For patients who are old and pay a low hospital bill, the probability of freckles is 76%. For patients who are old and pay a high hospital bill, the probability of freckles is 90%. The overall probability of old age is 46%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.17
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.46
0.54 * (0.17 - 0.08) + 0.46 * (0.90 - 0.76) = 0.09
0.09 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9884,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 50%. For patients who pay a low hospital bill, the probability of freckles is 67%. For people who pay a high hospital bill, the probability of freckles is 21%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.21
0.50*0.21 - 0.50*0.67 = 0.45
0.45 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 50%. For patients who pay a low hospital bill, the probability of freckles is 67%. For people who pay a high hospital bill, the probability of freckles is 21%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.21
0.50*0.21 - 0.50*0.67 = 0.45
0.45 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9892,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 3%. For patients who are young and pay a high hospital bill, the probability of freckles is 14%. For patients who are old and pay a low hospital bill, the probability of freckles is 77%. For patients who are old and pay a high hospital bill, the probability of freckles is 92%. The overall probability of old age is 59%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.14
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.59
0.41 * (0.14 - 0.03) + 0.59 * (0.92 - 0.77) = 0.12
0.12 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 3%. For patients who are young and pay a high hospital bill, the probability of freckles is 14%. For patients who are old and pay a low hospital bill, the probability of freckles is 77%. For patients who are old and pay a high hospital bill, the probability of freckles is 92%. The overall probability of old age is 59%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.14
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.59
0.41 * (0.14 - 0.03) + 0.59 * (0.92 - 0.77) = 0.12
0.12 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 46%. The probability of low hospital bill and freckles is 33%. The probability of high hospital bill and freckles is 20%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.20
0.20/0.46 - 0.33/0.54 = -0.18
-0.18 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 10%. For patients who are young and pay a high hospital bill, the probability of freckles is 18%. For patients who are old and pay a low hospital bill, the probability of freckles is 76%. For patients who are old and pay a high hospital bill, the probability of freckles is 87%. The overall probability of old age is 42%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.10
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.87
P(V1=1) = 0.42
0.58 * (0.18 - 0.10) + 0.42 * (0.87 - 0.76) = 0.08
0.08 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 57%. For patients who pay a low hospital bill, the probability of freckles is 69%. For people who pay a high hospital bill, the probability of freckles is 22%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.22
0.57*0.22 - 0.43*0.69 = 0.43
0.43 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9907,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 57%. The probability of low hospital bill and freckles is 29%. The probability of high hospital bill and freckles is 13%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.13
0.13/0.57 - 0.29/0.43 = -0.46
-0.46 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 5%. For patients who are young and pay a high hospital bill, the probability of freckles is 19%. For patients who are old and pay a low hospital bill, the probability of freckles is 80%. For patients who are old and pay a high hospital bill, the probability of freckles is 93%. The overall probability of old age is 42%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.42
0.58 * (0.19 - 0.05) + 0.42 * (0.93 - 0.80) = 0.14
0.14 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 5%. For patients who are young and pay a high hospital bill, the probability of freckles is 19%. For patients who are old and pay a low hospital bill, the probability of freckles is 80%. For patients who are old and pay a high hospital bill, the probability of freckles is 93%. The overall probability of old age is 42%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.42
0.58 * (0.19 - 0.05) + 0.42 * (0.93 - 0.80) = 0.14
0.14 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 4%. For patients who are young and pay a high hospital bill, the probability of freckles is 17%. For patients who are old and pay a low hospital bill, the probability of freckles is 84%. For patients who are old and pay a high hospital bill, the probability of freckles is 89%. The overall probability of old age is 46%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.17
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.89
P(V1=1) = 0.46
0.54 * (0.17 - 0.04) + 0.46 * (0.89 - 0.84) = 0.10
0.10 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 4%. For patients who are young and pay a high hospital bill, the probability of freckles is 17%. For patients who are old and pay a low hospital bill, the probability of freckles is 84%. For patients who are old and pay a high hospital bill, the probability of freckles is 89%. The overall probability of old age is 46%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.17
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.89
P(V1=1) = 0.46
0.54 * (0.17 - 0.04) + 0.46 * (0.89 - 0.84) = 0.13
0.13 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 58%. For patients who pay a low hospital bill, the probability of freckles is 79%. For people who pay a high hospital bill, the probability of freckles is 26%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.26
0.58*0.26 - 0.42*0.79 = 0.47
0.47 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 58%. The probability of low hospital bill and freckles is 33%. The probability of high hospital bill and freckles is 15%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.15
0.15/0.58 - 0.33/0.42 = -0.53
-0.53 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 58%. The probability of low hospital bill and freckles is 33%. The probability of high hospital bill and freckles is 15%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.15
0.15/0.58 - 0.33/0.42 = -0.53
-0.53 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 1%. For patients who are young and pay a high hospital bill, the probability of freckles is 14%. For patients who are old and pay a low hospital bill, the probability of freckles is 76%. For patients who are old and pay a high hospital bill, the probability of freckles is 89%. The overall probability of old age is 54%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.01
P(Y=1 | V1=0, X=1) = 0.14
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.89
P(V1=1) = 0.54
0.46 * (0.14 - 0.01) + 0.54 * (0.89 - 0.76) = 0.13
0.13 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. For patients who pay a low hospital bill, the probability of freckles is 67%. For people who pay a high hospital bill, the probability of freckles is 30%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.30
0.51*0.30 - 0.49*0.67 = 0.48
0.48 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 51%. The probability of low hospital bill and freckles is 33%. The probability of high hospital bill and freckles is 15%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.15
0.15/0.51 - 0.33/0.49 = -0.37
-0.37 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 0%. For patients who are young and pay a high hospital bill, the probability of freckles is 11%. For patients who are old and pay a low hospital bill, the probability of freckles is 75%. For patients who are old and pay a high hospital bill, the probability of freckles is 83%. The overall probability of old age is 57%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.11
P(Y=1 | V1=1, X=0) = 0.75
P(Y=1 | V1=1, X=1) = 0.83
P(V1=1) = 0.57
0.43 * (0.11 - 0.00) + 0.57 * (0.83 - 0.75) = 0.09
0.09 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 0%. For patients who are young and pay a high hospital bill, the probability of freckles is 11%. For patients who are old and pay a low hospital bill, the probability of freckles is 75%. For patients who are old and pay a high hospital bill, the probability of freckles is 83%. The overall probability of old age is 57%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.11
P(Y=1 | V1=1, X=0) = 0.75
P(Y=1 | V1=1, X=1) = 0.83
P(V1=1) = 0.57
0.43 * (0.11 - 0.00) + 0.57 * (0.83 - 0.75) = 0.11
0.11 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 0%. For patients who are young and pay a high hospital bill, the probability of freckles is 11%. For patients who are old and pay a low hospital bill, the probability of freckles is 75%. For patients who are old and pay a high hospital bill, the probability of freckles is 83%. The overall probability of old age is 57%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.11
P(Y=1 | V1=1, X=0) = 0.75
P(Y=1 | V1=1, X=1) = 0.83
P(V1=1) = 0.57
0.43 * (0.11 - 0.00) + 0.57 * (0.83 - 0.75) = 0.11
0.11 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 40%. For patients who pay a low hospital bill, the probability of freckles is 70%. For people who pay a high hospital bill, the probability of freckles is 13%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.13
0.40*0.13 - 0.60*0.70 = 0.46
0.46 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 40%. For patients who pay a low hospital bill, the probability of freckles is 70%. For people who pay a high hospital bill, the probability of freckles is 13%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.13
0.40*0.13 - 0.60*0.70 = 0.46
0.46 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 2%. For patients who are young and pay a high hospital bill, the probability of freckles is 17%. For patients who are old and pay a low hospital bill, the probability of freckles is 81%. For patients who are old and pay a high hospital bill, the probability of freckles is 96%. The overall probability of old age is 45%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.17
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.45
0.55 * (0.17 - 0.02) + 0.45 * (0.96 - 0.81) = 0.15
0.15 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 2%. For patients who are young and pay a high hospital bill, the probability of freckles is 17%. For patients who are old and pay a low hospital bill, the probability of freckles is 81%. For patients who are old and pay a high hospital bill, the probability of freckles is 96%. The overall probability of old age is 45%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.17
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.45
0.55 * (0.17 - 0.02) + 0.45 * (0.96 - 0.81) = 0.15
0.15 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 39%. The probability of low hospital bill and freckles is 36%. The probability of high hospital bill and freckles is 8%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.08
0.08/0.39 - 0.36/0.61 = -0.38
-0.38 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 20%. For patients who are young and pay a high hospital bill, the probability of freckles is 31%. For patients who are old and pay a low hospital bill, the probability of freckles is 87%. For patients who are old and pay a high hospital bill, the probability of freckles is 99%. The overall probability of old age is 47%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.20
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.47
0.53 * (0.31 - 0.20) + 0.47 * (0.99 - 0.87) = 0.12
0.12 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 20%. For patients who are young and pay a high hospital bill, the probability of freckles is 31%. For patients who are old and pay a low hospital bill, the probability of freckles is 87%. For patients who are old and pay a high hospital bill, the probability of freckles is 99%. The overall probability of old age is 47%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.20
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.47
0.53 * (0.31 - 0.20) + 0.47 * (0.99 - 0.87) = 0.12
0.12 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 20%. For patients who are young and pay a high hospital bill, the probability of freckles is 31%. For patients who are old and pay a low hospital bill, the probability of freckles is 87%. For patients who are old and pay a high hospital bill, the probability of freckles is 99%. The overall probability of old age is 47%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.20
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.47
0.53 * (0.31 - 0.20) + 0.47 * (0.99 - 0.87) = 0.12
0.12 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 53%. The probability of low hospital bill and freckles is 39%. The probability of high hospital bill and freckles is 19%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.19
0.19/0.53 - 0.39/0.47 = -0.47
-0.47 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 5%. For patients who are young and pay a high hospital bill, the probability of freckles is 17%. For patients who are old and pay a low hospital bill, the probability of freckles is 80%. For patients who are old and pay a high hospital bill, the probability of freckles is 91%. The overall probability of old age is 55%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.17
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.55
0.45 * (0.17 - 0.05) + 0.55 * (0.91 - 0.80) = 0.11
0.11 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
9975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 72%. For patients who pay a low hospital bill, the probability of freckles is 77%. For people who pay a high hospital bill, the probability of freckles is 46%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.72
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.46
0.72*0.46 - 0.28*0.77 = 0.54
0.54 > 0",confounding,simpson_hospital,1,marginal,P(Y)
9978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
9981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 11%. For patients who are young and pay a high hospital bill, the probability of freckles is 19%. For patients who are old and pay a low hospital bill, the probability of freckles is 78%. For patients who are old and pay a high hospital bill, the probability of freckles is 92%. The overall probability of old age is 52%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.11
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.52
0.48 * (0.19 - 0.11) + 0.52 * (0.92 - 0.78) = 0.11
0.11 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 47%. The probability of low hospital bill and freckles is 37%. The probability of high hospital bill and freckles is 13%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.13
0.13/0.47 - 0.37/0.53 = -0.42
-0.42 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 7%. For patients who are young and pay a high hospital bill, the probability of freckles is 18%. For patients who are old and pay a low hospital bill, the probability of freckles is 80%. For patients who are old and pay a high hospital bill, the probability of freckles is 92%. The overall probability of old age is 51%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.51
0.49 * (0.18 - 0.07) + 0.51 * (0.92 - 0.80) = 0.12
0.12 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
9997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 49%. The probability of low hospital bill and freckles is 33%. The probability of high hospital bill and freckles is 17%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.17
0.17/0.49 - 0.33/0.51 = -0.29
-0.29 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
9999,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
10000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 12%. For patients who are young and pay a high hospital bill, the probability of freckles is 23%. For patients who are old and pay a low hospital bill, the probability of freckles is 82%. For patients who are old and pay a high hospital bill, the probability of freckles is 89%. The overall probability of old age is 51%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.12
P(Y=1 | V1=0, X=1) = 0.23
P(Y=1 | V1=1, X=0) = 0.82
P(Y=1 | V1=1, X=1) = 0.89
P(V1=1) = 0.51
0.49 * (0.23 - 0.12) + 0.51 * (0.89 - 0.82) = 0.09
0.09 > 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10002,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 12%. For patients who are young and pay a high hospital bill, the probability of freckles is 23%. For patients who are old and pay a low hospital bill, the probability of freckles is 82%. For patients who are old and pay a high hospital bill, the probability of freckles is 89%. The overall probability of old age is 51%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.12
P(Y=1 | V1=0, X=1) = 0.23
P(Y=1 | V1=1, X=0) = 0.82
P(Y=1 | V1=1, X=1) = 0.89
P(V1=1) = 0.51
0.49 * (0.23 - 0.12) + 0.51 * (0.89 - 0.82) = 0.11
0.11 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10003,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 12%. For patients who are young and pay a high hospital bill, the probability of freckles is 23%. For patients who are old and pay a low hospital bill, the probability of freckles is 82%. For patients who are old and pay a high hospital bill, the probability of freckles is 89%. The overall probability of old age is 51%.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.12
P(Y=1 | V1=0, X=1) = 0.23
P(Y=1 | V1=1, X=0) = 0.82
P(Y=1 | V1=1, X=1) = 0.89
P(V1=1) = 0.51
0.49 * (0.23 - 0.12) + 0.51 * (0.89 - 0.82) = 0.11
0.11 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 53%. For patients who pay a low hospital bill, the probability of freckles is 78%. For people who pay a high hospital bill, the probability of freckles is 31%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.31
0.53*0.31 - 0.47*0.78 = 0.53
0.53 > 0",confounding,simpson_hospital,1,marginal,P(Y)
10008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look directly at how hospital costs correlates with freckles in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
10009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
10012,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. For patients who are young and pay a low hospital bill, the probability of freckles is 8%. For patients who are young and pay a high hospital bill, the probability of freckles is 20%. For patients who are old and pay a low hospital bill, the probability of freckles is 81%. For patients who are old and pay a high hospital bill, the probability of freckles is 94%. The overall probability of old age is 42%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.42
0.58 * (0.20 - 0.08) + 0.42 * (0.94 - 0.81) = 0.12
0.12 > 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. The overall probability of high hospital bill is 57%. The probability of low hospital bill and freckles is 25%. The probability of high hospital bill and freckles is 20%.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.20
0.20/0.57 - 0.25/0.43 = -0.23
-0.23 < 0",confounding,simpson_hospital,1,correlation,P(Y | X)
10019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. Method 1: We look at how hospital costs correlates with freckles case by case according to age. Method 2: We look directly at how hospital costs correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
10022,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 34%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 62%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 94%. The overall probability of large kidney stone is 42%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.34
P(Y=1 | V1=1, X=0) = 0.62
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.42
0.58 * (0.34 - 0.04) + 0.42 * (0.94 - 0.62) = 0.30
0.30 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 57%. For patients not receiving treatment, the probability of thick lips is 57%. For patients receiving treatment, the probability of thick lips is 37%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.37
0.57*0.37 - 0.43*0.57 = 0.46
0.46 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 57%. For patients not receiving treatment, the probability of thick lips is 57%. For patients receiving treatment, the probability of thick lips is 37%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.37
0.57*0.37 - 0.43*0.57 = 0.46
0.46 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 57%. The probability of receives no treatment and thick lips is 25%. The probability of receives treatment and thick lips is 21%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.21
0.21/0.57 - 0.25/0.43 = -0.20
-0.20 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 57%. The probability of receives no treatment and thick lips is 25%. The probability of receives treatment and thick lips is 21%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.21
0.21/0.57 - 0.25/0.43 = -0.20
-0.20 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10028,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 16%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 79%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 90%. The overall probability of large kidney stone is 49%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.16
P(Y=1 | V1=1, X=0) = 0.79
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.49
0.51 * (0.16 - 0.06) + 0.49 * (0.90 - 0.79) = 0.10
0.10 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10033,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 16%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 79%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 90%. The overall probability of large kidney stone is 49%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.16
P(Y=1 | V1=1, X=0) = 0.79
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.49
0.51 * (0.16 - 0.06) + 0.49 * (0.90 - 0.79) = 0.10
0.10 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10036,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 55%. The probability of receives no treatment and thick lips is 28%. The probability of receives treatment and thick lips is 20%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.20
0.20/0.55 - 0.28/0.45 = -0.25
-0.25 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 36%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 64%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 97%. The overall probability of large kidney stone is 40%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.64
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.40
0.60 * (0.36 - 0.04) + 0.40 * (0.97 - 0.64) = 0.32
0.32 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 36%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 64%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 97%. The overall probability of large kidney stone is 40%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.64
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.40
0.60 * (0.36 - 0.04) + 0.40 * (0.97 - 0.64) = 0.32
0.32 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 36%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 64%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 97%. The overall probability of large kidney stone is 40%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.64
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.40
0.60 * (0.36 - 0.04) + 0.40 * (0.97 - 0.64) = 0.32
0.32 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 57%. For patients not receiving treatment, the probability of thick lips is 58%. For patients receiving treatment, the probability of thick lips is 38%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.38
0.57*0.38 - 0.43*0.58 = 0.47
0.47 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 57%. The probability of receives no treatment and thick lips is 25%. The probability of receives treatment and thick lips is 21%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.21
0.21/0.57 - 0.25/0.43 = -0.21
-0.21 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 57%. The probability of receives no treatment and thick lips is 25%. The probability of receives treatment and thick lips is 21%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.21
0.21/0.57 - 0.25/0.43 = -0.21
-0.21 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 0%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 14%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 78%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 90%. The overall probability of large kidney stone is 47%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.14
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.47
0.53 * (0.14 - 0.00) + 0.47 * (0.90 - 0.78) = 0.13
0.13 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10062,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 38%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 63%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 95%. The overall probability of large kidney stone is 50%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.38
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.50
0.50 * (0.38 - 0.06) + 0.50 * (0.95 - 0.63) = 0.32
0.32 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 38%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 63%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 95%. The overall probability of large kidney stone is 50%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.38
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.50
0.50 * (0.38 - 0.06) + 0.50 * (0.95 - 0.63) = 0.32
0.32 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10070,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 3%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 15%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 79%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 60%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.15
P(Y=1 | V1=1, X=0) = 0.79
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.60
0.40 * (0.15 - 0.03) + 0.60 * (0.91 - 0.79) = 0.13
0.13 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 3%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 15%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 79%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 60%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.15
P(Y=1 | V1=1, X=0) = 0.79
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.60
0.40 * (0.15 - 0.03) + 0.60 * (0.91 - 0.79) = 0.13
0.13 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10074,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 55%. For patients not receiving treatment, the probability of thick lips is 78%. For patients receiving treatment, the probability of thick lips is 36%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.36
0.55*0.36 - 0.45*0.78 = 0.55
0.55 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 55%. For patients not receiving treatment, the probability of thick lips is 78%. For patients receiving treatment, the probability of thick lips is 36%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.36
0.55*0.36 - 0.45*0.78 = 0.55
0.55 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 52%. For patients not receiving treatment, the probability of thick lips is 60%. For patients receiving treatment, the probability of thick lips is 39%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.52*0.39 - 0.48*0.60 = 0.49
0.49 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 2%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 12%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 75%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 88%. The overall probability of large kidney stone is 43%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.12
P(Y=1 | V1=1, X=0) = 0.75
P(Y=1 | V1=1, X=1) = 0.88
P(V1=1) = 0.43
0.57 * (0.12 - 0.02) + 0.43 * (0.88 - 0.75) = 0.11
0.11 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10094,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 52%. For patients not receiving treatment, the probability of thick lips is 60%. For patients receiving treatment, the probability of thick lips is 20%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.20
0.52*0.20 - 0.48*0.60 = 0.39
0.39 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 52%. The probability of receives no treatment and thick lips is 29%. The probability of receives treatment and thick lips is 10%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.10
0.10/0.52 - 0.29/0.48 = -0.40
-0.40 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10103,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 1%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 35%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 63%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 94%. The overall probability of large kidney stone is 50%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.01
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.50
0.50 * (0.35 - 0.01) + 0.50 * (0.94 - 0.63) = 0.33
0.33 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 48%. For patients not receiving treatment, the probability of thick lips is 57%. For patients receiving treatment, the probability of thick lips is 38%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.38
0.48*0.38 - 0.52*0.57 = 0.47
0.47 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 48%. The probability of receives no treatment and thick lips is 30%. The probability of receives treatment and thick lips is 18%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.18
0.18/0.48 - 0.30/0.52 = -0.19
-0.19 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10110,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 19%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 80%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 93%. The overall probability of large kidney stone is 50%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.50
0.50 * (0.19 - 0.06) + 0.50 * (0.93 - 0.80) = 0.13
0.13 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 19%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 80%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 93%. The overall probability of large kidney stone is 50%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.50
0.50 * (0.19 - 0.06) + 0.50 * (0.93 - 0.80) = 0.13
0.13 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 37%. For patients not receiving treatment, the probability of thick lips is 63%. For patients receiving treatment, the probability of thick lips is 22%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.22
0.37*0.22 - 0.63*0.63 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 37%. The probability of receives no treatment and thick lips is 39%. The probability of receives treatment and thick lips is 8%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.08
0.08/0.37 - 0.39/0.63 = -0.40
-0.40 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 3%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 35%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 63%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 93%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.54
0.46 * (0.35 - 0.03) + 0.54 * (0.93 - 0.63) = 0.31
0.31 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 46%. For patients not receiving treatment, the probability of thick lips is 60%. For patients receiving treatment, the probability of thick lips is 39%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.46*0.39 - 0.54*0.60 = 0.50
0.50 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10125,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 46%. For patients not receiving treatment, the probability of thick lips is 60%. For patients receiving treatment, the probability of thick lips is 39%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.46*0.39 - 0.54*0.60 = 0.50
0.50 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 46%. The probability of receives no treatment and thick lips is 32%. The probability of receives treatment and thick lips is 18%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.18
0.18/0.46 - 0.32/0.54 = -0.21
-0.21 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10129,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 7%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 18%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 81%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.54
0.46 * (0.18 - 0.07) + 0.54 * (0.91 - 0.81) = 0.11
0.11 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 7%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 18%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 81%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 54%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.54
0.46 * (0.18 - 0.07) + 0.54 * (0.91 - 0.81) = 0.11
0.11 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 7%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 18%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 81%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.54
0.46 * (0.18 - 0.07) + 0.54 * (0.91 - 0.81) = 0.11
0.11 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 31%. The probability of receives no treatment and thick lips is 43%. The probability of receives treatment and thick lips is 8%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.08
0.08/0.31 - 0.43/0.69 = -0.37
-0.37 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 3%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 37%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 64%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 95%. The overall probability of large kidney stone is 46%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.37
P(Y=1 | V1=1, X=0) = 0.64
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.46
0.54 * (0.37 - 0.03) + 0.46 * (0.95 - 0.64) = 0.32
0.32 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10143,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 3%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 37%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 64%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 95%. The overall probability of large kidney stone is 46%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.37
P(Y=1 | V1=1, X=0) = 0.64
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.46
0.54 * (0.37 - 0.03) + 0.46 * (0.95 - 0.64) = 0.34
0.34 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 52%. For patients not receiving treatment, the probability of thick lips is 60%. For patients receiving treatment, the probability of thick lips is 39%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.52*0.39 - 0.48*0.60 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 65%. For patients not receiving treatment, the probability of thick lips is 72%. For patients receiving treatment, the probability of thick lips is 46%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.65
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.46
0.65*0.46 - 0.35*0.72 = 0.55
0.55 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 8%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 38%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 64%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 97%. The overall probability of large kidney stone is 50%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.38
P(Y=1 | V1=1, X=0) = 0.64
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.50
0.50 * (0.38 - 0.08) + 0.50 * (0.97 - 0.64) = 0.32
0.32 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 44%. The probability of receives no treatment and thick lips is 32%. The probability of receives treatment and thick lips is 17%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.17
0.17/0.44 - 0.32/0.56 = -0.19
-0.19 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 21%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 86%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 97%. The overall probability of large kidney stone is 41%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.86
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.41
0.59 * (0.21 - 0.06) + 0.41 * (0.97 - 0.86) = 0.13
0.13 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10173,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 21%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 86%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 97%. The overall probability of large kidney stone is 41%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.86
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.41
0.59 * (0.21 - 0.06) + 0.41 * (0.97 - 0.86) = 0.15
0.15 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 58%. The probability of receives no treatment and thick lips is 31%. The probability of receives treatment and thick lips is 16%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.16
0.16/0.58 - 0.31/0.42 = -0.46
-0.46 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 3%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 33%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 60%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 93%. The overall probability of large kidney stone is 49%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.33
P(Y=1 | V1=1, X=0) = 0.60
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.49
0.51 * (0.33 - 0.03) + 0.49 * (0.93 - 0.60) = 0.31
0.31 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 10%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 23%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 84%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 96%. The overall probability of large kidney stone is 43%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.10
P(Y=1 | V1=0, X=1) = 0.23
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.43
0.57 * (0.23 - 0.10) + 0.43 * (0.96 - 0.84) = 0.12
0.12 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 10%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 23%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 84%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 96%. The overall probability of large kidney stone is 43%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.10
P(Y=1 | V1=0, X=1) = 0.23
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.43
0.57 * (0.23 - 0.10) + 0.43 * (0.96 - 0.84) = 0.12
0.12 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 75%. The probability of receives no treatment and thick lips is 18%. The probability of receives treatment and thick lips is 33%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.75
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.33
0.33/0.75 - 0.18/0.25 = -0.27
-0.27 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 0%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 31%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 58%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 53%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.58
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.53
0.47 * (0.31 - 0.00) + 0.53 * (0.91 - 0.58) = 0.32
0.32 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10202,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 0%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 31%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 58%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 53%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.58
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.53
0.47 * (0.31 - 0.00) + 0.53 * (0.91 - 0.58) = 0.31
0.31 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 49%. For patients not receiving treatment, the probability of thick lips is 53%. For patients receiving treatment, the probability of thick lips is 38%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.38
0.49*0.38 - 0.51*0.53 = 0.46
0.46 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 49%. For patients not receiving treatment, the probability of thick lips is 53%. For patients receiving treatment, the probability of thick lips is 38%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.38
0.49*0.38 - 0.51*0.53 = 0.46
0.46 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10208,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 13%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 26%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 89%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 99%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.13
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.89
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.54
0.46 * (0.26 - 0.13) + 0.54 * (0.99 - 0.89) = 0.12
0.12 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 13%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 26%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 89%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 99%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.13
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.89
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.54
0.46 * (0.26 - 0.13) + 0.54 * (0.99 - 0.89) = 0.12
0.12 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 64%. For patients not receiving treatment, the probability of thick lips is 80%. For patients receiving treatment, the probability of thick lips is 51%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.64
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.51
0.64*0.51 - 0.36*0.80 = 0.61
0.61 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 64%. The probability of receives no treatment and thick lips is 29%. The probability of receives treatment and thick lips is 33%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.33
0.33/0.64 - 0.29/0.36 = -0.29
-0.29 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10219,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 5%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 36%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 63%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 95%. The overall probability of large kidney stone is 53%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.53
0.47 * (0.36 - 0.05) + 0.53 * (0.95 - 0.63) = 0.31
0.31 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 5%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 36%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 63%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 95%. The overall probability of large kidney stone is 53%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.53
0.47 * (0.36 - 0.05) + 0.53 * (0.95 - 0.63) = 0.31
0.31 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 50%. The probability of receives no treatment and thick lips is 30%. The probability of receives treatment and thick lips is 21%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.21
0.21/0.50 - 0.30/0.50 = -0.18
-0.18 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 11%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 22%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 87%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 97%. The overall probability of large kidney stone is 47%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.11
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.47
0.53 * (0.22 - 0.11) + 0.47 * (0.97 - 0.87) = 0.11
0.11 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 11%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 22%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 87%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 97%. The overall probability of large kidney stone is 47%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.11
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.47
0.53 * (0.22 - 0.11) + 0.47 * (0.97 - 0.87) = 0.11
0.11 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 73%. The probability of receives no treatment and thick lips is 21%. The probability of receives treatment and thick lips is 34%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.34
0.34/0.73 - 0.21/0.27 = -0.30
-0.30 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 36%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 63%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 94%. The overall probability of large kidney stone is 45%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.45
0.55 * (0.36 - 0.04) + 0.45 * (0.94 - 0.63) = 0.32
0.32 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 56%. For patients not receiving treatment, the probability of thick lips is 59%. For patients receiving treatment, the probability of thick lips is 40%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.40
0.56*0.40 - 0.44*0.59 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10248,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 3%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 13%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 78%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 42%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.13
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.42
0.58 * (0.13 - 0.03) + 0.42 * (0.91 - 0.78) = 0.12
0.12 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 3%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 13%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 78%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 91%. The overall probability of large kidney stone is 42%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.13
P(Y=1 | V1=1, X=0) = 0.78
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.42
0.58 * (0.13 - 0.03) + 0.42 * (0.91 - 0.78) = 0.11
0.11 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 67%. The probability of receives no treatment and thick lips is 23%. The probability of receives treatment and thick lips is 19%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.67
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.19
0.19/0.67 - 0.23/0.33 = -0.42
-0.42 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 35%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 61%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 92%. The overall probability of large kidney stone is 47%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.61
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.47
0.53 * (0.35 - 0.04) + 0.47 * (0.92 - 0.61) = 0.31
0.31 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 52%. For patients not receiving treatment, the probability of thick lips is 56%. For patients receiving treatment, the probability of thick lips is 37%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.37
0.52*0.37 - 0.48*0.56 = 0.47
0.47 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 52%. The probability of receives no treatment and thick lips is 27%. The probability of receives treatment and thick lips is 19%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.19
0.19/0.52 - 0.27/0.48 = -0.19
-0.19 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 48%. For patients not receiving treatment, the probability of thick lips is 64%. For patients receiving treatment, the probability of thick lips is 29%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.29
0.48*0.29 - 0.52*0.64 = 0.47
0.47 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 48%. The probability of receives no treatment and thick lips is 33%. The probability of receives treatment and thick lips is 14%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.14
0.14/0.48 - 0.33/0.52 = -0.35
-0.35 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10280,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 35%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 61%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 93%. The overall probability of large kidney stone is 41%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.61
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.41
0.59 * (0.35 - 0.04) + 0.41 * (0.93 - 0.61) = 0.31
0.31 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10281,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 35%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 61%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 93%. The overall probability of large kidney stone is 41%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.61
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.41
0.59 * (0.35 - 0.04) + 0.41 * (0.93 - 0.61) = 0.31
0.31 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10282,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 4%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 35%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 61%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 93%. The overall probability of large kidney stone is 41%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.61
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.41
0.59 * (0.35 - 0.04) + 0.41 * (0.93 - 0.61) = 0.31
0.31 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 53%. For patients not receiving treatment, the probability of thick lips is 51%. For patients receiving treatment, the probability of thick lips is 37%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.37
0.53*0.37 - 0.47*0.51 = 0.44
0.44 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 53%. The probability of receives no treatment and thick lips is 24%. The probability of receives treatment and thick lips is 20%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.20
0.20/0.53 - 0.24/0.47 = -0.14
-0.14 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 8%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 18%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 81%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 92%. The overall probability of large kidney stone is 56%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.56
0.44 * (0.18 - 0.08) + 0.56 * (0.92 - 0.81) = 0.10
0.10 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 60%. For patients not receiving treatment, the probability of thick lips is 77%. For patients receiving treatment, the probability of thick lips is 41%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.41
0.60*0.41 - 0.40*0.77 = 0.56
0.56 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 60%. The probability of receives no treatment and thick lips is 31%. The probability of receives treatment and thick lips is 25%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.25
0.25/0.60 - 0.31/0.40 = -0.35
-0.35 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10298,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 7%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 38%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 66%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 96%. The overall probability of large kidney stone is 42%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.38
P(Y=1 | V1=1, X=0) = 0.66
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.42
0.58 * (0.38 - 0.07) + 0.42 * (0.96 - 0.66) = 0.31
0.31 > 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 56%. For patients not receiving treatment, the probability of thick lips is 57%. For patients receiving treatment, the probability of thick lips is 42%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.42
0.56*0.42 - 0.44*0.57 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
10306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 56%. The probability of receives no treatment and thick lips is 25%. The probability of receives treatment and thick lips is 23%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.23
0.23/0.56 - 0.25/0.44 = -0.16
-0.16 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look directly at how treatment correlates with lip thickness in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. Method 1: We look at how treatment correlates with lip thickness case by case according to kidney stone size. Method 2: We look directly at how treatment correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
10312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 20%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 83%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 94%. The overall probability of large kidney stone is 46%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.83
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.46
0.54 * (0.20 - 0.06) + 0.46 * (0.94 - 0.83) = 0.12
0.12 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. For patients who have small kidney stones and not receiving treatment, the probability of thick lips is 6%. For patients who have small kidney stones and receiving treatment, the probability of thick lips is 20%. For patients who have large kidney stones and not receiving treatment, the probability of thick lips is 83%. For patients who have large kidney stones and receiving treatment, the probability of thick lips is 94%. The overall probability of large kidney stone is 46%.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.83
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.46
0.54 * (0.20 - 0.06) + 0.46 * (0.94 - 0.83) = 0.12
0.12 > 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. The overall probability of receives treatment is 77%. The probability of receives no treatment and thick lips is 17%. The probability of receives treatment and thick lips is 33%.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.33
0.33/0.77 - 0.17/0.23 = -0.31
-0.31 < 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
10328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 38%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 64%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 95%. The overall probability of pre-conditions is 45%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.38
P(Y=1 | V1=1, X=0) = 0.64
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.45
0.55 * (0.38 - 0.05) + 0.45 * (0.95 - 0.64) = 0.32
0.32 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 38%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 64%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 95%. The overall probability of pre-conditions is 45%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.38
P(Y=1 | V1=1, X=0) = 0.64
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.45
0.55 * (0.38 - 0.05) + 0.45 * (0.95 - 0.64) = 0.33
0.33 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 49%. For people refusing the vaccine, the probability of being lactose intolerant is 55%. For people getting the vaccine, the probability of being lactose intolerant is 41%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.41
0.49*0.41 - 0.51*0.55 = 0.48
0.48 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10340,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 14%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 25%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 87%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 98%. The overall probability of pre-conditions is 47%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.14
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.47
0.53 * (0.25 - 0.14) + 0.47 * (0.98 - 0.87) = 0.11
0.11 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 14%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 25%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 87%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 98%. The overall probability of pre-conditions is 47%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.14
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.87
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.47
0.53 * (0.25 - 0.14) + 0.47 * (0.98 - 0.87) = 0.11
0.11 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 49%. For people refusing the vaccine, the probability of being lactose intolerant is 75%. For people getting the vaccine, the probability of being lactose intolerant is 32%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.32
0.49*0.32 - 0.51*0.75 = 0.54
0.54 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10349,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 27%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 70%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 91%. The overall probability of pre-conditions is 45%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.27
P(Y=1 | V1=1, X=0) = 0.70
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.45
0.55 * (0.27 - 0.05) + 0.45 * (0.91 - 0.70) = 0.22
0.22 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 27%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 70%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 91%. The overall probability of pre-conditions is 45%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.27
P(Y=1 | V1=1, X=0) = 0.70
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.45
0.55 * (0.27 - 0.05) + 0.45 * (0.91 - 0.70) = 0.23
0.23 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 27%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 70%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 91%. The overall probability of pre-conditions is 45%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.27
P(Y=1 | V1=1, X=0) = 0.70
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.45
0.55 * (0.27 - 0.05) + 0.45 * (0.91 - 0.70) = 0.23
0.23 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 47%. For people refusing the vaccine, the probability of being lactose intolerant is 58%. For people getting the vaccine, the probability of being lactose intolerant is 29%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.29
0.47*0.29 - 0.53*0.58 = 0.44
0.44 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 47%. The probability of vaccine refusal and being lactose intolerant is 31%. The probability of getting the vaccine and being lactose intolerant is 14%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.14
0.14/0.47 - 0.31/0.53 = -0.29
-0.29 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 37%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 65%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 96%. The overall probability of pre-conditions is 41%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.37
P(Y=1 | V1=1, X=0) = 0.65
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.41
0.59 * (0.37 - 0.07) + 0.41 * (0.96 - 0.65) = 0.31
0.31 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 37%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 65%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 96%. The overall probability of pre-conditions is 41%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.37
P(Y=1 | V1=1, X=0) = 0.65
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.41
0.59 * (0.37 - 0.07) + 0.41 * (0.96 - 0.65) = 0.30
0.30 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 56%. The probability of vaccine refusal and being lactose intolerant is 26%. The probability of getting the vaccine and being lactose intolerant is 22%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.22
0.22/0.56 - 0.26/0.44 = -0.20
-0.20 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 8%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 19%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 84%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 97%. The overall probability of pre-conditions is 57%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.57
0.43 * (0.19 - 0.08) + 0.57 * (0.97 - 0.84) = 0.12
0.12 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10373,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 8%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 19%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 84%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 97%. The overall probability of pre-conditions is 57%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.08
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.57
0.43 * (0.19 - 0.08) + 0.57 * (0.97 - 0.84) = 0.12
0.12 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 9%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 32%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 75%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 98%. The overall probability of pre-conditions is 54%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.09
P(Y=1 | V1=0, X=1) = 0.32
P(Y=1 | V1=1, X=0) = 0.75
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.54
0.46 * (0.32 - 0.09) + 0.54 * (0.98 - 0.75) = 0.23
0.23 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 9%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 32%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 75%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 98%. The overall probability of pre-conditions is 54%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.09
P(Y=1 | V1=0, X=1) = 0.32
P(Y=1 | V1=1, X=0) = 0.75
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.54
0.46 * (0.32 - 0.09) + 0.54 * (0.98 - 0.75) = 0.23
0.23 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 52%. The probability of vaccine refusal and being lactose intolerant is 35%. The probability of getting the vaccine and being lactose intolerant is 21%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.21
0.21/0.52 - 0.35/0.48 = -0.32
-0.32 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 52%. The probability of vaccine refusal and being lactose intolerant is 35%. The probability of getting the vaccine and being lactose intolerant is 21%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.21
0.21/0.52 - 0.35/0.48 = -0.32
-0.32 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10389,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 37%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 65%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 98%. The overall probability of pre-conditions is 52%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.37
P(Y=1 | V1=1, X=0) = 0.65
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.52
0.48 * (0.37 - 0.05) + 0.52 * (0.98 - 0.65) = 0.32
0.32 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 47%. For people refusing the vaccine, the probability of being lactose intolerant is 60%. For people getting the vaccine, the probability of being lactose intolerant is 42%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.42
0.47*0.42 - 0.53*0.60 = 0.52
0.52 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 47%. The probability of vaccine refusal and being lactose intolerant is 31%. The probability of getting the vaccine and being lactose intolerant is 20%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.20
0.20/0.47 - 0.31/0.53 = -0.18
-0.18 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 47%. The probability of vaccine refusal and being lactose intolerant is 31%. The probability of getting the vaccine and being lactose intolerant is 20%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.20
0.20/0.47 - 0.31/0.53 = -0.18
-0.18 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 6%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 19%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 85%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 96%. The overall probability of pre-conditions is 55%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.96
P(V1=1) = 0.55
0.45 * (0.19 - 0.06) + 0.55 * (0.96 - 0.85) = 0.13
0.13 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 39%. The probability of vaccine refusal and being lactose intolerant is 45%. The probability of getting the vaccine and being lactose intolerant is 9%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.09
0.09/0.39 - 0.45/0.61 = -0.51
-0.51 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 39%. The probability of vaccine refusal and being lactose intolerant is 45%. The probability of getting the vaccine and being lactose intolerant is 9%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.09
0.09/0.39 - 0.45/0.61 = -0.51
-0.51 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10408,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10411,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 0%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 28%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 73%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 95%. The overall probability of pre-conditions is 52%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.28
P(Y=1 | V1=1, X=0) = 0.73
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.52
0.48 * (0.28 - 0.00) + 0.52 * (0.95 - 0.73) = 0.24
0.24 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 0%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 28%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 73%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 95%. The overall probability of pre-conditions is 52%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.28
P(Y=1 | V1=1, X=0) = 0.73
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.52
0.48 * (0.28 - 0.00) + 0.52 * (0.95 - 0.73) = 0.27
0.27 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 0%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 28%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 73%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 95%. The overall probability of pre-conditions is 52%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.00
P(Y=1 | V1=0, X=1) = 0.28
P(Y=1 | V1=1, X=0) = 0.73
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.52
0.48 * (0.28 - 0.00) + 0.52 * (0.95 - 0.73) = 0.27
0.27 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 52%. For people refusing the vaccine, the probability of being lactose intolerant is 70%. For people getting the vaccine, the probability of being lactose intolerant is 36%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.36
0.52*0.36 - 0.48*0.70 = 0.51
0.51 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 52%. For people refusing the vaccine, the probability of being lactose intolerant is 70%. For people getting the vaccine, the probability of being lactose intolerant is 36%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.36
0.52*0.36 - 0.48*0.70 = 0.51
0.51 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 52%. The probability of vaccine refusal and being lactose intolerant is 34%. The probability of getting the vaccine and being lactose intolerant is 19%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.19
0.19/0.52 - 0.34/0.48 = -0.34
-0.34 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 37%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 62%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 94%. The overall probability of pre-conditions is 51%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.37
P(Y=1 | V1=1, X=0) = 0.62
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.51
0.49 * (0.37 - 0.05) + 0.51 * (0.94 - 0.62) = 0.32
0.32 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 37%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 62%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 94%. The overall probability of pre-conditions is 51%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.37
P(Y=1 | V1=1, X=0) = 0.62
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.51
0.49 * (0.37 - 0.05) + 0.51 * (0.94 - 0.62) = 0.32
0.32 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 10%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 20%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 83%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 97%. The overall probability of pre-conditions is 44%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.10
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.83
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.44
0.56 * (0.20 - 0.10) + 0.44 * (0.97 - 0.83) = 0.12
0.12 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 10%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 20%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 83%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 97%. The overall probability of pre-conditions is 44%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.10
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.83
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.44
0.56 * (0.20 - 0.10) + 0.44 * (0.97 - 0.83) = 0.12
0.12 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10432,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 10%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 20%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 83%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 97%. The overall probability of pre-conditions is 44%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.10
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.83
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.44
0.56 * (0.20 - 0.10) + 0.44 * (0.97 - 0.83) = 0.11
0.11 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10435,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 50%. For people refusing the vaccine, the probability of being lactose intolerant is 65%. For people getting the vaccine, the probability of being lactose intolerant is 31%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.31
0.50*0.31 - 0.50*0.65 = 0.48
0.48 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 6%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 27%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 69%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 93%. The overall probability of pre-conditions is 51%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.06
P(Y=1 | V1=0, X=1) = 0.27
P(Y=1 | V1=1, X=0) = 0.69
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.51
0.49 * (0.27 - 0.06) + 0.51 * (0.93 - 0.69) = 0.23
0.23 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10445,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 49%. For people refusing the vaccine, the probability of being lactose intolerant is 66%. For people getting the vaccine, the probability of being lactose intolerant is 32%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.32
0.49*0.32 - 0.51*0.66 = 0.50
0.50 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 49%. The probability of vaccine refusal and being lactose intolerant is 33%. The probability of getting the vaccine and being lactose intolerant is 16%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.16
0.16/0.49 - 0.33/0.51 = -0.34
-0.34 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 2%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 32%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 59%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 91%. The overall probability of pre-conditions is 50%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.32
P(Y=1 | V1=1, X=0) = 0.59
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.50
0.50 * (0.32 - 0.02) + 0.50 * (0.91 - 0.59) = 0.31
0.31 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 2%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 32%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 59%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 91%. The overall probability of pre-conditions is 50%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.32
P(Y=1 | V1=1, X=0) = 0.59
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.50
0.50 * (0.32 - 0.02) + 0.50 * (0.91 - 0.59) = 0.30
0.30 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 49%. For people refusing the vaccine, the probability of being lactose intolerant is 55%. For people getting the vaccine, the probability of being lactose intolerant is 35%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.35
0.49*0.35 - 0.51*0.55 = 0.46
0.46 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 49%. The probability of vaccine refusal and being lactose intolerant is 28%. The probability of getting the vaccine and being lactose intolerant is 17%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.17
0.17/0.49 - 0.28/0.51 = -0.20
-0.20 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 11%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 22%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 86%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 98%. The overall probability of pre-conditions is 56%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.11
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.86
P(Y=1 | V1=1, X=1) = 0.98
P(V1=1) = 0.56
0.44 * (0.22 - 0.11) + 0.56 * (0.98 - 0.86) = 0.11
0.11 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 65%. The probability of vaccine refusal and being lactose intolerant is 29%. The probability of getting the vaccine and being lactose intolerant is 31%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.31
0.31/0.65 - 0.29/0.35 = -0.37
-0.37 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 44%. For people refusing the vaccine, the probability of being lactose intolerant is 68%. For people getting the vaccine, the probability of being lactose intolerant is 40%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.40
0.44*0.40 - 0.56*0.68 = 0.56
0.56 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 36%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 62%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 92%. The overall probability of pre-conditions is 54%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.62
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.54
0.46 * (0.36 - 0.05) + 0.54 * (0.92 - 0.62) = 0.30
0.30 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 36%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 62%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 92%. The overall probability of pre-conditions is 54%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.62
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.54
0.46 * (0.36 - 0.05) + 0.54 * (0.92 - 0.62) = 0.30
0.30 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 5%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 36%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 62%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 92%. The overall probability of pre-conditions is 54%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.05
P(Y=1 | V1=0, X=1) = 0.36
P(Y=1 | V1=1, X=0) = 0.62
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.54
0.46 * (0.36 - 0.05) + 0.54 * (0.92 - 0.62) = 0.30
0.30 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10491,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 18%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 81%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 94%. The overall probability of pre-conditions is 50%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.50
0.50 * (0.18 - 0.07) + 0.50 * (0.94 - 0.81) = 0.12
0.12 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10492,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 18%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 81%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 94%. The overall probability of pre-conditions is 50%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.50
0.50 * (0.18 - 0.07) + 0.50 * (0.94 - 0.81) = 0.11
0.11 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 28%. For people refusing the vaccine, the probability of being lactose intolerant is 55%. For people getting the vaccine, the probability of being lactose intolerant is 29%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.28
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.29
0.28*0.29 - 0.72*0.55 = 0.47
0.47 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 28%. For people refusing the vaccine, the probability of being lactose intolerant is 55%. For people getting the vaccine, the probability of being lactose intolerant is 29%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.28
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.29
0.28*0.29 - 0.72*0.55 = 0.47
0.47 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 3%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 26%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 70%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 92%. The overall probability of pre-conditions is 42%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.03
P(Y=1 | V1=0, X=1) = 0.26
P(Y=1 | V1=1, X=0) = 0.70
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.42
0.58 * (0.26 - 0.03) + 0.42 * (0.92 - 0.70) = 0.22
0.22 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 59%. For people refusing the vaccine, the probability of being lactose intolerant is 59%. For people getting the vaccine, the probability of being lactose intolerant is 34%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.34
0.59*0.34 - 0.41*0.59 = 0.44
0.44 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 59%. The probability of vaccine refusal and being lactose intolerant is 24%. The probability of getting the vaccine and being lactose intolerant is 20%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.20
0.20/0.59 - 0.24/0.41 = -0.26
-0.26 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 59%. The probability of vaccine refusal and being lactose intolerant is 24%. The probability of getting the vaccine and being lactose intolerant is 20%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.20
0.20/0.59 - 0.24/0.41 = -0.26
-0.26 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 39%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 66%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 99%. The overall probability of pre-conditions is 58%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.39
P(Y=1 | V1=1, X=0) = 0.66
P(Y=1 | V1=1, X=1) = 0.99
P(V1=1) = 0.58
0.42 * (0.39 - 0.07) + 0.58 * (0.99 - 0.66) = 0.32
0.32 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 45%. The probability of vaccine refusal and being lactose intolerant is 36%. The probability of getting the vaccine and being lactose intolerant is 20%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.20
0.20/0.45 - 0.36/0.55 = -0.21
-0.21 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 45%. The probability of vaccine refusal and being lactose intolerant is 36%. The probability of getting the vaccine and being lactose intolerant is 20%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.20
0.20/0.45 - 0.36/0.55 = -0.21
-0.21 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 10%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 21%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 85%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 97%. The overall probability of pre-conditions is 50%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.10
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.50
0.50 * (0.21 - 0.10) + 0.50 * (0.97 - 0.85) = 0.11
0.11 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 10%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 21%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 85%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 97%. The overall probability of pre-conditions is 50%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.10
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.97
P(V1=1) = 0.50
0.50 * (0.21 - 0.10) + 0.50 * (0.97 - 0.85) = 0.11
0.11 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 57%. The probability of vaccine refusal and being lactose intolerant is 32%. The probability of getting the vaccine and being lactose intolerant is 22%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.22
0.22/0.57 - 0.32/0.43 = -0.38
-0.38 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10527,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 57%. The probability of vaccine refusal and being lactose intolerant is 32%. The probability of getting the vaccine and being lactose intolerant is 22%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.22
0.22/0.57 - 0.32/0.43 = -0.38
-0.38 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 29%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 71%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 94%. The overall probability of pre-conditions is 59%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.29
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.94
P(V1=1) = 0.59
0.41 * (0.29 - 0.07) + 0.59 * (0.94 - 0.71) = 0.22
0.22 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 41%. For people refusing the vaccine, the probability of being lactose intolerant is 66%. For people getting the vaccine, the probability of being lactose intolerant is 37%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.37
0.41*0.37 - 0.59*0.66 = 0.54
0.54 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10535,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 41%. For people refusing the vaccine, the probability of being lactose intolerant is 66%. For people getting the vaccine, the probability of being lactose intolerant is 37%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.37
0.41*0.37 - 0.59*0.66 = 0.54
0.54 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10536,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 41%. The probability of vaccine refusal and being lactose intolerant is 39%. The probability of getting the vaccine and being lactose intolerant is 15%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.15
0.15/0.41 - 0.39/0.59 = -0.29
-0.29 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10539,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 2%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 33%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 62%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 95%. The overall probability of pre-conditions is 42%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.33
P(Y=1 | V1=1, X=0) = 0.62
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.42
0.58 * (0.33 - 0.02) + 0.42 * (0.95 - 0.62) = 0.32
0.32 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10542,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 2%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 33%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 62%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 95%. The overall probability of pre-conditions is 42%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.02
P(Y=1 | V1=0, X=1) = 0.33
P(Y=1 | V1=1, X=0) = 0.62
P(Y=1 | V1=1, X=1) = 0.95
P(V1=1) = 0.42
0.58 * (0.33 - 0.02) + 0.42 * (0.95 - 0.62) = 0.32
0.32 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 54%. The probability of vaccine refusal and being lactose intolerant is 24%. The probability of getting the vaccine and being lactose intolerant is 20%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.54
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.20
0.20/0.54 - 0.24/0.46 = -0.16
-0.16 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10554,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 52%. For people refusing the vaccine, the probability of being lactose intolerant is 67%. For people getting the vaccine, the probability of being lactose intolerant is 22%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.22
0.52*0.22 - 0.48*0.67 = 0.43
0.43 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 52%. For people refusing the vaccine, the probability of being lactose intolerant is 67%. For people getting the vaccine, the probability of being lactose intolerant is 22%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.22
0.52*0.22 - 0.48*0.67 = 0.43
0.43 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 52%. The probability of vaccine refusal and being lactose intolerant is 32%. The probability of getting the vaccine and being lactose intolerant is 11%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.11
0.11/0.52 - 0.32/0.48 = -0.45
-0.45 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10559,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 27%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 67%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 90%. The overall probability of pre-conditions is 52%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.27
P(Y=1 | V1=1, X=0) = 0.67
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.52
0.48 * (0.27 - 0.07) + 0.52 * (0.90 - 0.67) = 0.22
0.22 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 27%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 67%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 90%. The overall probability of pre-conditions is 52%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.27
P(Y=1 | V1=1, X=0) = 0.67
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.52
0.48 * (0.27 - 0.07) + 0.52 * (0.90 - 0.67) = 0.22
0.22 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 27%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 67%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 90%. The overall probability of pre-conditions is 52%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.27
P(Y=1 | V1=1, X=0) = 0.67
P(Y=1 | V1=1, X=1) = 0.90
P(V1=1) = 0.52
0.48 * (0.27 - 0.07) + 0.52 * (0.90 - 0.67) = 0.21
0.21 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 47%. For people refusing the vaccine, the probability of being lactose intolerant is 61%. For people getting the vaccine, the probability of being lactose intolerant is 33%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.33
0.47*0.33 - 0.53*0.61 = 0.49
0.49 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 47%. The probability of vaccine refusal and being lactose intolerant is 32%. The probability of getting the vaccine and being lactose intolerant is 16%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.16
0.16/0.47 - 0.32/0.53 = -0.27
-0.27 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 55%. The probability of vaccine refusal and being lactose intolerant is 27%. The probability of getting the vaccine and being lactose intolerant is 21%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.21
0.21/0.55 - 0.27/0.45 = -0.22
-0.22 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 18%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 81%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 92%. The overall probability of pre-conditions is 59%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.59
0.41 * (0.18 - 0.07) + 0.59 * (0.92 - 0.81) = 0.11
0.11 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 51%. For people refusing the vaccine, the probability of being lactose intolerant is 77%. For people getting the vaccine, the probability of being lactose intolerant is 37%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.37
0.51*0.37 - 0.49*0.77 = 0.56
0.56 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 51%. The probability of vaccine refusal and being lactose intolerant is 38%. The probability of getting the vaccine and being lactose intolerant is 19%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.19
0.19/0.51 - 0.38/0.49 = -0.40
-0.40 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 4%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 35%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 63%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 93%. The overall probability of pre-conditions is 55%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.55
0.45 * (0.35 - 0.04) + 0.55 * (0.93 - 0.63) = 0.31
0.31 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 4%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 35%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 63%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 93%. The overall probability of pre-conditions is 55%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.55
0.45 * (0.35 - 0.04) + 0.55 * (0.93 - 0.63) = 0.31
0.31 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 4%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 35%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 63%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 93%. The overall probability of pre-conditions is 55%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.04
P(Y=1 | V1=0, X=1) = 0.35
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.93
P(V1=1) = 0.55
0.45 * (0.35 - 0.04) + 0.55 * (0.93 - 0.63) = 0.31
0.31 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10603,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 18%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 80%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 91%. The overall probability of pre-conditions is 53%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.18
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.91
P(V1=1) = 0.53
0.47 * (0.18 - 0.07) + 0.53 * (0.91 - 0.80) = 0.11
0.11 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 35%. The probability of vaccine refusal and being lactose intolerant is 40%. The probability of getting the vaccine and being lactose intolerant is 9%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.09
0.09/0.35 - 0.40/0.65 = -0.36
-0.36 < 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
10609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look at how vaccination correlates with lactose intolerance case by case according to pre-conditions. Method 2: We look directly at how vaccination correlates with lactose intolerance in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 29%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 72%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 92%. The overall probability of pre-conditions is 52%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.29
P(Y=1 | V1=1, X=0) = 0.72
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.52
0.48 * (0.29 - 0.07) + 0.52 * (0.92 - 0.72) = 0.21
0.21 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 29%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 72%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 92%. The overall probability of pre-conditions is 52%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.29
P(Y=1 | V1=1, X=0) = 0.72
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.52
0.48 * (0.29 - 0.07) + 0.52 * (0.92 - 0.72) = 0.21
0.21 > 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. For people with no pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 7%. For people with no pre-conditions and getting the vaccine, the probability of being lactose intolerant is 29%. For people with pre-conditions and refusing the vaccine, the probability of being lactose intolerant is 72%. For people with pre-conditions and getting the vaccine, the probability of being lactose intolerant is 92%. The overall probability of pre-conditions is 52%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.07
P(Y=1 | V1=0, X=1) = 0.29
P(Y=1 | V1=1, X=0) = 0.72
P(Y=1 | V1=1, X=1) = 0.92
P(V1=1) = 0.52
0.48 * (0.29 - 0.07) + 0.52 * (0.92 - 0.72) = 0.22
0.22 > 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10614,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 51%. For people refusing the vaccine, the probability of being lactose intolerant is 65%. For people getting the vaccine, the probability of being lactose intolerant is 39%.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.39
0.51*0.39 - 0.49*0.65 = 0.51
0.51 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10615,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. The overall probability of getting the vaccine is 51%. For people refusing the vaccine, the probability of being lactose intolerant is 65%. For people getting the vaccine, the probability of being lactose intolerant is 39%.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.39
0.51*0.39 - 0.49*0.65 = 0.51
0.51 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
10618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. Method 1: We look directly at how vaccination correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
10624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 37%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 30%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 84%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 55%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 77%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 100%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 30%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 64%. The overall probability of good health is 93%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.30
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0, V2=0) = 0.77
P(V3=1 | X=0, V2=1) = 1.00
P(V3=1 | X=1, V2=0) = 0.30
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.93
0.93 * 0.30 * (0.64 - 0.30)+ 0.07 * 0.30 * (1.00 - 0.77)= 0.11
0.11 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 37%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 30%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 84%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 55%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 77%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 100%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 30%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 64%. The overall probability of good health is 93%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.30
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0, V2=0) = 0.77
P(V3=1 | X=0, V2=1) = 1.00
P(V3=1 | X=1, V2=0) = 0.30
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.93
0.93 * (0.55 - 0.84) * 1.00 + 0.07 * (0.30 - 0.37) * 0.30 = 0.25
0.25 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 18%. The probability of nonsmoking mother and freckles is 25%. The probability of smoking mother and freckles is 12%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.12
0.12/0.18 - 0.25/0.82 = 0.36
0.36 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look at how maternal smoking status correlates with freckles case by case according to infant's birth weight. Method 2: We look directly at how maternal smoking status correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10633,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 37%. For infants with smoking mothers, the probability of freckles is 70%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.70
0.70 - 0.37 = 0.33
0.33 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 37%. For infants with smoking mothers, the probability of freckles is 70%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.70
0.70 - 0.37 = 0.33
0.33 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10639,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 53%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 25%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 78%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 49%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 38%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 68%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 6%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 43%. The overall probability of good health is 58%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.25
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.38
P(V3=1 | X=0, V2=1) = 0.68
P(V3=1 | X=1, V2=0) = 0.06
P(V3=1 | X=1, V2=1) = 0.43
P(V2=1) = 0.58
0.58 * 0.25 * (0.43 - 0.06)+ 0.42 * 0.25 * (0.68 - 0.38)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 9%. For infants with nonsmoking mothers, the probability of freckles is 37%. For infants with smoking mothers, the probability of freckles is 70%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.70
0.09*0.70 - 0.91*0.37 = 0.40
0.40 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 9%. For infants with nonsmoking mothers, the probability of freckles is 37%. For infants with smoking mothers, the probability of freckles is 70%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.70
0.09*0.70 - 0.91*0.37 = 0.40
0.40 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 9%. The probability of nonsmoking mother and freckles is 34%. The probability of smoking mother and freckles is 7%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.07
0.07/0.09 - 0.34/0.91 = 0.32
0.32 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 23%. For infants with smoking mothers, the probability of freckles is 58%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.58
0.58 - 0.23 = 0.36
0.36 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 23%. For infants with smoking mothers, the probability of freckles is 58%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.58
0.58 - 0.23 = 0.36
0.36 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 35%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 7%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 60%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 34%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 39%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 50%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 5%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 6%. The overall probability of good health is 41%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.07
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.05
P(V3=1 | X=1, V2=1) = 0.06
P(V2=1) = 0.41
0.41 * (0.34 - 0.60) * 0.50 + 0.59 * (0.07 - 0.35) * 0.05 = 0.26
0.26 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 15%. The probability of nonsmoking mother and freckles is 19%. The probability of smoking mother and freckles is 9%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.09
0.09/0.15 - 0.19/0.85 = 0.36
0.36 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 70%. For infants with smoking mothers, the probability of freckles is 77%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.77
0.77 - 0.70 = 0.08
0.08 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10663,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 70%. For infants with smoking mothers, the probability of freckles is 77%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.77
0.77 - 0.70 = 0.08
0.08 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 70%. For infants with smoking mothers, the probability of freckles is 77%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.77
0.77 - 0.70 = 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 70%. For infants with smoking mothers, the probability of freckles is 77%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.77
0.77 - 0.70 = 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 82%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 63%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 87%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 60%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 44%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 70%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 17%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 39%. The overall probability of good health is 85%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.44
P(V3=1 | X=0, V2=1) = 0.70
P(V3=1 | X=1, V2=0) = 0.17
P(V3=1 | X=1, V2=1) = 0.39
P(V2=1) = 0.85
0.85 * 0.63 * (0.39 - 0.17)+ 0.15 * 0.63 * (0.70 - 0.44)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10670,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 10%. For infants with nonsmoking mothers, the probability of freckles is 70%. For infants with smoking mothers, the probability of freckles is 77%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.77
0.10*0.77 - 0.90*0.70 = 0.70
0.70 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 10%. The probability of nonsmoking mother and freckles is 62%. The probability of smoking mother and freckles is 8%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.62
P(Y=1, X=1=1) = 0.08
0.08/0.10 - 0.62/0.90 = 0.08
0.08 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 54%. For infants with smoking mothers, the probability of freckles is 58%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.58
0.58 - 0.54 = 0.04
0.04 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 54%. For infants with smoking mothers, the probability of freckles is 58%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.58
0.58 - 0.54 = 0.04
0.04 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 54%. For infants with smoking mothers, the probability of freckles is 58%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.58
0.58 - 0.54 = 0.04
0.04 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10681,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 72%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 39%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 71%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 32%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 44%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 78%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 22%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 52%. The overall probability of good health is 46%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.32
P(V3=1 | X=0, V2=0) = 0.44
P(V3=1 | X=0, V2=1) = 0.78
P(V3=1 | X=1, V2=0) = 0.22
P(V3=1 | X=1, V2=1) = 0.52
P(V2=1) = 0.46
0.46 * 0.39 * (0.52 - 0.22)+ 0.54 * 0.39 * (0.78 - 0.44)= 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 72%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 39%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 71%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 32%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 44%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 78%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 22%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 52%. The overall probability of good health is 46%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.32
P(V3=1 | X=0, V2=0) = 0.44
P(V3=1 | X=0, V2=1) = 0.78
P(V3=1 | X=1, V2=0) = 0.22
P(V3=1 | X=1, V2=1) = 0.52
P(V2=1) = 0.46
0.46 * (0.32 - 0.71) * 0.78 + 0.54 * (0.39 - 0.72) * 0.22 = -0.06
-0.06 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 4%. For infants with nonsmoking mothers, the probability of freckles is 54%. For infants with smoking mothers, the probability of freckles is 58%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.58
0.04*0.58 - 0.96*0.54 = 0.54
0.54 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 4%. For infants with nonsmoking mothers, the probability of freckles is 54%. For infants with smoking mothers, the probability of freckles is 58%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.58
0.04*0.58 - 0.96*0.54 = 0.54
0.54 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 4%. The probability of nonsmoking mother and freckles is 50%. The probability of smoking mother and freckles is 2%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.02
0.02/0.04 - 0.50/0.96 = 0.05
0.05 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look at how maternal smoking status correlates with freckles case by case according to infant's birth weight. Method 2: We look directly at how maternal smoking status correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10693,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 28%. For infants with smoking mothers, the probability of freckles is 44%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.44
0.44 - 0.28 = 0.16
0.16 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 55%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 13%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 54%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 23%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 68%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 62%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 29%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 36%. The overall probability of good health is 43%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.55
P(Y=1 | X=0, V3=1) = 0.13
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.23
P(V3=1 | X=0, V2=0) = 0.68
P(V3=1 | X=0, V2=1) = 0.62
P(V3=1 | X=1, V2=0) = 0.29
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.43
0.43 * (0.23 - 0.54) * 0.62 + 0.57 * (0.13 - 0.55) * 0.29 = 0.06
0.06 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 14%. For infants with nonsmoking mothers, the probability of freckles is 28%. For infants with smoking mothers, the probability of freckles is 44%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.44
0.14*0.44 - 0.86*0.28 = 0.30
0.30 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 14%. The probability of nonsmoking mother and freckles is 24%. The probability of smoking mother and freckles is 6%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.06
0.06/0.14 - 0.24/0.86 = 0.16
0.16 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 14%. The probability of nonsmoking mother and freckles is 24%. The probability of smoking mother and freckles is 6%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.06
0.06/0.14 - 0.24/0.86 = 0.16
0.16 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look at how maternal smoking status correlates with freckles case by case according to infant's birth weight. Method 2: We look directly at how maternal smoking status correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 28%. For infants with smoking mothers, the probability of freckles is 65%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.65
0.65 - 0.28 = 0.37
0.37 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 28%. For infants with smoking mothers, the probability of freckles is 65%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.65
0.65 - 0.28 = 0.37
0.37 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 46%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 21%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 74%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 47%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 51%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 72%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 3%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 35%. The overall probability of good health is 90%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.21
P(Y=1 | X=1, V3=0) = 0.74
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.72
P(V3=1 | X=1, V2=0) = 0.03
P(V3=1 | X=1, V2=1) = 0.35
P(V2=1) = 0.90
0.90 * 0.21 * (0.35 - 0.03)+ 0.10 * 0.21 * (0.72 - 0.51)= 0.10
0.10 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 46%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 21%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 74%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 47%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 51%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 72%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 3%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 35%. The overall probability of good health is 90%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.21
P(Y=1 | X=1, V3=0) = 0.74
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.72
P(V3=1 | X=1, V2=0) = 0.03
P(V3=1 | X=1, V2=1) = 0.35
P(V2=1) = 0.90
0.90 * (0.47 - 0.74) * 0.72 + 0.10 * (0.21 - 0.46) * 0.03 = 0.26
0.26 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 5%. For infants with nonsmoking mothers, the probability of freckles is 28%. For infants with smoking mothers, the probability of freckles is 65%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.65
0.05*0.65 - 0.95*0.28 = 0.30
0.30 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10713,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 5%. For infants with nonsmoking mothers, the probability of freckles is 28%. For infants with smoking mothers, the probability of freckles is 65%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.65
0.05*0.65 - 0.95*0.28 = 0.30
0.30 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 5%. The probability of nonsmoking mother and freckles is 27%. The probability of smoking mother and freckles is 3%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.27/0.95 = 0.37
0.37 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 5%. The probability of nonsmoking mother and freckles is 27%. The probability of smoking mother and freckles is 3%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.27/0.95 = 0.37
0.37 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 42%. For infants with smoking mothers, the probability of freckles is 75%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.75
0.75 - 0.42 = 0.33
0.33 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 42%. For infants with smoking mothers, the probability of freckles is 75%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.75
0.75 - 0.42 = 0.33
0.33 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 42%. For infants with smoking mothers, the probability of freckles is 75%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.75
0.75 - 0.42 = 0.33
0.33 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 60%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 32%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 85%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 56%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 47%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 74%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 23%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 48%. The overall probability of good health is 55%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.32
P(Y=1 | X=1, V3=0) = 0.85
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.47
P(V3=1 | X=0, V2=1) = 0.74
P(V3=1 | X=1, V2=0) = 0.23
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.55
0.55 * 0.32 * (0.48 - 0.23)+ 0.45 * 0.32 * (0.74 - 0.47)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 60%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 32%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 85%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 56%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 47%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 74%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 23%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 48%. The overall probability of good health is 55%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.32
P(Y=1 | X=1, V3=0) = 0.85
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.47
P(V3=1 | X=0, V2=1) = 0.74
P(V3=1 | X=1, V2=0) = 0.23
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.55
0.55 * 0.32 * (0.48 - 0.23)+ 0.45 * 0.32 * (0.74 - 0.47)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 22%. For infants with smoking mothers, the probability of freckles is 66%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.66
0.66 - 0.22 = 0.44
0.44 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10742,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 12%. The probability of nonsmoking mother and freckles is 19%. The probability of smoking mother and freckles is 8%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.08
0.08/0.12 - 0.19/0.88 = 0.44
0.44 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10743,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 12%. The probability of nonsmoking mother and freckles is 19%. The probability of smoking mother and freckles is 8%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.08
0.08/0.12 - 0.19/0.88 = 0.44
0.44 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 47%. For infants with smoking mothers, the probability of freckles is 57%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.57
0.57 - 0.47 = 0.11
0.11 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 70%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 44%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 67%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 48%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 69%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 90%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 29%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 52%. The overall probability of good health is 97%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.48
P(V3=1 | X=0, V2=0) = 0.69
P(V3=1 | X=0, V2=1) = 0.90
P(V3=1 | X=1, V2=0) = 0.29
P(V3=1 | X=1, V2=1) = 0.52
P(V2=1) = 0.97
0.97 * 0.44 * (0.52 - 0.29)+ 0.03 * 0.44 * (0.90 - 0.69)= 0.11
0.11 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 7%. The probability of nonsmoking mother and freckles is 44%. The probability of smoking mother and freckles is 4%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.44/0.93 = 0.11
0.11 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 24%. For infants with smoking mothers, the probability of freckles is 32%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.32
0.32 - 0.24 = 0.08
0.08 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10764,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 48%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 20%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 55%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 9%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 73%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 94%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 35%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 67%. The overall probability of good health is 54%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.09
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.94
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.54
0.54 * 0.20 * (0.67 - 0.35)+ 0.46 * 0.20 * (0.94 - 0.73)= 0.10
0.10 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 48%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 20%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 55%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 9%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 73%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 94%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 35%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 67%. The overall probability of good health is 54%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.09
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.94
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.54
0.54 * 0.20 * (0.67 - 0.35)+ 0.46 * 0.20 * (0.94 - 0.73)= 0.10
0.10 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 48%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 20%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 55%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 9%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 73%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 94%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 35%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 67%. The overall probability of good health is 54%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.09
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.94
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.54
0.54 * (0.09 - 0.55) * 0.94 + 0.46 * (0.20 - 0.48) * 0.35 = -0.08
-0.08 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 12%. For infants with nonsmoking mothers, the probability of freckles is 24%. For infants with smoking mothers, the probability of freckles is 32%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.32
0.12*0.32 - 0.88*0.24 = 0.25
0.25 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 33%. For infants with smoking mothers, the probability of freckles is 41%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.41
0.41 - 0.33 = 0.08
0.08 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 56%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 22%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 49%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 14%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 72%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 59%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 30%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 20%. The overall probability of good health is 52%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.22
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.14
P(V3=1 | X=0, V2=0) = 0.72
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.30
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.52
0.52 * (0.14 - 0.49) * 0.59 + 0.48 * (0.22 - 0.56) * 0.30 = -0.06
-0.06 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 8%. For infants with nonsmoking mothers, the probability of freckles is 33%. For infants with smoking mothers, the probability of freckles is 41%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.41
0.08*0.41 - 0.92*0.33 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 8%. The probability of nonsmoking mother and freckles is 31%. The probability of smoking mother and freckles is 3%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.31/0.92 = 0.07
0.07 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 33%. For infants with smoking mothers, the probability of freckles is 67%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.67
0.67 - 0.33 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10794,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 50%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 29%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 75%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 58%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 57%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 85%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 18%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 49%. The overall probability of good health is 85%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.50
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.75
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.57
P(V3=1 | X=0, V2=1) = 0.85
P(V3=1 | X=1, V2=0) = 0.18
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.85
0.85 * (0.58 - 0.75) * 0.85 + 0.15 * (0.29 - 0.50) * 0.18 = 0.27
0.27 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 40%. For infants with smoking mothers, the probability of freckles is 86%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.86
0.86 - 0.40 = 0.45
0.45 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 70%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 29%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 97%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 65%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 47%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 94%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 17%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 60%. The overall probability of good health is 49%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.65
P(V3=1 | X=0, V2=0) = 0.47
P(V3=1 | X=0, V2=1) = 0.94
P(V3=1 | X=1, V2=0) = 0.17
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.49
0.49 * 0.29 * (0.60 - 0.17)+ 0.51 * 0.29 * (0.94 - 0.47)= 0.11
0.11 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 15%. The probability of nonsmoking mother and freckles is 35%. The probability of smoking mother and freckles is 13%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.13
0.13/0.15 - 0.35/0.85 = 0.44
0.44 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 46%. For infants with smoking mothers, the probability of freckles is 84%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.84
0.84 - 0.46 = 0.38
0.38 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 19%. For infants with nonsmoking mothers, the probability of freckles is 46%. For infants with smoking mothers, the probability of freckles is 84%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.84
0.19*0.84 - 0.81*0.46 = 0.54
0.54 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 19%. The probability of nonsmoking mother and freckles is 37%. The probability of smoking mother and freckles is 16%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.16
0.16/0.19 - 0.37/0.81 = 0.38
0.38 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 49%. For infants with smoking mothers, the probability of freckles is 61%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.61
0.61 - 0.49 = 0.11
0.11 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10834,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 65%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 44%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 69%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 47%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 42%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 80%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 11%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 45%. The overall probability of good health is 82%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.80
P(V3=1 | X=1, V2=0) = 0.11
P(V3=1 | X=1, V2=1) = 0.45
P(V2=1) = 0.82
0.82 * 0.44 * (0.45 - 0.11)+ 0.18 * 0.44 * (0.80 - 0.42)= 0.09
0.09 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 10%. For infants with nonsmoking mothers, the probability of freckles is 49%. For infants with smoking mothers, the probability of freckles is 61%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.61
0.10*0.61 - 0.90*0.49 = 0.51
0.51 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 47%. For infants with smoking mothers, the probability of freckles is 50%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.50
0.50 - 0.47 = 0.03
0.03 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 47%. For infants with smoking mothers, the probability of freckles is 50%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.50
0.50 - 0.47 = 0.03
0.03 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10850,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 64%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 35%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 64%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 28%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 46%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 80%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 24%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 58%. The overall probability of good health is 42%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.46
P(V3=1 | X=0, V2=1) = 0.80
P(V3=1 | X=1, V2=0) = 0.24
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.42
0.42 * (0.28 - 0.64) * 0.80 + 0.58 * (0.35 - 0.64) * 0.24 = -0.05
-0.05 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 19%. For infants with nonsmoking mothers, the probability of freckles is 47%. For infants with smoking mothers, the probability of freckles is 50%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.50
0.19*0.50 - 0.81*0.47 = 0.47
0.47 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 42%. For infants with smoking mothers, the probability of freckles is 59%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.59
0.59 - 0.42 = 0.17
0.17 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 61%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 32%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 66%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 33%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 64%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 69%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 30%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 9%. The overall probability of good health is 45%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.61
P(Y=1 | X=0, V3=1) = 0.32
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.33
P(V3=1 | X=0, V2=0) = 0.64
P(V3=1 | X=0, V2=1) = 0.69
P(V3=1 | X=1, V2=0) = 0.30
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.45
0.45 * 0.32 * (0.09 - 0.30)+ 0.55 * 0.32 * (0.69 - 0.64)= 0.13
0.13 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 8%. For infants with nonsmoking mothers, the probability of freckles is 42%. For infants with smoking mothers, the probability of freckles is 59%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.59
0.08*0.59 - 0.92*0.42 = 0.43
0.43 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 8%. The probability of nonsmoking mother and freckles is 39%. The probability of smoking mother and freckles is 4%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.04
0.04/0.08 - 0.39/0.92 = 0.17
0.17 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look at how maternal smoking status correlates with freckles case by case according to infant's birth weight. Method 2: We look directly at how maternal smoking status correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10878,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 37%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 32%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 73%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 52%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 66%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 99%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 39%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 77%. The overall probability of good health is 95%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.32
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.52
P(V3=1 | X=0, V2=0) = 0.66
P(V3=1 | X=0, V2=1) = 0.99
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.77
P(V2=1) = 0.95
0.95 * (0.52 - 0.73) * 0.99 + 0.05 * (0.32 - 0.37) * 0.39 = 0.20
0.20 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 18%. For infants with nonsmoking mothers, the probability of freckles is 32%. For infants with smoking mothers, the probability of freckles is 58%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.58
0.18*0.58 - 0.82*0.32 = 0.37
0.37 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 18%. The probability of nonsmoking mother and freckles is 26%. The probability of smoking mother and freckles is 10%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.10
0.10/0.18 - 0.26/0.82 = 0.25
0.25 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 27%. For infants with smoking mothers, the probability of freckles is 65%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.65
0.65 - 0.27 = 0.38
0.38 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 45%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 19%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 73%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 48%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 43%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 83%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 21%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 42%. The overall probability of good health is 59%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.48
P(V3=1 | X=0, V2=0) = 0.43
P(V3=1 | X=0, V2=1) = 0.83
P(V3=1 | X=1, V2=0) = 0.21
P(V3=1 | X=1, V2=1) = 0.42
P(V2=1) = 0.59
0.59 * 0.19 * (0.42 - 0.21)+ 0.41 * 0.19 * (0.83 - 0.43)= 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 45%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 19%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 73%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 48%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 43%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 83%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 21%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 42%. The overall probability of good health is 59%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.48
P(V3=1 | X=0, V2=0) = 0.43
P(V3=1 | X=0, V2=1) = 0.83
P(V3=1 | X=1, V2=0) = 0.21
P(V3=1 | X=1, V2=1) = 0.42
P(V2=1) = 0.59
0.59 * 0.19 * (0.42 - 0.21)+ 0.41 * 0.19 * (0.83 - 0.43)= 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 45%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 19%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 73%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 48%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 43%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 83%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 21%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 42%. The overall probability of good health is 59%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.48
P(V3=1 | X=0, V2=0) = 0.43
P(V3=1 | X=0, V2=1) = 0.83
P(V3=1 | X=1, V2=0) = 0.21
P(V3=1 | X=1, V2=1) = 0.42
P(V2=1) = 0.59
0.59 * (0.48 - 0.73) * 0.83 + 0.41 * (0.19 - 0.45) * 0.21 = 0.30
0.30 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10899,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 62%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 31%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 96%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 60%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 81%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 76%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 33%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 42%. The overall probability of good health is 45%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.96
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.81
P(V3=1 | X=0, V2=1) = 0.76
P(V3=1 | X=1, V2=0) = 0.33
P(V3=1 | X=1, V2=1) = 0.42
P(V2=1) = 0.45
0.45 * 0.31 * (0.42 - 0.33)+ 0.55 * 0.31 * (0.76 - 0.81)= 0.13
0.13 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 62%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 31%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 96%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 60%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 81%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 76%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 33%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 42%. The overall probability of good health is 45%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.96
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.81
P(V3=1 | X=0, V2=1) = 0.76
P(V3=1 | X=1, V2=0) = 0.33
P(V3=1 | X=1, V2=1) = 0.42
P(V2=1) = 0.45
0.45 * (0.60 - 0.96) * 0.76 + 0.55 * (0.31 - 0.62) * 0.33 = 0.30
0.30 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 19%. For infants with nonsmoking mothers, the probability of freckles is 38%. For infants with smoking mothers, the probability of freckles is 82%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.82
0.19*0.82 - 0.81*0.38 = 0.46
0.46 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 19%. The probability of nonsmoking mother and freckles is 31%. The probability of smoking mother and freckles is 15%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.15
0.15/0.19 - 0.31/0.81 = 0.45
0.45 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 19%. The probability of nonsmoking mother and freckles is 31%. The probability of smoking mother and freckles is 15%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.15
0.15/0.19 - 0.31/0.81 = 0.45
0.45 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 46%. For infants with smoking mothers, the probability of freckles is 61%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.61
0.61 - 0.46 = 0.15
0.15 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 46%. For infants with smoking mothers, the probability of freckles is 61%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.61
0.61 - 0.46 = 0.15
0.15 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 68%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 41%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 70%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 40%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 23%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 85%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 2%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 32%. The overall probability of good health is 91%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.70
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.23
P(V3=1 | X=0, V2=1) = 0.85
P(V3=1 | X=1, V2=0) = 0.02
P(V3=1 | X=1, V2=1) = 0.32
P(V2=1) = 0.91
0.91 * 0.41 * (0.32 - 0.02)+ 0.09 * 0.41 * (0.85 - 0.23)= 0.17
0.17 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 68%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 41%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 70%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 40%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 23%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 85%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 2%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 32%. The overall probability of good health is 91%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.70
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.23
P(V3=1 | X=0, V2=1) = 0.85
P(V3=1 | X=1, V2=0) = 0.02
P(V3=1 | X=1, V2=1) = 0.32
P(V2=1) = 0.91
0.91 * (0.40 - 0.70) * 0.85 + 0.09 * (0.41 - 0.68) * 0.02 = -0.01
-0.01 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 18%. For infants with nonsmoking mothers, the probability of freckles is 46%. For infants with smoking mothers, the probability of freckles is 61%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.61
0.18*0.61 - 0.82*0.46 = 0.49
0.49 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 18%. The probability of nonsmoking mother and freckles is 38%. The probability of smoking mother and freckles is 11%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.11
0.11/0.18 - 0.38/0.82 = 0.15
0.15 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 41%. For infants with smoking mothers, the probability of freckles is 53%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.53
0.53 - 0.41 = 0.12
0.12 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10929,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 41%. For infants with smoking mothers, the probability of freckles is 53%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.53
0.53 - 0.41 = 0.12
0.12 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10930,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 41%. For infants with smoking mothers, the probability of freckles is 53%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.53
0.53 - 0.41 = 0.12
0.12 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 41%. For infants with smoking mothers, the probability of freckles is 53%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.53
0.53 - 0.41 = 0.12
0.12 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 58%. For infants with smoking mothers, the probability of freckles is 68%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.68
0.68 - 0.58 = 0.10
0.10 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 77%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 47%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 79%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 36%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 67%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 64%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 34%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 20%. The overall probability of good health is 57%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.36
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.64
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.57
0.57 * 0.47 * (0.20 - 0.34)+ 0.43 * 0.47 * (0.64 - 0.67)= 0.12
0.12 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 77%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 47%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 79%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 36%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 67%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 64%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 34%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 20%. The overall probability of good health is 57%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.36
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.64
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.57
0.57 * (0.36 - 0.79) * 0.64 + 0.43 * (0.47 - 0.77) * 0.34 = -0.07
-0.07 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 20%. For infants with nonsmoking mothers, the probability of freckles is 58%. For infants with smoking mothers, the probability of freckles is 68%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.68
0.20*0.68 - 0.80*0.58 = 0.59
0.59 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 20%. The probability of nonsmoking mother and freckles is 46%. The probability of smoking mother and freckles is 13%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.13
0.13/0.20 - 0.46/0.80 = 0.10
0.10 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 20%. The probability of nonsmoking mother and freckles is 46%. The probability of smoking mother and freckles is 13%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.13
0.13/0.20 - 0.46/0.80 = 0.10
0.10 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 46%. For infants with smoking mothers, the probability of freckles is 80%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.80
0.80 - 0.46 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 46%. For infants with smoking mothers, the probability of freckles is 80%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.80
0.80 - 0.46 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 66%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 37%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 92%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 64%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 50%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 80%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 20%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 59%. The overall probability of good health is 59%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.37
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.64
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.80
P(V3=1 | X=1, V2=0) = 0.20
P(V3=1 | X=1, V2=1) = 0.59
P(V2=1) = 0.59
0.59 * 0.37 * (0.59 - 0.20)+ 0.41 * 0.37 * (0.80 - 0.50)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 66%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 37%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 92%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 64%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 50%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 80%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 20%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 59%. The overall probability of good health is 59%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.37
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.64
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.80
P(V3=1 | X=1, V2=0) = 0.20
P(V3=1 | X=1, V2=1) = 0.59
P(V2=1) = 0.59
0.59 * 0.37 * (0.59 - 0.20)+ 0.41 * 0.37 * (0.80 - 0.50)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10965,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 11%. For infants with nonsmoking mothers, the probability of freckles is 46%. For infants with smoking mothers, the probability of freckles is 80%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.80
0.11*0.80 - 0.89*0.46 = 0.50
0.50 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 11%. The probability of nonsmoking mother and freckles is 41%. The probability of smoking mother and freckles is 9%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.09
0.09/0.11 - 0.41/0.89 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look at how maternal smoking status correlates with freckles case by case according to infant's birth weight. Method 2: We look directly at how maternal smoking status correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 12%. For infants with smoking mothers, the probability of freckles is 52%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.52
0.52 - 0.12 = 0.40
0.40 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 36%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 3%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 62%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 31%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 76%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 69%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 37%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 28%. The overall probability of good health is 52%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.03
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.31
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.69
P(V3=1 | X=1, V2=0) = 0.37
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.52
0.52 * (0.31 - 0.62) * 0.69 + 0.48 * (0.03 - 0.36) * 0.37 = 0.28
0.28 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
10980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 6%. The probability of nonsmoking mother and freckles is 12%. The probability of smoking mother and freckles is 3%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.03
0.03/0.06 - 0.12/0.94 = 0.40
0.40 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
10982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look at how maternal smoking status correlates with freckles case by case according to infant's birth weight. Method 2: We look directly at how maternal smoking status correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 45%. For infants with smoking mothers, the probability of freckles is 69%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.69
0.69 - 0.45 = 0.25
0.25 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
10986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 45%. For infants with smoking mothers, the probability of freckles is 69%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.69
0.69 - 0.45 = 0.25
0.25 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
10988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 88%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 42%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 81%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 56%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 98%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 92%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 47%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 47%. The overall probability of good health is 44%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.81
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.98
P(V3=1 | X=0, V2=1) = 0.92
P(V3=1 | X=1, V2=0) = 0.47
P(V3=1 | X=1, V2=1) = 0.47
P(V2=1) = 0.44
0.44 * 0.42 * (0.47 - 0.47)+ 0.56 * 0.42 * (0.92 - 0.98)= 0.22
0.22 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
10992,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 5%. For infants with nonsmoking mothers, the probability of freckles is 45%. For infants with smoking mothers, the probability of freckles is 69%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.69
0.05*0.69 - 0.95*0.45 = 0.46
0.46 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 5%. For infants with nonsmoking mothers, the probability of freckles is 45%. For infants with smoking mothers, the probability of freckles is 69%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.69
0.05*0.69 - 0.95*0.45 = 0.46
0.46 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
10996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look at how maternal smoking status correlates with freckles case by case according to infant's birth weight. Method 2: We look directly at how maternal smoking status correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
10999,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 44%. For infants with smoking mothers, the probability of freckles is 79%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.79
0.79 - 0.44 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 44%. For infants with smoking mothers, the probability of freckles is 79%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.79
0.79 - 0.44 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11003,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 57%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 40%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 86%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 64%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 35%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 82%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 5%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 38%. The overall probability of good health is 86%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.64
P(V3=1 | X=0, V2=0) = 0.35
P(V3=1 | X=0, V2=1) = 0.82
P(V3=1 | X=1, V2=0) = 0.05
P(V3=1 | X=1, V2=1) = 0.38
P(V2=1) = 0.86
0.86 * 0.40 * (0.38 - 0.05)+ 0.14 * 0.40 * (0.82 - 0.35)= 0.11
0.11 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 57%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 40%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 86%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 64%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 35%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 82%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 5%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 38%. The overall probability of good health is 86%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.64
P(V3=1 | X=0, V2=0) = 0.35
P(V3=1 | X=0, V2=1) = 0.82
P(V3=1 | X=1, V2=0) = 0.05
P(V3=1 | X=1, V2=1) = 0.38
P(V2=1) = 0.86
0.86 * (0.64 - 0.86) * 0.82 + 0.14 * (0.40 - 0.57) * 0.05 = 0.23
0.23 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 16%. For infants with nonsmoking mothers, the probability of freckles is 44%. For infants with smoking mothers, the probability of freckles is 79%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.79
0.16*0.79 - 0.84*0.44 = 0.50
0.50 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
11008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 16%. The probability of nonsmoking mother and freckles is 37%. The probability of smoking mother and freckles is 12%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.12
0.12/0.16 - 0.37/0.84 = 0.35
0.35 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
11010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look at how maternal smoking status correlates with freckles case by case according to infant's birth weight. Method 2: We look directly at how maternal smoking status correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
11011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
11014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 62%. For infants with smoking mothers, the probability of freckles is 74%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.74
0.74 - 0.62 = 0.11
0.11 > 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 85%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 50%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 81%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 56%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 39%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 65%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 1%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 31%. The overall probability of good health is 95%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.81
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.65
P(V3=1 | X=1, V2=0) = 0.01
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.95
0.95 * 0.50 * (0.31 - 0.01)+ 0.05 * 0.50 * (0.65 - 0.39)= 0.13
0.13 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 85%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 50%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 81%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 56%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 39%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 65%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 1%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 31%. The overall probability of good health is 95%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.81
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.65
P(V3=1 | X=1, V2=0) = 0.01
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.95
0.95 * 0.50 * (0.31 - 0.01)+ 0.05 * 0.50 * (0.65 - 0.39)= 0.13
0.13 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 85%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 50%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 81%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 56%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 39%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 65%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 1%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 31%. The overall probability of good health is 95%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.81
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.65
P(V3=1 | X=1, V2=0) = 0.01
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.95
0.95 * (0.56 - 0.81) * 0.65 + 0.05 * (0.50 - 0.85) * 0.01 = 0.02
0.02 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11022,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 6%. The probability of nonsmoking mother and freckles is 59%. The probability of smoking mother and freckles is 4%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.04
0.04/0.06 - 0.59/0.94 = 0.11
0.11 > 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
11025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. Method 1: We look directly at how maternal smoking status correlates with freckles in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
11027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers, the probability of freckles is 61%. For infants with smoking mothers, the probability of freckles is 80%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.80
0.80 - 0.61 = 0.19
0.19 > 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 81%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 53%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 92%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 51%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 53%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 84%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 13%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 41%. The overall probability of good health is 48%.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.81
P(Y=1 | X=0, V3=1) = 0.53
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.84
P(V3=1 | X=1, V2=0) = 0.13
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.48
0.48 * 0.53 * (0.41 - 0.13)+ 0.52 * 0.53 * (0.84 - 0.53)= 0.12
0.12 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 81%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 53%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 92%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 51%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 53%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 84%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 13%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 41%. The overall probability of good health is 48%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.81
P(Y=1 | X=0, V3=1) = 0.53
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.84
P(V3=1 | X=1, V2=0) = 0.13
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.48
0.48 * 0.53 * (0.41 - 0.13)+ 0.52 * 0.53 * (0.84 - 0.53)= 0.12
0.12 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11033,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. For infants with nonsmoking mothers and low infant birth weight, the probability of freckles is 81%. For infants with nonsmoking mothers and normal infant birth weight, the probability of freckles is 53%. For infants with smoking mothers and low infant birth weight, the probability of freckles is 92%. For infants with smoking mothers and normal infant birth weight, the probability of freckles is 51%. For infants with nonsmoking mothers and with poor health, the probability of normal infant birth weight is 53%. For infants with nonsmoking mothers and with good health, the probability of normal infant birth weight is 84%. For infants with smoking mothers and with poor health, the probability of normal infant birth weight is 13%. For infants with smoking mothers and with good health, the probability of normal infant birth weight is 41%. The overall probability of good health is 48%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.81
P(Y=1 | X=0, V3=1) = 0.53
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.53
P(V3=1 | X=0, V2=1) = 0.84
P(V3=1 | X=1, V2=0) = 0.13
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.48
0.48 * (0.51 - 0.92) * 0.84 + 0.52 * (0.53 - 0.81) * 0.13 = 0.02
0.02 > 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. The overall probability of smoking mother is 19%. For infants with nonsmoking mothers, the probability of freckles is 61%. For infants with smoking mothers, the probability of freckles is 80%.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.80
0.19*0.80 - 0.81*0.61 = 0.64
0.64 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
11040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 15%. For smokers, the probability of high tar deposit is 67%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 37%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 81%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 38%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 76%. The overall probability of smoking is 57%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.15
P(V3=1 | X=1) = 0.67
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.81
P(Y=1 | X=1, V3=0) = 0.38
P(Y=1 | X=1, V3=1) = 0.76
P(X=1) = 0.57
(0.67 - 0.15)* (0.76 * 0.57) + (0.33 - 0.85) * (0.81 * 0.43) = 0.21
0.21 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 37%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 71%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 82%. For nonsmokers, the probability of high tar deposit is 32%. For smokers, the probability of high tar deposit is 84%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.82
P(V3=1 | X=0) = 0.32
P(V3=1 | X=1) = 0.84
0.82 * (0.84 - 0.32) + 0.71 * (0.16 - 0.68) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 32%. For smokers, the probability of high tar deposit is 84%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 37%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 71%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 82%. The overall probability of smoking is 47%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.32
P(V3=1 | X=1) = 0.84
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.82
P(X=1) = 0.47
0.84 - 0.32 * (0.82 * 0.47 + 0.71 * 0.53)= 0.17
0.17 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 47%. For nonsmokers, the probability of being allergic to peanuts is 48%. For smokers, the probability of being allergic to peanuts is 77%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.77
0.47*0.77 - 0.53*0.48 = 0.62
0.62 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 47%. The probability of nonsmoking and being allergic to peanuts is 26%. The probability of smoking and being allergic to peanuts is 36%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.36
0.36/0.47 - 0.26/0.53 = 0.29
0.29 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 18%. For smokers, the probability of high tar deposit is 70%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 82%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 40%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 74%. The overall probability of smoking is 42%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.18
P(V3=1 | X=1) = 0.70
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.74
P(X=1) = 0.42
(0.70 - 0.18)* (0.74 * 0.42) + (0.30 - 0.82) * (0.82 * 0.58) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 18%. For smokers, the probability of high tar deposit is 70%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 82%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 40%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 74%. The overall probability of smoking is 42%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.18
P(V3=1 | X=1) = 0.70
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.74
P(X=1) = 0.42
(0.70 - 0.18)* (0.74 * 0.42) + (0.30 - 0.82) * (0.82 * 0.58) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 18%. For smokers, the probability of high tar deposit is 70%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 82%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 40%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 74%. The overall probability of smoking is 42%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.18
P(V3=1 | X=1) = 0.70
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.74
P(X=1) = 0.42
0.70 - 0.18 * (0.74 * 0.42 + 0.82 * 0.58)= 0.17
0.17 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11070,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 42%. For nonsmokers, the probability of being allergic to peanuts is 55%. For smokers, the probability of being allergic to peanuts is 64%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.64
0.42*0.64 - 0.58*0.55 = 0.58
0.58 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 42%. For nonsmokers, the probability of being allergic to peanuts is 55%. For smokers, the probability of being allergic to peanuts is 64%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.64
0.42*0.64 - 0.58*0.55 = 0.58
0.58 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 42%. The probability of nonsmoking and being allergic to peanuts is 32%. The probability of smoking and being allergic to peanuts is 27%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.27
0.27/0.42 - 0.32/0.58 = 0.09
0.09 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 33%. For smokers, the probability of high tar deposit is 88%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 20%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 61%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 20%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 55%. The overall probability of smoking is 52%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.33
P(V3=1 | X=1) = 0.88
P(Y=1 | X=0, V3=0) = 0.20
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.20
P(Y=1 | X=1, V3=1) = 0.55
P(X=1) = 0.52
(0.88 - 0.33)* (0.55 * 0.52) + (0.12 - 0.67) * (0.61 * 0.48) = 0.21
0.21 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 20%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 61%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 20%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 55%. For nonsmokers, the probability of high tar deposit is 33%. For smokers, the probability of high tar deposit is 88%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.20
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.20
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0) = 0.33
P(V3=1 | X=1) = 0.88
0.55 * (0.88 - 0.33) + 0.61 * (0.12 - 0.67) = 0.19
0.19 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 52%. The probability of nonsmoking and being allergic to peanuts is 16%. The probability of smoking and being allergic to peanuts is 26%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.26
0.26/0.52 - 0.16/0.48 = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 6%. For smokers, the probability of high tar deposit is 42%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 33%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 76%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 52%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 87%. The overall probability of smoking is 58%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.06
P(V3=1 | X=1) = 0.42
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.87
P(X=1) = 0.58
(0.42 - 0.06)* (0.87 * 0.58) + (0.58 - 0.94) * (0.76 * 0.42) = 0.14
0.14 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 58%. The probability of nonsmoking and being allergic to peanuts is 15%. The probability of smoking and being allergic to peanuts is 39%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.39
0.39/0.58 - 0.15/0.42 = 0.31
0.31 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 96%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 70%. For nonsmokers, the probability of high tar deposit is 62%. For smokers, the probability of high tar deposit is 93%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.96
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0) = 0.62
P(V3=1 | X=1) = 0.93
0.70 * (0.93 - 0.62) + 0.96 * (0.07 - 0.38) = 0.14
0.14 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11104,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 62%. For smokers, the probability of high tar deposit is 93%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 96%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 70%. The overall probability of smoking is 51%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.62
P(V3=1 | X=1) = 0.93
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.96
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.70
P(X=1) = 0.51
0.93 - 0.62 * (0.70 * 0.51 + 0.96 * 0.49)= 0.15
0.15 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 62%. For smokers, the probability of high tar deposit is 93%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 96%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 70%. The overall probability of smoking is 51%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.62
P(V3=1 | X=1) = 0.93
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.96
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.70
P(X=1) = 0.51
0.93 - 0.62 * (0.70 * 0.51 + 0.96 * 0.49)= 0.15
0.15 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 7%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 60%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 13%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 67%. For nonsmokers, the probability of high tar deposit is 21%. For smokers, the probability of high tar deposit is 67%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.07
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.13
P(Y=1 | X=1, V3=1) = 0.67
P(V3=1 | X=0) = 0.21
P(V3=1 | X=1) = 0.67
0.67 * (0.67 - 0.21) + 0.60 * (0.33 - 0.79) = 0.25
0.25 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11117,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 21%. For smokers, the probability of high tar deposit is 67%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 7%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 60%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 13%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 67%. The overall probability of smoking is 55%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.21
P(V3=1 | X=1) = 0.67
P(Y=1 | X=0, V3=0) = 0.07
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.13
P(Y=1 | X=1, V3=1) = 0.67
P(X=1) = 0.55
0.67 - 0.21 * (0.67 * 0.55 + 0.60 * 0.45)= 0.25
0.25 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 55%. For nonsmokers, the probability of being allergic to peanuts is 18%. For smokers, the probability of being allergic to peanuts is 50%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.50
0.55*0.50 - 0.45*0.18 = 0.35
0.35 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 55%. For nonsmokers, the probability of being allergic to peanuts is 18%. For smokers, the probability of being allergic to peanuts is 50%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.50
0.55*0.50 - 0.45*0.18 = 0.35
0.35 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 55%. The probability of nonsmoking and being allergic to peanuts is 8%. The probability of smoking and being allergic to peanuts is 27%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.27
0.27/0.55 - 0.08/0.45 = 0.32
0.32 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 53%. For smokers, the probability of high tar deposit is 94%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 69%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 31%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 55%. The overall probability of smoking is 63%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.53
P(V3=1 | X=1) = 0.94
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.31
P(Y=1 | X=1, V3=1) = 0.55
P(X=1) = 0.63
(0.94 - 0.53)* (0.55 * 0.63) + (0.06 - 0.47) * (0.69 * 0.37) = 0.10
0.10 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 69%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 31%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 55%. For nonsmokers, the probability of high tar deposit is 53%. For smokers, the probability of high tar deposit is 94%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.31
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0) = 0.53
P(V3=1 | X=1) = 0.94
0.55 * (0.94 - 0.53) + 0.69 * (0.06 - 0.47) = 0.10
0.10 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 69%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 31%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 55%. For nonsmokers, the probability of high tar deposit is 53%. For smokers, the probability of high tar deposit is 94%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.31
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0) = 0.53
P(V3=1 | X=1) = 0.94
0.55 * (0.94 - 0.53) + 0.69 * (0.06 - 0.47) = 0.10
0.10 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 63%. For nonsmokers, the probability of being allergic to peanuts is 57%. For smokers, the probability of being allergic to peanuts is 53%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.53
0.63*0.53 - 0.37*0.57 = 0.55
0.55 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 28%. For smokers, the probability of high tar deposit is 58%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 27%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 62%. The overall probability of smoking is 58%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.28
P(V3=1 | X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.27
P(Y=1 | X=1, V3=1) = 0.62
P(X=1) = 0.58
(0.58 - 0.28)* (0.62 * 0.58) + (0.42 - 0.72) * (0.77 * 0.42) = 0.10
0.10 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 28%. For smokers, the probability of high tar deposit is 58%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 27%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 62%. The overall probability of smoking is 58%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.28
P(V3=1 | X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.27
P(Y=1 | X=1, V3=1) = 0.62
P(X=1) = 0.58
(0.58 - 0.28)* (0.62 * 0.58) + (0.42 - 0.72) * (0.77 * 0.42) = 0.10
0.10 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 28%. For smokers, the probability of high tar deposit is 58%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 27%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 62%. The overall probability of smoking is 58%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.28
P(V3=1 | X=1) = 0.58
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.27
P(Y=1 | X=1, V3=1) = 0.62
P(X=1) = 0.58
0.58 - 0.28 * (0.62 * 0.58 + 0.77 * 0.42)= 0.10
0.10 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 58%. The probability of nonsmoking and being allergic to peanuts is 23%. The probability of smoking and being allergic to peanuts is 27%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.27
0.27/0.58 - 0.23/0.42 = -0.10
-0.10 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 21%. For smokers, the probability of high tar deposit is 64%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 29%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 67%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 31%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 70%. The overall probability of smoking is 55%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.21
P(V3=1 | X=1) = 0.64
P(Y=1 | X=0, V3=0) = 0.29
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.31
P(Y=1 | X=1, V3=1) = 0.70
P(X=1) = 0.55
(0.64 - 0.21)* (0.70 * 0.55) + (0.36 - 0.79) * (0.67 * 0.45) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 55%. For nonsmokers, the probability of being allergic to peanuts is 37%. For smokers, the probability of being allergic to peanuts is 56%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.56
0.55*0.56 - 0.45*0.37 = 0.47
0.47 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 55%. The probability of nonsmoking and being allergic to peanuts is 16%. The probability of smoking and being allergic to peanuts is 31%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.31
0.31/0.55 - 0.16/0.45 = 0.19
0.19 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11157,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 55%. The probability of nonsmoking and being allergic to peanuts is 16%. The probability of smoking and being allergic to peanuts is 31%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.31
0.31/0.55 - 0.16/0.45 = 0.19
0.19 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11162,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 42%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 72%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 42%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 72%. For nonsmokers, the probability of high tar deposit is 31%. For smokers, the probability of high tar deposit is 80%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.72
P(V3=1 | X=0) = 0.31
P(V3=1 | X=1) = 0.80
0.72 * (0.80 - 0.31) + 0.72 * (0.20 - 0.69) = 0.15
0.15 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 62%. For nonsmokers, the probability of being allergic to peanuts is 51%. For smokers, the probability of being allergic to peanuts is 66%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.62
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.66
0.62*0.66 - 0.38*0.51 = 0.60
0.60 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 62%. The probability of nonsmoking and being allergic to peanuts is 19%. The probability of smoking and being allergic to peanuts is 41%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.62
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.41
0.41/0.62 - 0.19/0.38 = 0.15
0.15 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 37%. For nonsmokers, the probability of being allergic to peanuts is 46%. For smokers, the probability of being allergic to peanuts is 43%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.43
0.37*0.43 - 0.63*0.46 = 0.44
0.44 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 37%. For nonsmokers, the probability of being allergic to peanuts is 46%. For smokers, the probability of being allergic to peanuts is 43%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.43
0.37*0.43 - 0.63*0.46 = 0.44
0.44 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 37%. The probability of nonsmoking and being allergic to peanuts is 29%. The probability of smoking and being allergic to peanuts is 16%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.16
0.16/0.37 - 0.29/0.63 = -0.02
-0.02 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 37%. The probability of nonsmoking and being allergic to peanuts is 29%. The probability of smoking and being allergic to peanuts is 16%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.16
0.16/0.37 - 0.29/0.63 = -0.02
-0.02 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 72%. For nonsmokers, the probability of being allergic to peanuts is 40%. For smokers, the probability of being allergic to peanuts is 53%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.72
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.53
0.72*0.53 - 0.28*0.40 = 0.50
0.50 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11192,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 72%. The probability of nonsmoking and being allergic to peanuts is 11%. The probability of smoking and being allergic to peanuts is 38%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.72
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.38
0.38/0.72 - 0.11/0.28 = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11198,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 35%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 63%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers, the probability of high tar deposit is 22%. For smokers, the probability of high tar deposit is 73%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0) = 0.22
P(V3=1 | X=1) = 0.73
0.49 * (0.73 - 0.22) + 0.63 * (0.27 - 0.78) = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 22%. For smokers, the probability of high tar deposit is 73%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 35%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 63%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 49%. The overall probability of smoking is 61%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.22
P(V3=1 | X=1) = 0.73
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.49
P(X=1) = 0.61
0.73 - 0.22 * (0.49 * 0.61 + 0.63 * 0.39)= 0.13
0.13 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 22%. For smokers, the probability of high tar deposit is 73%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 35%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 63%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 49%. The overall probability of smoking is 61%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.22
P(V3=1 | X=1) = 0.73
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.49
P(X=1) = 0.61
0.73 - 0.22 * (0.49 * 0.61 + 0.63 * 0.39)= 0.13
0.13 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11203,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 61%. For nonsmokers, the probability of being allergic to peanuts is 41%. For smokers, the probability of being allergic to peanuts is 43%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.61
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.43
0.61*0.43 - 0.39*0.41 = 0.43
0.43 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11209,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 16%. For smokers, the probability of high tar deposit is 93%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 23%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 50%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 12%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 38%. The overall probability of smoking is 50%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.16
P(V3=1 | X=1) = 0.93
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.12
P(Y=1 | X=1, V3=1) = 0.38
P(X=1) = 0.50
(0.93 - 0.16)* (0.38 * 0.50) + (0.07 - 0.84) * (0.50 * 0.50) = 0.20
0.20 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 16%. For smokers, the probability of high tar deposit is 93%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 23%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 50%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 12%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 38%. The overall probability of smoking is 50%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.16
P(V3=1 | X=1) = 0.93
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.12
P(Y=1 | X=1, V3=1) = 0.38
P(X=1) = 0.50
0.93 - 0.16 * (0.38 * 0.50 + 0.50 * 0.50)= 0.20
0.20 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 16%. For smokers, the probability of high tar deposit is 93%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 23%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 50%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 12%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 38%. The overall probability of smoking is 50%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.16
P(V3=1 | X=1) = 0.93
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.12
P(Y=1 | X=1, V3=1) = 0.38
P(X=1) = 0.50
0.93 - 0.16 * (0.38 * 0.50 + 0.50 * 0.50)= 0.20
0.20 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 50%. The probability of nonsmoking and being allergic to peanuts is 14%. The probability of smoking and being allergic to peanuts is 18%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.18
0.18/0.50 - 0.14/0.50 = 0.09
0.09 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 41%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 67%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 40%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 68%. For nonsmokers, the probability of high tar deposit is 34%. For smokers, the probability of high tar deposit is 83%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0) = 0.34
P(V3=1 | X=1) = 0.83
0.68 * (0.83 - 0.34) + 0.67 * (0.17 - 0.66) = 0.14
0.14 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 34%. For smokers, the probability of high tar deposit is 83%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 41%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 67%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 40%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 68%. The overall probability of smoking is 42%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.34
P(V3=1 | X=1) = 0.83
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.68
P(X=1) = 0.42
0.83 - 0.34 * (0.68 * 0.42 + 0.67 * 0.58)= 0.13
0.13 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 42%. For nonsmokers, the probability of being allergic to peanuts is 50%. For smokers, the probability of being allergic to peanuts is 63%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.63
0.42*0.63 - 0.58*0.50 = 0.55
0.55 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 42%. The probability of nonsmoking and being allergic to peanuts is 29%. The probability of smoking and being allergic to peanuts is 27%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.27
0.27/0.42 - 0.29/0.58 = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 45%. For smokers, the probability of high tar deposit is 67%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 30%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 52%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 23%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 44%. The overall probability of smoking is 50%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.45
P(V3=1 | X=1) = 0.67
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.23
P(Y=1 | X=1, V3=1) = 0.44
P(X=1) = 0.50
(0.67 - 0.45)* (0.44 * 0.50) + (0.33 - 0.55) * (0.52 * 0.50) = 0.05
0.05 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 45%. For smokers, the probability of high tar deposit is 67%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 30%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 52%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 23%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 44%. The overall probability of smoking is 50%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.45
P(V3=1 | X=1) = 0.67
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.23
P(Y=1 | X=1, V3=1) = 0.44
P(X=1) = 0.50
0.67 - 0.45 * (0.44 * 0.50 + 0.52 * 0.50)= 0.05
0.05 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 50%. For nonsmokers, the probability of being allergic to peanuts is 40%. For smokers, the probability of being allergic to peanuts is 37%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.37
0.50*0.37 - 0.50*0.40 = 0.39
0.39 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 50%. For nonsmokers, the probability of being allergic to peanuts is 40%. For smokers, the probability of being allergic to peanuts is 37%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.37
0.50*0.37 - 0.50*0.40 = 0.39
0.39 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 50%. The probability of nonsmoking and being allergic to peanuts is 20%. The probability of smoking and being allergic to peanuts is 19%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.19
0.19/0.50 - 0.20/0.50 = -0.03
-0.03 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 19%. For smokers, the probability of high tar deposit is 70%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 45%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 70%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 32%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 59%. The overall probability of smoking is 48%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.70
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.70
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.59
P(X=1) = 0.48
(0.70 - 0.19)* (0.59 * 0.48) + (0.30 - 0.81) * (0.70 * 0.52) = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 45%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 70%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 32%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 59%. For nonsmokers, the probability of high tar deposit is 19%. For smokers, the probability of high tar deposit is 70%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.70
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.59
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.70
0.59 * (0.70 - 0.19) + 0.70 * (0.30 - 0.81) = 0.14
0.14 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11248,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 19%. For smokers, the probability of high tar deposit is 70%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 45%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 70%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 32%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 59%. The overall probability of smoking is 48%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.70
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.70
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.59
P(X=1) = 0.48
0.70 - 0.19 * (0.59 * 0.48 + 0.70 * 0.52)= 0.13
0.13 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 48%. For nonsmokers, the probability of being allergic to peanuts is 50%. For smokers, the probability of being allergic to peanuts is 51%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.51
0.48*0.51 - 0.52*0.50 = 0.50
0.50 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 19%. For smokers, the probability of high tar deposit is 71%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 57%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 26%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 58%. The overall probability of smoking is 38%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.71
P(Y=1 | X=0, V3=0) = 0.25
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.26
P(Y=1 | X=1, V3=1) = 0.58
P(X=1) = 0.38
(0.71 - 0.19)* (0.58 * 0.38) + (0.29 - 0.81) * (0.57 * 0.62) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 19%. For smokers, the probability of high tar deposit is 71%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 57%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 26%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 58%. The overall probability of smoking is 38%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.71
P(Y=1 | X=0, V3=0) = 0.25
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.26
P(Y=1 | X=1, V3=1) = 0.58
P(X=1) = 0.38
(0.71 - 0.19)* (0.58 * 0.38) + (0.29 - 0.81) * (0.57 * 0.62) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 57%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 26%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 58%. For nonsmokers, the probability of high tar deposit is 19%. For smokers, the probability of high tar deposit is 71%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.25
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.26
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.71
0.58 * (0.71 - 0.19) + 0.57 * (0.29 - 0.81) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 57%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 26%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 58%. For nonsmokers, the probability of high tar deposit is 19%. For smokers, the probability of high tar deposit is 71%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.25
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.26
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.71
0.58 * (0.71 - 0.19) + 0.57 * (0.29 - 0.81) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 19%. For smokers, the probability of high tar deposit is 71%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 25%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 57%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 26%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 58%. The overall probability of smoking is 38%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.19
P(V3=1 | X=1) = 0.71
P(Y=1 | X=0, V3=0) = 0.25
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.26
P(Y=1 | X=1, V3=1) = 0.58
P(X=1) = 0.38
0.71 - 0.19 * (0.58 * 0.38 + 0.57 * 0.62)= 0.17
0.17 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11262,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 38%. For nonsmokers, the probability of being allergic to peanuts is 31%. For smokers, the probability of being allergic to peanuts is 49%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.38
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.49
0.38*0.49 - 0.62*0.31 = 0.38
0.38 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 25%. For smokers, the probability of high tar deposit is 78%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 34%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 59%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 42%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 69%. The overall probability of smoking is 76%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.25
P(V3=1 | X=1) = 0.78
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.69
P(X=1) = 0.76
(0.78 - 0.25)* (0.69 * 0.76) + (0.22 - 0.75) * (0.59 * 0.24) = 0.14
0.14 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 25%. For smokers, the probability of high tar deposit is 78%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 34%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 59%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 42%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 69%. The overall probability of smoking is 76%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.25
P(V3=1 | X=1) = 0.78
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.69
P(X=1) = 0.76
(0.78 - 0.25)* (0.69 * 0.76) + (0.22 - 0.75) * (0.59 * 0.24) = 0.14
0.14 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 34%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 59%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 42%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 69%. For nonsmokers, the probability of high tar deposit is 25%. For smokers, the probability of high tar deposit is 78%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.69
P(V3=1 | X=0) = 0.25
P(V3=1 | X=1) = 0.78
0.69 * (0.78 - 0.25) + 0.59 * (0.22 - 0.75) = 0.14
0.14 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 76%. For nonsmokers, the probability of being allergic to peanuts is 40%. For smokers, the probability of being allergic to peanuts is 63%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.76
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.63
0.76*0.63 - 0.24*0.40 = 0.57
0.57 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 76%. For nonsmokers, the probability of being allergic to peanuts is 40%. For smokers, the probability of being allergic to peanuts is 63%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.76
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.63
0.76*0.63 - 0.24*0.40 = 0.57
0.57 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11280,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 43%. For smokers, the probability of high tar deposit is 64%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 76%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 16%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 55%. The overall probability of smoking is 48%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.43
P(V3=1 | X=1) = 0.64
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.55
P(X=1) = 0.48
(0.64 - 0.43)* (0.55 * 0.48) + (0.36 - 0.57) * (0.76 * 0.52) = 0.07
0.07 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 76%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 16%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 55%. For nonsmokers, the probability of high tar deposit is 43%. For smokers, the probability of high tar deposit is 64%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0) = 0.43
P(V3=1 | X=1) = 0.64
0.55 * (0.64 - 0.43) + 0.76 * (0.36 - 0.57) = 0.08
0.08 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 43%. For smokers, the probability of high tar deposit is 64%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 76%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 16%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 55%. The overall probability of smoking is 48%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.43
P(V3=1 | X=1) = 0.64
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.55
P(X=1) = 0.48
0.64 - 0.43 * (0.55 * 0.48 + 0.76 * 0.52)= 0.07
0.07 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 48%. The probability of nonsmoking and being allergic to peanuts is 30%. The probability of smoking and being allergic to peanuts is 20%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.20
0.20/0.48 - 0.30/0.52 = -0.16
-0.16 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 42%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 83%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 48%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 74%. For nonsmokers, the probability of high tar deposit is 56%. For smokers, the probability of high tar deposit is 83%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0) = 0.56
P(V3=1 | X=1) = 0.83
0.74 * (0.83 - 0.56) + 0.83 * (0.17 - 0.44) = 0.07
0.07 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 56%. For smokers, the probability of high tar deposit is 83%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 42%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 83%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 48%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 74%. The overall probability of smoking is 45%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.56
P(V3=1 | X=1) = 0.83
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.74
P(X=1) = 0.45
0.83 - 0.56 * (0.74 * 0.45 + 0.83 * 0.55)= 0.09
0.09 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 45%. The probability of nonsmoking and being allergic to peanuts is 36%. The probability of smoking and being allergic to peanuts is 31%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.31
0.31/0.45 - 0.36/0.55 = 0.05
0.05 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 45%. The probability of nonsmoking and being allergic to peanuts is 36%. The probability of smoking and being allergic to peanuts is 31%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.31
0.31/0.45 - 0.36/0.55 = 0.05
0.05 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 44%. For smokers, the probability of high tar deposit is 79%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 20%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 46%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 35%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 58%. The overall probability of smoking is 59%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.44
P(V3=1 | X=1) = 0.79
P(Y=1 | X=0, V3=0) = 0.20
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.58
P(X=1) = 0.59
0.79 - 0.44 * (0.58 * 0.59 + 0.46 * 0.41)= 0.09
0.09 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 44%. For smokers, the probability of high tar deposit is 79%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 20%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 46%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 35%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 58%. The overall probability of smoking is 59%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.44
P(V3=1 | X=1) = 0.79
P(Y=1 | X=0, V3=0) = 0.20
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.58
P(X=1) = 0.59
0.79 - 0.44 * (0.58 * 0.59 + 0.46 * 0.41)= 0.09
0.09 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 41%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 66%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 27%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 53%. For nonsmokers, the probability of high tar deposit is 9%. For smokers, the probability of high tar deposit is 87%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.27
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0) = 0.09
P(V3=1 | X=1) = 0.87
0.53 * (0.87 - 0.09) + 0.66 * (0.13 - 0.91) = 0.20
0.20 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11321,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 9%. For smokers, the probability of high tar deposit is 87%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 41%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 66%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 27%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 53%. The overall probability of smoking is 44%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.09
P(V3=1 | X=1) = 0.87
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.27
P(Y=1 | X=1, V3=1) = 0.53
P(X=1) = 0.44
0.87 - 0.09 * (0.53 * 0.44 + 0.66 * 0.56)= 0.20
0.20 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 44%. For nonsmokers, the probability of being allergic to peanuts is 44%. For smokers, the probability of being allergic to peanuts is 50%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.50
0.44*0.50 - 0.56*0.44 = 0.46
0.46 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 36%. For smokers, the probability of high tar deposit is 84%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 12%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 44%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 15%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 50%. The overall probability of smoking is 67%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.36
P(V3=1 | X=1) = 0.84
P(Y=1 | X=0, V3=0) = 0.12
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.15
P(Y=1 | X=1, V3=1) = 0.50
P(X=1) = 0.67
(0.84 - 0.36)* (0.50 * 0.67) + (0.16 - 0.64) * (0.44 * 0.33) = 0.16
0.16 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 12%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 44%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 15%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 50%. For nonsmokers, the probability of high tar deposit is 36%. For smokers, the probability of high tar deposit is 84%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.12
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.15
P(Y=1 | X=1, V3=1) = 0.50
P(V3=1 | X=0) = 0.36
P(V3=1 | X=1) = 0.84
0.50 * (0.84 - 0.36) + 0.44 * (0.16 - 0.64) = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 67%. The probability of nonsmoking and being allergic to peanuts is 8%. The probability of smoking and being allergic to peanuts is 29%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.67
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.29
0.29/0.67 - 0.08/0.33 = 0.20
0.20 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 71%. For nonsmokers, the probability of high tar deposit is 33%. For smokers, the probability of high tar deposit is 64%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0) = 0.33
P(V3=1 | X=1) = 0.64
0.71 * (0.64 - 0.33) + 0.77 * (0.36 - 0.67) = 0.08
0.08 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 71%. For nonsmokers, the probability of high tar deposit is 33%. For smokers, the probability of high tar deposit is 64%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0) = 0.33
P(V3=1 | X=1) = 0.64
0.71 * (0.64 - 0.33) + 0.77 * (0.36 - 0.67) = 0.08
0.08 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 33%. For smokers, the probability of high tar deposit is 64%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 49%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 44%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 71%. The overall probability of smoking is 12%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.33
P(V3=1 | X=1) = 0.64
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.71
P(X=1) = 0.12
0.64 - 0.33 * (0.71 * 0.12 + 0.77 * 0.88)= 0.08
0.08 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 12%. For nonsmokers, the probability of being allergic to peanuts is 58%. For smokers, the probability of being allergic to peanuts is 61%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.61
0.12*0.61 - 0.88*0.58 = 0.59
0.59 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 18%. For smokers, the probability of high tar deposit is 64%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 46%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 17%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 43%. The overall probability of smoking is 49%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.18
P(V3=1 | X=1) = 0.64
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.17
P(Y=1 | X=1, V3=1) = 0.43
P(X=1) = 0.49
(0.64 - 0.18)* (0.43 * 0.49) + (0.36 - 0.82) * (0.77 * 0.51) = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 18%. For smokers, the probability of high tar deposit is 64%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 46%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 17%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 43%. The overall probability of smoking is 49%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.18
P(V3=1 | X=1) = 0.64
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.17
P(Y=1 | X=1, V3=1) = 0.43
P(X=1) = 0.49
(0.64 - 0.18)* (0.43 * 0.49) + (0.36 - 0.82) * (0.77 * 0.51) = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 46%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 17%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 43%. For nonsmokers, the probability of high tar deposit is 18%. For smokers, the probability of high tar deposit is 64%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.17
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0) = 0.18
P(V3=1 | X=1) = 0.64
0.43 * (0.64 - 0.18) + 0.77 * (0.36 - 0.82) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 46%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 17%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 43%. For nonsmokers, the probability of high tar deposit is 18%. For smokers, the probability of high tar deposit is 64%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.17
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0) = 0.18
P(V3=1 | X=1) = 0.64
0.43 * (0.64 - 0.18) + 0.77 * (0.36 - 0.82) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 18%. For smokers, the probability of high tar deposit is 64%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 46%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 77%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 17%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 43%. The overall probability of smoking is 49%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.18
P(V3=1 | X=1) = 0.64
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.17
P(Y=1 | X=1, V3=1) = 0.43
P(X=1) = 0.49
0.64 - 0.18 * (0.43 * 0.49 + 0.77 * 0.51)= 0.13
0.13 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11360,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 49%. The probability of nonsmoking and being allergic to peanuts is 26%. The probability of smoking and being allergic to peanuts is 17%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.17
0.17/0.49 - 0.26/0.51 = -0.17
-0.17 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 49%. For nonsmokers, the probability of being allergic to peanuts is 32%. For smokers, the probability of being allergic to peanuts is 50%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.50
0.49*0.50 - 0.51*0.32 = 0.41
0.41 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 49%. For nonsmokers, the probability of being allergic to peanuts is 32%. For smokers, the probability of being allergic to peanuts is 50%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.50
0.49*0.50 - 0.51*0.32 = 0.41
0.41 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 49%. The probability of nonsmoking and being allergic to peanuts is 16%. The probability of smoking and being allergic to peanuts is 24%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.24
0.24/0.49 - 0.16/0.51 = 0.19
0.19 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11373,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 49%. The probability of nonsmoking and being allergic to peanuts is 16%. The probability of smoking and being allergic to peanuts is 24%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.24
0.24/0.49 - 0.16/0.51 = 0.19
0.19 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look at how smoking correlates with peanut allergy case by case according to gender. Method 2: We look directly at how smoking correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 34%. For smokers, the probability of high tar deposit is 70%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 33%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 62%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 19%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 52%. The overall probability of smoking is 29%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.34
P(V3=1 | X=1) = 0.70
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.19
P(Y=1 | X=1, V3=1) = 0.52
P(X=1) = 0.29
(0.70 - 0.34)* (0.52 * 0.29) + (0.30 - 0.66) * (0.62 * 0.71) = 0.11
0.11 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11378,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 33%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 62%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 19%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 52%. For nonsmokers, the probability of high tar deposit is 34%. For smokers, the probability of high tar deposit is 70%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.19
P(Y=1 | X=1, V3=1) = 0.52
P(V3=1 | X=0) = 0.34
P(V3=1 | X=1) = 0.70
0.52 * (0.70 - 0.34) + 0.62 * (0.30 - 0.66) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 33%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 62%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 19%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 52%. For nonsmokers, the probability of high tar deposit is 34%. For smokers, the probability of high tar deposit is 70%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.19
P(Y=1 | X=1, V3=1) = 0.52
P(V3=1 | X=0) = 0.34
P(V3=1 | X=1) = 0.70
0.52 * (0.70 - 0.34) + 0.62 * (0.30 - 0.66) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 34%. For smokers, the probability of high tar deposit is 70%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 33%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 62%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 19%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 52%. The overall probability of smoking is 29%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.34
P(V3=1 | X=1) = 0.70
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.19
P(Y=1 | X=1, V3=1) = 0.52
P(X=1) = 0.29
0.70 - 0.34 * (0.52 * 0.29 + 0.62 * 0.71)= 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 29%. For nonsmokers, the probability of being allergic to peanuts is 43%. For smokers, the probability of being allergic to peanuts is 42%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.42
0.29*0.42 - 0.71*0.43 = 0.42
0.42 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 29%. For nonsmokers, the probability of being allergic to peanuts is 43%. For smokers, the probability of being allergic to peanuts is 42%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.42
0.29*0.42 - 0.71*0.43 = 0.42
0.42 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 29%. The probability of nonsmoking and being allergic to peanuts is 30%. The probability of smoking and being allergic to peanuts is 12%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.29
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.12
0.12/0.29 - 0.30/0.71 = -0.01
-0.01 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11389,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 54%. For smokers, the probability of high tar deposit is 92%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 39%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 67%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 32%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 61%. The overall probability of smoking is 14%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.54
P(V3=1 | X=1) = 0.92
P(Y=1 | X=0, V3=0) = 0.39
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.61
P(X=1) = 0.14
(0.92 - 0.54)* (0.61 * 0.14) + (0.08 - 0.46) * (0.67 * 0.86) = 0.11
0.11 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11390,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 39%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 67%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 32%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 61%. For nonsmokers, the probability of high tar deposit is 54%. For smokers, the probability of high tar deposit is 92%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.39
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0) = 0.54
P(V3=1 | X=1) = 0.92
0.61 * (0.92 - 0.54) + 0.67 * (0.08 - 0.46) = 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11392,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 54%. For smokers, the probability of high tar deposit is 92%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 39%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 67%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 32%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 61%. The overall probability of smoking is 14%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.54
P(V3=1 | X=1) = 0.92
P(Y=1 | X=0, V3=0) = 0.39
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.61
P(X=1) = 0.14
0.92 - 0.54 * (0.61 * 0.14 + 0.67 * 0.86)= 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 54%. For smokers, the probability of high tar deposit is 92%. For nonsmokers and with no tar deposit, the probability of being allergic to peanuts is 39%. For nonsmokers and with high tar deposit, the probability of being allergic to peanuts is 67%. For smokers and with no tar deposit, the probability of being allergic to peanuts is 32%. For smokers and with high tar deposit, the probability of being allergic to peanuts is 61%. The overall probability of smoking is 14%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.54
P(V3=1 | X=1) = 0.92
P(Y=1 | X=0, V3=0) = 0.39
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.61
P(X=1) = 0.14
0.92 - 0.54 * (0.61 * 0.14 + 0.67 * 0.86)= 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 14%. For nonsmokers, the probability of being allergic to peanuts is 54%. For smokers, the probability of being allergic to peanuts is 58%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.58
0.14*0.58 - 0.86*0.54 = 0.55
0.55 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
11397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. The overall probability of smoking is 14%. The probability of nonsmoking and being allergic to peanuts is 47%. The probability of smoking and being allergic to peanuts is 8%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.08
0.08/0.14 - 0.47/0.86 = 0.04
0.04 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
11398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. Method 1: We look directly at how smoking correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
11401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 60%. For people who listen to jazz, the probability of lung cancer is 65%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.65
0.65 - 0.60 = 0.05
0.05 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 52%. For people who do not listen to jazz and smokers, the probability of lung cancer is 86%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 48%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 17%. For people who do not listen to jazz and with high pollution, the probability of smoking is 30%. For people who listen to jazz and with low pollution, the probability of smoking is 52%. For people who listen to jazz and with high pollution, the probability of smoking is 60%. The overall probability of high pollution is 44%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.86
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.17
P(V3=1 | X=0, V2=1) = 0.30
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.44
0.44 * 0.86 * (0.60 - 0.52)+ 0.56 * 0.86 * (0.30 - 0.17)= 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 52%. For people who do not listen to jazz and smokers, the probability of lung cancer is 86%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 48%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 17%. For people who do not listen to jazz and with high pollution, the probability of smoking is 30%. For people who listen to jazz and with low pollution, the probability of smoking is 52%. For people who listen to jazz and with high pollution, the probability of smoking is 60%. The overall probability of high pollution is 44%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.86
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.17
P(V3=1 | X=0, V2=1) = 0.30
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.44
0.44 * (0.77 - 0.48) * 0.30 + 0.56 * (0.86 - 0.52) * 0.52 = -0.04
-0.04 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 13%. For people who do not listen to jazz, the probability of lung cancer is 60%. For people who listen to jazz, the probability of lung cancer is 65%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.65
0.13*0.65 - 0.87*0.60 = 0.61
0.61 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 44%. For people who listen to jazz, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.56
0.56 - 0.44 = 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 29%. For people who do not listen to jazz and smokers, the probability of lung cancer is 70%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 28%. For people who listen to jazz and smokers, the probability of lung cancer is 67%. For people who do not listen to jazz and with low pollution, the probability of smoking is 23%. For people who do not listen to jazz and with high pollution, the probability of smoking is 50%. For people who listen to jazz and with low pollution, the probability of smoking is 57%. For people who listen to jazz and with high pollution, the probability of smoking is 83%. The overall probability of high pollution is 52%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.29
P(Y=1 | X=0, V3=1) = 0.70
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.67
P(V3=1 | X=0, V2=0) = 0.23
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.83
P(V2=1) = 0.52
0.52 * 0.70 * (0.83 - 0.57)+ 0.48 * 0.70 * (0.50 - 0.23)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 29%. For people who do not listen to jazz and smokers, the probability of lung cancer is 70%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 28%. For people who listen to jazz and smokers, the probability of lung cancer is 67%. For people who do not listen to jazz and with low pollution, the probability of smoking is 23%. For people who do not listen to jazz and with high pollution, the probability of smoking is 50%. For people who listen to jazz and with low pollution, the probability of smoking is 57%. For people who listen to jazz and with high pollution, the probability of smoking is 83%. The overall probability of high pollution is 52%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.29
P(Y=1 | X=0, V3=1) = 0.70
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.67
P(V3=1 | X=0, V2=0) = 0.23
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.83
P(V2=1) = 0.52
0.52 * (0.67 - 0.28) * 0.50 + 0.48 * (0.70 - 0.29) * 0.57 = 0.01
0.01 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 20%. For people who do not listen to jazz, the probability of lung cancer is 44%. For people who listen to jazz, the probability of lung cancer is 56%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.56
0.20*0.56 - 0.80*0.44 = 0.47
0.47 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 20%. For people who do not listen to jazz, the probability of lung cancer is 44%. For people who listen to jazz, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.56
0.20*0.56 - 0.80*0.44 = 0.47
0.47 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 51%. For people who listen to jazz, the probability of lung cancer is 61%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.61
0.61 - 0.51 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 51%. For people who listen to jazz, the probability of lung cancer is 61%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.61
0.61 - 0.51 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 15%. The probability of not listening to jazz and lung cancer is 44%. The probability of listening to jazz and lung cancer is 9%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.09
0.09/0.15 - 0.44/0.85 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who do not listen to jazz and smokers, the probability of lung cancer is 80%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 70%. For people who do not listen to jazz and with low pollution, the probability of smoking is 7%. For people who do not listen to jazz and with high pollution, the probability of smoking is 46%. For people who listen to jazz and with low pollution, the probability of smoking is 33%. For people who listen to jazz and with high pollution, the probability of smoking is 69%. The overall probability of high pollution is 47%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.80
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0, V2=0) = 0.07
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.33
P(V3=1 | X=1, V2=1) = 0.69
P(V2=1) = 0.47
0.47 * 0.80 * (0.69 - 0.33)+ 0.53 * 0.80 * (0.46 - 0.07)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 19%. For people who do not listen to jazz, the probability of lung cancer is 46%. For people who listen to jazz, the probability of lung cancer is 52%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.52
0.19*0.52 - 0.81*0.46 = 0.48
0.48 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 19%. The probability of not listening to jazz and lung cancer is 37%. The probability of listening to jazz and lung cancer is 10%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.10
0.10/0.19 - 0.37/0.81 = 0.06
0.06 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 19%. The probability of not listening to jazz and lung cancer is 37%. The probability of listening to jazz and lung cancer is 10%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.10
0.10/0.19 - 0.37/0.81 = 0.06
0.06 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 22%. For people who listen to jazz, the probability of lung cancer is 36%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.36
0.36 - 0.22 = 0.14
0.14 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 15%. For people who do not listen to jazz and smokers, the probability of lung cancer is 47%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 21%. For people who listen to jazz and smokers, the probability of lung cancer is 40%. For people who do not listen to jazz and with low pollution, the probability of smoking is 15%. For people who do not listen to jazz and with high pollution, the probability of smoking is 27%. For people who listen to jazz and with low pollution, the probability of smoking is 87%. For people who listen to jazz and with high pollution, the probability of smoking is 63%. The overall probability of high pollution is 41%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.15
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.21
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.15
P(V3=1 | X=0, V2=1) = 0.27
P(V3=1 | X=1, V2=0) = 0.87
P(V3=1 | X=1, V2=1) = 0.63
P(V2=1) = 0.41
0.41 * (0.40 - 0.21) * 0.27 + 0.59 * (0.47 - 0.15) * 0.87 = -0.02
-0.02 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.56
0.56 - 0.40 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 56%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.56
0.56 - 0.40 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11473,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.56
0.56 - 0.40 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 31%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 4%. For people who do not listen to jazz and with high pollution, the probability of smoking is 31%. For people who listen to jazz and with low pollution, the probability of smoking is 24%. For people who listen to jazz and with high pollution, the probability of smoking is 66%. The overall probability of high pollution is 58%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.04
P(V3=1 | X=0, V2=1) = 0.31
P(V3=1 | X=1, V2=0) = 0.24
P(V3=1 | X=1, V2=1) = 0.66
P(V2=1) = 0.58
0.58 * 0.78 * (0.66 - 0.24)+ 0.42 * 0.78 * (0.31 - 0.04)= 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 31%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 4%. For people who do not listen to jazz and with high pollution, the probability of smoking is 31%. For people who listen to jazz and with low pollution, the probability of smoking is 24%. For people who listen to jazz and with high pollution, the probability of smoking is 66%. The overall probability of high pollution is 58%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.04
P(V3=1 | X=0, V2=1) = 0.31
P(V3=1 | X=1, V2=0) = 0.24
P(V3=1 | X=1, V2=1) = 0.66
P(V2=1) = 0.58
0.58 * (0.77 - 0.35) * 0.31 + 0.42 * (0.78 - 0.31) * 0.24 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 31%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 4%. For people who do not listen to jazz and with high pollution, the probability of smoking is 31%. For people who listen to jazz and with low pollution, the probability of smoking is 24%. For people who listen to jazz and with high pollution, the probability of smoking is 66%. The overall probability of high pollution is 58%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.04
P(V3=1 | X=0, V2=1) = 0.31
P(V3=1 | X=1, V2=0) = 0.24
P(V3=1 | X=1, V2=1) = 0.66
P(V2=1) = 0.58
0.58 * (0.77 - 0.35) * 0.31 + 0.42 * (0.78 - 0.31) * 0.24 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 2%. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.56
0.02*0.56 - 0.98*0.40 = 0.41
0.41 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 2%. The probability of not listening to jazz and lung cancer is 39%. The probability of listening to jazz and lung cancer is 1%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.39/0.98 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 39%. For people who listen to jazz, the probability of lung cancer is 48%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.48
0.48 - 0.39 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 25%. For people who do not listen to jazz and smokers, the probability of lung cancer is 64%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 31%. For people who listen to jazz and smokers, the probability of lung cancer is 54%. For people who do not listen to jazz and with low pollution, the probability of smoking is 34%. For people who do not listen to jazz and with high pollution, the probability of smoking is 42%. For people who listen to jazz and with low pollution, the probability of smoking is 77%. For people who listen to jazz and with high pollution, the probability of smoking is 68%. The overall probability of high pollution is 50%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.25
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.31
P(Y=1 | X=1, V3=1) = 0.54
P(V3=1 | X=0, V2=0) = 0.34
P(V3=1 | X=0, V2=1) = 0.42
P(V3=1 | X=1, V2=0) = 0.77
P(V3=1 | X=1, V2=1) = 0.68
P(V2=1) = 0.50
0.50 * 0.64 * (0.68 - 0.77)+ 0.50 * 0.64 * (0.42 - 0.34)= 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11492,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 16%. For people who do not listen to jazz, the probability of lung cancer is 39%. For people who listen to jazz, the probability of lung cancer is 48%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.48
0.16*0.48 - 0.84*0.39 = 0.41
0.41 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11497,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 46%. For people who listen to jazz, the probability of lung cancer is 56%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.56
0.56 - 0.46 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 34%. For people who do not listen to jazz and smokers, the probability of lung cancer is 66%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 32%. For people who listen to jazz and smokers, the probability of lung cancer is 62%. For people who do not listen to jazz and with low pollution, the probability of smoking is 25%. For people who do not listen to jazz and with high pollution, the probability of smoking is 56%. For people who listen to jazz and with low pollution, the probability of smoking is 69%. For people who listen to jazz and with high pollution, the probability of smoking is 93%. The overall probability of high pollution is 41%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.62
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.69
P(V3=1 | X=1, V2=1) = 0.93
P(V2=1) = 0.41
0.41 * 0.66 * (0.93 - 0.69)+ 0.59 * 0.66 * (0.56 - 0.25)= 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. For people who do not listen to jazz, the probability of lung cancer is 46%. For people who listen to jazz, the probability of lung cancer is 56%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.56
0.07*0.56 - 0.93*0.46 = 0.47
0.47 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. For people who do not listen to jazz, the probability of lung cancer is 46%. For people who listen to jazz, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.56
0.07*0.56 - 0.93*0.46 = 0.47
0.47 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. The probability of not listening to jazz and lung cancer is 43%. The probability of listening to jazz and lung cancer is 4%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.43/0.93 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11514,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 66%. For people who listen to jazz, the probability of lung cancer is 81%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.81
0.81 - 0.66 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 66%. For people who listen to jazz, the probability of lung cancer is 81%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.81
0.81 - 0.66 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 53%. For people who do not listen to jazz and smokers, the probability of lung cancer is 80%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who listen to jazz and smokers, the probability of lung cancer is 82%. For people who do not listen to jazz and with low pollution, the probability of smoking is 49%. For people who do not listen to jazz and with high pollution, the probability of smoking is 43%. For people who listen to jazz and with low pollution, the probability of smoking is 92%. For people who listen to jazz and with high pollution, the probability of smoking is 99%. The overall probability of high pollution is 53%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.80
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.82
P(V3=1 | X=0, V2=0) = 0.49
P(V3=1 | X=0, V2=1) = 0.43
P(V3=1 | X=1, V2=0) = 0.92
P(V3=1 | X=1, V2=1) = 0.99
P(V2=1) = 0.53
0.53 * 0.80 * (0.99 - 0.92)+ 0.47 * 0.80 * (0.43 - 0.49)= 0.14
0.14 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 53%. For people who do not listen to jazz and smokers, the probability of lung cancer is 80%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who listen to jazz and smokers, the probability of lung cancer is 82%. For people who do not listen to jazz and with low pollution, the probability of smoking is 49%. For people who do not listen to jazz and with high pollution, the probability of smoking is 43%. For people who listen to jazz and with low pollution, the probability of smoking is 92%. For people who listen to jazz and with high pollution, the probability of smoking is 99%. The overall probability of high pollution is 53%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.80
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.82
P(V3=1 | X=0, V2=0) = 0.49
P(V3=1 | X=0, V2=1) = 0.43
P(V3=1 | X=1, V2=0) = 0.92
P(V3=1 | X=1, V2=1) = 0.99
P(V2=1) = 0.53
0.53 * (0.82 - 0.42) * 0.43 + 0.47 * (0.80 - 0.53) * 0.92 = 0.01
0.01 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 53%. For people who do not listen to jazz and smokers, the probability of lung cancer is 80%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who listen to jazz and smokers, the probability of lung cancer is 82%. For people who do not listen to jazz and with low pollution, the probability of smoking is 49%. For people who do not listen to jazz and with high pollution, the probability of smoking is 43%. For people who listen to jazz and with low pollution, the probability of smoking is 92%. For people who listen to jazz and with high pollution, the probability of smoking is 99%. The overall probability of high pollution is 53%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.80
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.82
P(V3=1 | X=0, V2=0) = 0.49
P(V3=1 | X=0, V2=1) = 0.43
P(V3=1 | X=1, V2=0) = 0.92
P(V3=1 | X=1, V2=1) = 0.99
P(V2=1) = 0.53
0.53 * (0.82 - 0.42) * 0.43 + 0.47 * (0.80 - 0.53) * 0.92 = 0.01
0.01 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. For people who do not listen to jazz, the probability of lung cancer is 66%. For people who listen to jazz, the probability of lung cancer is 81%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.81
0.07*0.81 - 0.93*0.66 = 0.67
0.67 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 49%. For people who listen to jazz, the probability of lung cancer is 53%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.53
0.53 - 0.49 = 0.04
0.04 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 49%. For people who listen to jazz, the probability of lung cancer is 53%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.53
0.53 - 0.49 = 0.04
0.04 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 49%. For people who listen to jazz, the probability of lung cancer is 53%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.53
0.53 - 0.49 = 0.04
0.04 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 30%. For people who do not listen to jazz and smokers, the probability of lung cancer is 67%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 20%. For people who listen to jazz and smokers, the probability of lung cancer is 63%. For people who do not listen to jazz and with low pollution, the probability of smoking is 33%. For people who do not listen to jazz and with high pollution, the probability of smoking is 65%. For people who listen to jazz and with low pollution, the probability of smoking is 53%. For people who listen to jazz and with high pollution, the probability of smoking is 96%. The overall probability of high pollution is 55%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.20
P(Y=1 | X=1, V3=1) = 0.63
P(V3=1 | X=0, V2=0) = 0.33
P(V3=1 | X=0, V2=1) = 0.65
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.96
P(V2=1) = 0.55
0.55 * 0.67 * (0.96 - 0.53)+ 0.45 * 0.67 * (0.65 - 0.33)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11533,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 30%. For people who do not listen to jazz and smokers, the probability of lung cancer is 67%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 20%. For people who listen to jazz and smokers, the probability of lung cancer is 63%. For people who do not listen to jazz and with low pollution, the probability of smoking is 33%. For people who do not listen to jazz and with high pollution, the probability of smoking is 65%. For people who listen to jazz and with low pollution, the probability of smoking is 53%. For people who listen to jazz and with high pollution, the probability of smoking is 96%. The overall probability of high pollution is 55%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.20
P(Y=1 | X=1, V3=1) = 0.63
P(V3=1 | X=0, V2=0) = 0.33
P(V3=1 | X=0, V2=1) = 0.65
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.96
P(V2=1) = 0.55
0.55 * (0.63 - 0.20) * 0.65 + 0.45 * (0.67 - 0.30) * 0.53 = -0.02
-0.02 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 8%. For people who do not listen to jazz, the probability of lung cancer is 49%. For people who listen to jazz, the probability of lung cancer is 53%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.53
0.08*0.53 - 0.92*0.49 = 0.49
0.49 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11535,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 8%. For people who do not listen to jazz, the probability of lung cancer is 49%. For people who listen to jazz, the probability of lung cancer is 53%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.53
0.08*0.53 - 0.92*0.49 = 0.49
0.49 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11539,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 56%. For people who listen to jazz, the probability of lung cancer is 67%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.67
0.67 - 0.56 = 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11542,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 56%. For people who listen to jazz, the probability of lung cancer is 67%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.67
0.67 - 0.56 = 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 56%. For people who listen to jazz, the probability of lung cancer is 67%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.67
0.67 - 0.56 = 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 48%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 49%. For people who listen to jazz and smokers, the probability of lung cancer is 79%. For people who do not listen to jazz and with low pollution, the probability of smoking is 25%. For people who do not listen to jazz and with high pollution, the probability of smoking is 25%. For people who listen to jazz and with low pollution, the probability of smoking is 59%. For people who listen to jazz and with high pollution, the probability of smoking is 61%. The overall probability of high pollution is 54%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.79
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.61
P(V2=1) = 0.54
0.54 * 0.78 * (0.61 - 0.59)+ 0.46 * 0.78 * (0.25 - 0.25)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 48%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 49%. For people who listen to jazz and smokers, the probability of lung cancer is 79%. For people who do not listen to jazz and with low pollution, the probability of smoking is 25%. For people who do not listen to jazz and with high pollution, the probability of smoking is 25%. For people who listen to jazz and with low pollution, the probability of smoking is 59%. For people who listen to jazz and with high pollution, the probability of smoking is 61%. The overall probability of high pollution is 54%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.79
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.61
P(V2=1) = 0.54
0.54 * 0.78 * (0.61 - 0.59)+ 0.46 * 0.78 * (0.25 - 0.25)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 48%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 49%. For people who listen to jazz and smokers, the probability of lung cancer is 79%. For people who do not listen to jazz and with low pollution, the probability of smoking is 25%. For people who do not listen to jazz and with high pollution, the probability of smoking is 25%. For people who listen to jazz and with low pollution, the probability of smoking is 59%. For people who listen to jazz and with high pollution, the probability of smoking is 61%. The overall probability of high pollution is 54%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.79
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.61
P(V2=1) = 0.54
0.54 * (0.79 - 0.49) * 0.25 + 0.46 * (0.78 - 0.48) * 0.59 = 0.01
0.01 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 48%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 49%. For people who listen to jazz and smokers, the probability of lung cancer is 79%. For people who do not listen to jazz and with low pollution, the probability of smoking is 25%. For people who do not listen to jazz and with high pollution, the probability of smoking is 25%. For people who listen to jazz and with low pollution, the probability of smoking is 59%. For people who listen to jazz and with high pollution, the probability of smoking is 61%. The overall probability of high pollution is 54%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.79
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.61
P(V2=1) = 0.54
0.54 * (0.79 - 0.49) * 0.25 + 0.46 * (0.78 - 0.48) * 0.59 = 0.01
0.01 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 11%. The probability of not listening to jazz and lung cancer is 50%. The probability of listening to jazz and lung cancer is 7%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.07
0.07/0.11 - 0.50/0.89 = 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11558,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 36%. For people who do not listen to jazz and smokers, the probability of lung cancer is 73%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 29%. For people who listen to jazz and smokers, the probability of lung cancer is 74%. For people who do not listen to jazz and with low pollution, the probability of smoking is 31%. For people who do not listen to jazz and with high pollution, the probability of smoking is 74%. For people who listen to jazz and with low pollution, the probability of smoking is 65%. For people who listen to jazz and with high pollution, the probability of smoking is 100%. The overall probability of high pollution is 42%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.73
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.31
P(V3=1 | X=0, V2=1) = 0.74
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 1.00
P(V2=1) = 0.42
0.42 * 0.73 * (1.00 - 0.65)+ 0.58 * 0.73 * (0.74 - 0.31)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 12%. For people who do not listen to jazz, the probability of lung cancer is 54%. For people who listen to jazz, the probability of lung cancer is 64%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.64
0.12*0.64 - 0.88*0.54 = 0.55
0.55 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 12%. For people who do not listen to jazz, the probability of lung cancer is 54%. For people who listen to jazz, the probability of lung cancer is 64%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.64
0.12*0.64 - 0.88*0.54 = 0.55
0.55 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 64%. For people who listen to jazz, the probability of lung cancer is 77%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.77
0.77 - 0.64 = 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 52%. For people who do not listen to jazz and smokers, the probability of lung cancer is 80%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 81%. For people who do not listen to jazz and with low pollution, the probability of smoking is 50%. For people who do not listen to jazz and with high pollution, the probability of smoking is 39%. For people who listen to jazz and with low pollution, the probability of smoking is 85%. For people who listen to jazz and with high pollution, the probability of smoking is 98%. The overall probability of high pollution is 51%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.80
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.98
P(V2=1) = 0.51
0.51 * 0.80 * (0.98 - 0.85)+ 0.49 * 0.80 * (0.39 - 0.50)= 0.14
0.14 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 52%. For people who do not listen to jazz and smokers, the probability of lung cancer is 80%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 81%. For people who do not listen to jazz and with low pollution, the probability of smoking is 50%. For people who do not listen to jazz and with high pollution, the probability of smoking is 39%. For people who listen to jazz and with low pollution, the probability of smoking is 85%. For people who listen to jazz and with high pollution, the probability of smoking is 98%. The overall probability of high pollution is 51%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.80
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.98
P(V2=1) = 0.51
0.51 * (0.81 - 0.35) * 0.39 + 0.49 * (0.80 - 0.52) * 0.85 = -0.03
-0.03 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 8%. For people who do not listen to jazz, the probability of lung cancer is 64%. For people who listen to jazz, the probability of lung cancer is 77%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.77
0.08*0.77 - 0.92*0.64 = 0.65
0.65 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 8%. For people who do not listen to jazz, the probability of lung cancer is 64%. For people who listen to jazz, the probability of lung cancer is 77%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.77
0.08*0.77 - 0.92*0.64 = 0.65
0.65 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 8%. The probability of not listening to jazz and lung cancer is 59%. The probability of listening to jazz and lung cancer is 7%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.07
0.07/0.08 - 0.59/0.92 = 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11580,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 60%. For people who listen to jazz, the probability of lung cancer is 63%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.63
0.63 - 0.60 = 0.02
0.02 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 45%. For people who do not listen to jazz and smokers, the probability of lung cancer is 89%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 33%. For people who listen to jazz and smokers, the probability of lung cancer is 75%. For people who do not listen to jazz and with low pollution, the probability of smoking is 21%. For people who do not listen to jazz and with high pollution, the probability of smoking is 47%. For people who listen to jazz and with low pollution, the probability of smoking is 56%. For people who listen to jazz and with high pollution, the probability of smoking is 83%. The overall probability of high pollution is 57%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.75
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.83
P(V2=1) = 0.57
0.57 * (0.75 - 0.33) * 0.47 + 0.43 * (0.89 - 0.45) * 0.56 = -0.09
-0.09 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 45%. For people who do not listen to jazz and smokers, the probability of lung cancer is 89%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 33%. For people who listen to jazz and smokers, the probability of lung cancer is 75%. For people who do not listen to jazz and with low pollution, the probability of smoking is 21%. For people who do not listen to jazz and with high pollution, the probability of smoking is 47%. For people who listen to jazz and with low pollution, the probability of smoking is 56%. For people who listen to jazz and with high pollution, the probability of smoking is 83%. The overall probability of high pollution is 57%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.75
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.83
P(V2=1) = 0.57
0.57 * (0.75 - 0.33) * 0.47 + 0.43 * (0.89 - 0.45) * 0.56 = -0.09
-0.09 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 13%. For people who do not listen to jazz, the probability of lung cancer is 60%. For people who listen to jazz, the probability of lung cancer is 63%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.63
0.13*0.63 - 0.87*0.60 = 0.60
0.60 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 13%. The probability of not listening to jazz and lung cancer is 53%. The probability of listening to jazz and lung cancer is 8%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.08
0.08/0.13 - 0.53/0.87 = 0.02
0.02 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 33%. For people who listen to jazz, the probability of lung cancer is 40%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.40
0.40 - 0.33 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11602,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 26%. For people who do not listen to jazz and smokers, the probability of lung cancer is 51%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 22%. For people who listen to jazz and smokers, the probability of lung cancer is 51%. For people who do not listen to jazz and with low pollution, the probability of smoking is 30%. For people who do not listen to jazz and with high pollution, the probability of smoking is 27%. For people who listen to jazz and with low pollution, the probability of smoking is 54%. For people who listen to jazz and with high pollution, the probability of smoking is 65%. The overall probability of high pollution is 54%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.26
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.22
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.30
P(V3=1 | X=0, V2=1) = 0.27
P(V3=1 | X=1, V2=0) = 0.54
P(V3=1 | X=1, V2=1) = 0.65
P(V2=1) = 0.54
0.54 * (0.51 - 0.22) * 0.27 + 0.46 * (0.51 - 0.26) * 0.54 = -0.02
-0.02 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11607,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 4%. The probability of not listening to jazz and lung cancer is 32%. The probability of listening to jazz and lung cancer is 1%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.01
0.01/0.04 - 0.32/0.96 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 54%. For people who listen to jazz, the probability of lung cancer is 63%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.63
0.63 - 0.54 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11615,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 41%. For people who do not listen to jazz and smokers, the probability of lung cancer is 79%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 36%. For people who listen to jazz and smokers, the probability of lung cancer is 79%. For people who do not listen to jazz and with low pollution, the probability of smoking is 24%. For people who do not listen to jazz and with high pollution, the probability of smoking is 48%. For people who listen to jazz and with low pollution, the probability of smoking is 51%. For people who listen to jazz and with high pollution, the probability of smoking is 74%. The overall probability of high pollution is 48%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.79
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.79
P(V3=1 | X=0, V2=0) = 0.24
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.74
P(V2=1) = 0.48
0.48 * 0.79 * (0.74 - 0.51)+ 0.52 * 0.79 * (0.48 - 0.24)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 41%. For people who do not listen to jazz and smokers, the probability of lung cancer is 79%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 36%. For people who listen to jazz and smokers, the probability of lung cancer is 79%. For people who do not listen to jazz and with low pollution, the probability of smoking is 24%. For people who do not listen to jazz and with high pollution, the probability of smoking is 48%. For people who listen to jazz and with low pollution, the probability of smoking is 51%. For people who listen to jazz and with high pollution, the probability of smoking is 74%. The overall probability of high pollution is 48%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.79
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.79
P(V3=1 | X=0, V2=0) = 0.24
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.74
P(V2=1) = 0.48
0.48 * (0.79 - 0.36) * 0.48 + 0.52 * (0.79 - 0.41) * 0.51 = 0.00
0.00 = 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11619,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. For people who do not listen to jazz, the probability of lung cancer is 54%. For people who listen to jazz, the probability of lung cancer is 63%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.63
0.07*0.63 - 0.93*0.54 = 0.54
0.54 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11620,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. The probability of not listening to jazz and lung cancer is 51%. The probability of listening to jazz and lung cancer is 4%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.51
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.51/0.93 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. The probability of not listening to jazz and lung cancer is 51%. The probability of listening to jazz and lung cancer is 4%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.51
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.51/0.93 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 51%. For people who listen to jazz, the probability of lung cancer is 65%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.65
0.65 - 0.51 = 0.14
0.14 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who do not listen to jazz and smokers, the probability of lung cancer is 73%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 40%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 28%. For people who do not listen to jazz and with high pollution, the probability of smoking is 30%. For people who listen to jazz and with low pollution, the probability of smoking is 67%. For people who listen to jazz and with high pollution, the probability of smoking is 71%. The overall probability of high pollution is 55%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.73
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.28
P(V3=1 | X=0, V2=1) = 0.30
P(V3=1 | X=1, V2=0) = 0.67
P(V3=1 | X=1, V2=1) = 0.71
P(V2=1) = 0.55
0.55 * (0.77 - 0.40) * 0.30 + 0.45 * (0.73 - 0.42) * 0.67 = -0.00
0.00 = 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 3%. The probability of not listening to jazz and lung cancer is 50%. The probability of listening to jazz and lung cancer is 2%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.50/0.97 = 0.14
0.14 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 3%. The probability of not listening to jazz and lung cancer is 50%. The probability of listening to jazz and lung cancer is 2%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.50/0.97 = 0.14
0.14 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11639,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 43%. For people who listen to jazz, the probability of lung cancer is 58%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.58
0.58 - 0.43 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 37%. For people who do not listen to jazz and smokers, the probability of lung cancer is 88%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who listen to jazz and smokers, the probability of lung cancer is 75%. For people who do not listen to jazz and with low pollution, the probability of smoking is 0%. For people who do not listen to jazz and with high pollution, the probability of smoking is 25%. For people who listen to jazz and with low pollution, the probability of smoking is 39%. For people who listen to jazz and with high pollution, the probability of smoking is 59%. The overall probability of high pollution is 46%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.88
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.75
P(V3=1 | X=0, V2=0) = 0.00
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.59
P(V2=1) = 0.46
0.46 * 0.88 * (0.59 - 0.39)+ 0.54 * 0.88 * (0.25 - 0.00)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 37%. For people who do not listen to jazz and smokers, the probability of lung cancer is 88%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who listen to jazz and smokers, the probability of lung cancer is 75%. For people who do not listen to jazz and with low pollution, the probability of smoking is 0%. For people who do not listen to jazz and with high pollution, the probability of smoking is 25%. For people who listen to jazz and with low pollution, the probability of smoking is 39%. For people who listen to jazz and with high pollution, the probability of smoking is 59%. The overall probability of high pollution is 46%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.88
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.75
P(V3=1 | X=0, V2=0) = 0.00
P(V3=1 | X=0, V2=1) = 0.25
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.59
P(V2=1) = 0.46
0.46 * (0.75 - 0.42) * 0.25 + 0.54 * (0.88 - 0.37) * 0.39 = 0.05
0.05 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11652,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 37%. For people who listen to jazz, the probability of lung cancer is 50%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.50
0.50 - 0.37 = 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 37%. For people who listen to jazz, the probability of lung cancer is 50%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.50
0.50 - 0.37 = 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11654,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 37%. For people who listen to jazz, the probability of lung cancer is 50%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.50
0.50 - 0.37 = 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 33%. For people who do not listen to jazz and smokers, the probability of lung cancer is 72%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 33%. For people who listen to jazz and smokers, the probability of lung cancer is 66%. For people who do not listen to jazz and with low pollution, the probability of smoking is 6%. For people who do not listen to jazz and with high pollution, the probability of smoking is 16%. For people who listen to jazz and with low pollution, the probability of smoking is 53%. For people who listen to jazz and with high pollution, the probability of smoking is 49%. The overall probability of high pollution is 48%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.66
P(V3=1 | X=0, V2=0) = 0.06
P(V3=1 | X=0, V2=1) = 0.16
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.48
0.48 * 0.72 * (0.49 - 0.53)+ 0.52 * 0.72 * (0.16 - 0.06)= 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 33%. For people who do not listen to jazz and smokers, the probability of lung cancer is 72%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 33%. For people who listen to jazz and smokers, the probability of lung cancer is 66%. For people who do not listen to jazz and with low pollution, the probability of smoking is 6%. For people who do not listen to jazz and with high pollution, the probability of smoking is 16%. For people who listen to jazz and with low pollution, the probability of smoking is 53%. For people who listen to jazz and with high pollution, the probability of smoking is 49%. The overall probability of high pollution is 48%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.66
P(V3=1 | X=0, V2=0) = 0.06
P(V3=1 | X=0, V2=1) = 0.16
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.48
0.48 * (0.66 - 0.33) * 0.16 + 0.52 * (0.72 - 0.33) * 0.53 = -0.00
0.00 = 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 15%. For people who do not listen to jazz, the probability of lung cancer is 37%. For people who listen to jazz, the probability of lung cancer is 50%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.50
0.15*0.50 - 0.85*0.37 = 0.39
0.39 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 15%. The probability of not listening to jazz and lung cancer is 31%. The probability of listening to jazz and lung cancer is 7%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.07
0.07/0.15 - 0.31/0.85 = 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 39%. For people who listen to jazz, the probability of lung cancer is 48%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.48
0.48 - 0.39 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 30%. For people who do not listen to jazz and smokers, the probability of lung cancer is 74%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 29%. For people who listen to jazz and smokers, the probability of lung cancer is 66%. For people who do not listen to jazz and with low pollution, the probability of smoking is 10%. For people who do not listen to jazz and with high pollution, the probability of smoking is 33%. For people who listen to jazz and with low pollution, the probability of smoking is 37%. For people who listen to jazz and with high pollution, the probability of smoking is 70%. The overall probability of high pollution is 45%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.66
P(V3=1 | X=0, V2=0) = 0.10
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.37
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.45
0.45 * 0.74 * (0.70 - 0.37)+ 0.55 * 0.74 * (0.33 - 0.10)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 30%. For people who do not listen to jazz and smokers, the probability of lung cancer is 74%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 29%. For people who listen to jazz and smokers, the probability of lung cancer is 66%. For people who do not listen to jazz and with low pollution, the probability of smoking is 10%. For people who do not listen to jazz and with high pollution, the probability of smoking is 33%. For people who listen to jazz and with low pollution, the probability of smoking is 37%. For people who listen to jazz and with high pollution, the probability of smoking is 70%. The overall probability of high pollution is 45%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.30
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.66
P(V3=1 | X=0, V2=0) = 0.10
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.37
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.45
0.45 * (0.66 - 0.29) * 0.33 + 0.55 * (0.74 - 0.30) * 0.37 = 0.01
0.01 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11674,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 8%. For people who do not listen to jazz, the probability of lung cancer is 39%. For people who listen to jazz, the probability of lung cancer is 48%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.48
0.08*0.48 - 0.92*0.39 = 0.40
0.40 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 35%. For people who listen to jazz, the probability of lung cancer is 39%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.39
0.39 - 0.35 = 0.04
0.04 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 35%. For people who listen to jazz, the probability of lung cancer is 39%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.39
0.39 - 0.35 = 0.04
0.04 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 35%. For people who listen to jazz, the probability of lung cancer is 39%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.39
0.39 - 0.35 = 0.04
0.04 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11687,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 23%. For people who do not listen to jazz and smokers, the probability of lung cancer is 59%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 15%. For people who listen to jazz and smokers, the probability of lung cancer is 52%. For people who do not listen to jazz and with low pollution, the probability of smoking is 33%. For people who do not listen to jazz and with high pollution, the probability of smoking is 35%. For people who listen to jazz and with low pollution, the probability of smoking is 67%. For people who listen to jazz and with high pollution, the probability of smoking is 63%. The overall probability of high pollution is 42%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.15
P(Y=1 | X=1, V3=1) = 0.52
P(V3=1 | X=0, V2=0) = 0.33
P(V3=1 | X=0, V2=1) = 0.35
P(V3=1 | X=1, V2=0) = 0.67
P(V3=1 | X=1, V2=1) = 0.63
P(V2=1) = 0.42
0.42 * (0.52 - 0.15) * 0.35 + 0.58 * (0.59 - 0.23) * 0.67 = -0.08
-0.08 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 15%. The probability of not listening to jazz and lung cancer is 30%. The probability of listening to jazz and lung cancer is 6%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.06
0.06/0.15 - 0.30/0.85 = 0.04
0.04 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 15%. The probability of not listening to jazz and lung cancer is 30%. The probability of listening to jazz and lung cancer is 6%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.06
0.06/0.15 - 0.30/0.85 = 0.04
0.04 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 43%. For people who listen to jazz, the probability of lung cancer is 52%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.52
0.52 - 0.43 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 43%. For people who listen to jazz, the probability of lung cancer is 52%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.52
0.52 - 0.43 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 29%. For people who do not listen to jazz and smokers, the probability of lung cancer is 61%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 20%. For people who listen to jazz and smokers, the probability of lung cancer is 63%. For people who do not listen to jazz and with low pollution, the probability of smoking is 28%. For people who do not listen to jazz and with high pollution, the probability of smoking is 61%. For people who listen to jazz and with low pollution, the probability of smoking is 54%. For people who listen to jazz and with high pollution, the probability of smoking is 97%. The overall probability of high pollution is 45%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.29
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.20
P(Y=1 | X=1, V3=1) = 0.63
P(V3=1 | X=0, V2=0) = 0.28
P(V3=1 | X=0, V2=1) = 0.61
P(V3=1 | X=1, V2=0) = 0.54
P(V3=1 | X=1, V2=1) = 0.97
P(V2=1) = 0.45
0.45 * 0.61 * (0.97 - 0.54)+ 0.55 * 0.61 * (0.61 - 0.28)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. For people who do not listen to jazz, the probability of lung cancer is 43%. For people who listen to jazz, the probability of lung cancer is 52%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.52
0.07*0.52 - 0.93*0.43 = 0.43
0.43 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 7%. The probability of not listening to jazz and lung cancer is 40%. The probability of listening to jazz and lung cancer is 4%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.40/0.93 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 43%. For people who do not listen to jazz and smokers, the probability of lung cancer is 45%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 40%. For people who listen to jazz and smokers, the probability of lung cancer is 61%. For people who do not listen to jazz and with low pollution, the probability of smoking is 40%. For people who do not listen to jazz and with high pollution, the probability of smoking is 1%. For people who listen to jazz and with low pollution, the probability of smoking is 82%. For people who listen to jazz and with high pollution, the probability of smoking is 64%. The overall probability of high pollution is 46%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.01
P(V3=1 | X=1, V2=0) = 0.82
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.46
0.46 * 0.45 * (0.64 - 0.82)+ 0.54 * 0.45 * (0.01 - 0.40)= 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11713,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 43%. For people who do not listen to jazz and smokers, the probability of lung cancer is 45%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 40%. For people who listen to jazz and smokers, the probability of lung cancer is 61%. For people who do not listen to jazz and with low pollution, the probability of smoking is 40%. For people who do not listen to jazz and with high pollution, the probability of smoking is 1%. For people who listen to jazz and with low pollution, the probability of smoking is 82%. For people who listen to jazz and with high pollution, the probability of smoking is 64%. The overall probability of high pollution is 46%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.01
P(V3=1 | X=1, V2=0) = 0.82
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.46
0.46 * 0.45 * (0.64 - 0.82)+ 0.54 * 0.45 * (0.01 - 0.40)= 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 43%. For people who do not listen to jazz and smokers, the probability of lung cancer is 45%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 40%. For people who listen to jazz and smokers, the probability of lung cancer is 61%. For people who do not listen to jazz and with low pollution, the probability of smoking is 40%. For people who do not listen to jazz and with high pollution, the probability of smoking is 1%. For people who listen to jazz and with low pollution, the probability of smoking is 82%. For people who listen to jazz and with high pollution, the probability of smoking is 64%. The overall probability of high pollution is 46%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.01
P(V3=1 | X=1, V2=0) = 0.82
P(V3=1 | X=1, V2=1) = 0.64
P(V2=1) = 0.46
0.46 * (0.61 - 0.40) * 0.01 + 0.54 * (0.45 - 0.43) * 0.82 = -0.03
-0.03 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11716,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 10%. For people who do not listen to jazz, the probability of lung cancer is 44%. For people who listen to jazz, the probability of lung cancer is 55%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.55
0.10*0.55 - 0.90*0.44 = 0.45
0.45 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 10%. For people who do not listen to jazz, the probability of lung cancer is 44%. For people who listen to jazz, the probability of lung cancer is 55%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.55
0.10*0.55 - 0.90*0.44 = 0.45
0.45 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 10%. The probability of not listening to jazz and lung cancer is 39%. The probability of listening to jazz and lung cancer is 6%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.39/0.90 = 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 10%. The probability of not listening to jazz and lung cancer is 39%. The probability of listening to jazz and lung cancer is 6%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.39/0.90 = 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 58%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.58
0.58 - 0.52 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 58%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.58
0.58 - 0.52 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11724,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 58%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.58
0.58 - 0.52 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 58%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.58
0.58 - 0.52 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who do not listen to jazz and smokers, the probability of lung cancer is 71%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 66%. For people who do not listen to jazz and with low pollution, the probability of smoking is 29%. For people who do not listen to jazz and with high pollution, the probability of smoking is 58%. For people who listen to jazz and with low pollution, the probability of smoking is 64%. For people who listen to jazz and with high pollution, the probability of smoking is 84%. The overall probability of high pollution is 56%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.66
P(V3=1 | X=0, V2=0) = 0.29
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.84
P(V2=1) = 0.56
0.56 * 0.71 * (0.84 - 0.64)+ 0.44 * 0.71 * (0.58 - 0.29)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who do not listen to jazz and smokers, the probability of lung cancer is 71%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 66%. For people who do not listen to jazz and with low pollution, the probability of smoking is 29%. For people who do not listen to jazz and with high pollution, the probability of smoking is 58%. For people who listen to jazz and with low pollution, the probability of smoking is 64%. For people who listen to jazz and with high pollution, the probability of smoking is 84%. The overall probability of high pollution is 56%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.66
P(V3=1 | X=0, V2=0) = 0.29
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.84
P(V2=1) = 0.56
0.56 * (0.66 - 0.35) * 0.58 + 0.44 * (0.71 - 0.35) * 0.64 = -0.00
0.00 = 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who do not listen to jazz and smokers, the probability of lung cancer is 71%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 35%. For people who listen to jazz and smokers, the probability of lung cancer is 66%. For people who do not listen to jazz and with low pollution, the probability of smoking is 29%. For people who do not listen to jazz and with high pollution, the probability of smoking is 58%. For people who listen to jazz and with low pollution, the probability of smoking is 64%. For people who listen to jazz and with high pollution, the probability of smoking is 84%. The overall probability of high pollution is 56%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.66
P(V3=1 | X=0, V2=0) = 0.29
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.84
P(V2=1) = 0.56
0.56 * (0.66 - 0.35) * 0.58 + 0.44 * (0.71 - 0.35) * 0.64 = -0.00
0.00 = 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11732,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 13%. The probability of not listening to jazz and lung cancer is 44%. The probability of listening to jazz and lung cancer is 8%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.08
0.08/0.13 - 0.44/0.87 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 18%. The probability of not listening to jazz and lung cancer is 33%. The probability of listening to jazz and lung cancer is 8%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.08
0.08/0.18 - 0.33/0.82 = 0.05
0.05 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 54%. For people who listen to jazz, the probability of lung cancer is 64%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.64
0.64 - 0.54 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11752,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 54%. For people who listen to jazz, the probability of lung cancer is 64%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.64
0.64 - 0.54 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 21%. For people who do not listen to jazz and with high pollution, the probability of smoking is 47%. For people who listen to jazz and with low pollution, the probability of smoking is 45%. For people who listen to jazz and with high pollution, the probability of smoking is 78%. The overall probability of high pollution is 53%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.78
P(V2=1) = 0.53
0.53 * 0.78 * (0.78 - 0.45)+ 0.47 * 0.78 * (0.47 - 0.21)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 21%. For people who do not listen to jazz and with high pollution, the probability of smoking is 47%. For people who listen to jazz and with low pollution, the probability of smoking is 45%. For people who listen to jazz and with high pollution, the probability of smoking is 78%. The overall probability of high pollution is 53%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.78
P(V2=1) = 0.53
0.53 * 0.78 * (0.78 - 0.45)+ 0.47 * 0.78 * (0.47 - 0.21)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who do not listen to jazz and smokers, the probability of lung cancer is 78%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 42%. For people who listen to jazz and smokers, the probability of lung cancer is 77%. For people who do not listen to jazz and with low pollution, the probability of smoking is 21%. For people who do not listen to jazz and with high pollution, the probability of smoking is 47%. For people who listen to jazz and with low pollution, the probability of smoking is 45%. For people who listen to jazz and with high pollution, the probability of smoking is 78%. The overall probability of high pollution is 53%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.78
P(V2=1) = 0.53
0.53 * (0.77 - 0.42) * 0.47 + 0.47 * (0.78 - 0.42) * 0.45 = 0.03
0.03 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 20%. For people who do not listen to jazz, the probability of lung cancer is 54%. For people who listen to jazz, the probability of lung cancer is 64%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.64
0.20*0.64 - 0.80*0.54 = 0.56
0.56 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 40%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.40
0.40 - 0.28 = 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 40%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.40
0.40 - 0.28 = 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 40%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.40
0.40 - 0.28 = 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 24%. For people who do not listen to jazz and smokers, the probability of lung cancer is 49%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 17%. For people who listen to jazz and smokers, the probability of lung cancer is 58%. For people who do not listen to jazz and with low pollution, the probability of smoking is 16%. For people who do not listen to jazz and with high pollution, the probability of smoking is 12%. For people who listen to jazz and with low pollution, the probability of smoking is 45%. For people who listen to jazz and with high pollution, the probability of smoking is 67%. The overall probability of high pollution is 53%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.24
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.17
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.16
P(V3=1 | X=0, V2=1) = 0.12
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.53
0.53 * 0.49 * (0.67 - 0.45)+ 0.47 * 0.49 * (0.12 - 0.16)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 24%. For people who do not listen to jazz and smokers, the probability of lung cancer is 49%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 17%. For people who listen to jazz and smokers, the probability of lung cancer is 58%. For people who do not listen to jazz and with low pollution, the probability of smoking is 16%. For people who do not listen to jazz and with high pollution, the probability of smoking is 12%. For people who listen to jazz and with low pollution, the probability of smoking is 45%. For people who listen to jazz and with high pollution, the probability of smoking is 67%. The overall probability of high pollution is 53%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.24
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.17
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.16
P(V3=1 | X=0, V2=1) = 0.12
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.53
0.53 * (0.58 - 0.17) * 0.12 + 0.47 * (0.49 - 0.24) * 0.45 = -0.03
-0.03 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
11772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 2%. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 40%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.40
0.02*0.40 - 0.98*0.28 = 0.28
0.28 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11773,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 2%. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 40%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.40
0.02*0.40 - 0.98*0.28 = 0.28
0.28 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 2%. The probability of not listening to jazz and lung cancer is 27%. The probability of listening to jazz and lung cancer is 1%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.27/0.98 = 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 2%. The probability of not listening to jazz and lung cancer is 27%. The probability of listening to jazz and lung cancer is 1%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.27/0.98 = 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 58%. For people who listen to jazz, the probability of lung cancer is 68%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.68
0.68 - 0.58 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 10%. For people who do not listen to jazz, the probability of lung cancer is 58%. For people who listen to jazz, the probability of lung cancer is 68%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.68
0.10*0.68 - 0.90*0.58 = 0.59
0.59 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
11795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 66%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.66
0.66 - 0.52 = 0.14
0.14 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 37%. For people who do not listen to jazz and smokers, the probability of lung cancer is 83%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 30%. For people who listen to jazz and smokers, the probability of lung cancer is 78%. For people who do not listen to jazz and with low pollution, the probability of smoking is 14%. For people who do not listen to jazz and with high pollution, the probability of smoking is 44%. For people who listen to jazz and with low pollution, the probability of smoking is 61%. For people who listen to jazz and with high pollution, the probability of smoking is 87%. The overall probability of high pollution is 57%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.30
P(Y=1 | X=1, V3=1) = 0.78
P(V3=1 | X=0, V2=0) = 0.14
P(V3=1 | X=0, V2=1) = 0.44
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.87
P(V2=1) = 0.57
0.57 * 0.83 * (0.87 - 0.61)+ 0.43 * 0.83 * (0.44 - 0.14)= 0.14
0.14 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 11%. The probability of not listening to jazz and lung cancer is 46%. The probability of listening to jazz and lung cancer is 7%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.07
0.07/0.11 - 0.46/0.89 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to smoking. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 47%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.47
0.47 - 0.40 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not listen to jazz and nonsmokers, the probability of lung cancer is 27%. For people who do not listen to jazz and smokers, the probability of lung cancer is 58%. For people who listen to jazz and nonsmokers, the probability of lung cancer is 28%. For people who listen to jazz and smokers, the probability of lung cancer is 55%. For people who do not listen to jazz and with low pollution, the probability of smoking is 32%. For people who do not listen to jazz and with high pollution, the probability of smoking is 45%. For people who listen to jazz and with low pollution, the probability of smoking is 72%. For people who listen to jazz and with high pollution, the probability of smoking is 68%. The overall probability of high pollution is 53%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.27
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0, V2=0) = 0.32
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.68
P(V2=1) = 0.53
0.53 * 0.58 * (0.68 - 0.72)+ 0.47 * 0.58 * (0.45 - 0.32)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
11816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 13%. The probability of not listening to jazz and lung cancer is 34%. The probability of listening to jazz and lung cancer is 6%.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.06
0.06/0.13 - 0.34/0.87 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of listening to jazz is 13%. The probability of not listening to jazz and lung cancer is 34%. The probability of listening to jazz and lung cancer is 6%.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.06
0.06/0.13 - 0.34/0.87 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
11819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
11821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 51%. For people who listen to jazz, the probability of lung cancer is 61%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.61
0.61 - 0.51 = 0.09
0.09 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 8%. The probability of not listening to jazz and lung cancer is 47%. The probability of listening to jazz and lung cancer is 5%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.05
0.05/0.08 - 0.47/0.92 = 0.09
0.09 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11831,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 47%. For people who listen to jazz, the probability of lung cancer is 73%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.73
0.73 - 0.47 = 0.26
0.26 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 19%. For people who do not listen to jazz, the probability of lung cancer is 47%. For people who listen to jazz, the probability of lung cancer is 73%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.73
0.19*0.73 - 0.81*0.47 = 0.52
0.52 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 19%. The probability of not listening to jazz and lung cancer is 38%. The probability of listening to jazz and lung cancer is 14%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.14
0.14/0.19 - 0.38/0.81 = 0.26
0.26 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11844,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 50%. For people who listen to jazz, the probability of lung cancer is 73%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.73 - 0.50 = 0.23
0.23 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 50%. For people who listen to jazz, the probability of lung cancer is 73%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.73 - 0.50 = 0.23
0.23 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11848,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 50%. For people who listen to jazz, the probability of lung cancer is 73%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.73 - 0.50 = 0.23
0.23 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 50%. For people who listen to jazz, the probability of lung cancer is 73%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.73
0.73 - 0.50 = 0.23
0.23 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11857,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 36%. For people who listen to jazz, the probability of lung cancer is 57%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.57
0.57 - 0.36 = 0.21
0.21 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11862,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 2%. For people who do not listen to jazz, the probability of lung cancer is 36%. For people who listen to jazz, the probability of lung cancer is 57%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.57
0.02*0.57 - 0.98*0.36 = 0.37
0.37 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 2%. For people who do not listen to jazz, the probability of lung cancer is 36%. For people who listen to jazz, the probability of lung cancer is 57%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.57
0.02*0.57 - 0.98*0.36 = 0.37
0.37 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 2%. The probability of not listening to jazz and lung cancer is 36%. The probability of listening to jazz and lung cancer is 1%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.36/0.98 = 0.21
0.21 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 45%. For people who listen to jazz, the probability of lung cancer is 60%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.60
0.60 - 0.45 = 0.15
0.15 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 45%. For people who listen to jazz, the probability of lung cancer is 60%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.60
0.60 - 0.45 = 0.15
0.15 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 12%. For people who do not listen to jazz, the probability of lung cancer is 45%. For people who listen to jazz, the probability of lung cancer is 60%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.60
0.12*0.60 - 0.88*0.45 = 0.47
0.47 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 57%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.57
0.57 - 0.28 = 0.29
0.29 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 57%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.57
0.57 - 0.28 = 0.29
0.29 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 10%. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 57%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.57
0.10*0.57 - 0.90*0.28 = 0.31
0.31 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 10%. The probability of not listening to jazz and lung cancer is 25%. The probability of listening to jazz and lung cancer is 6%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.25/0.90 = 0.29
0.29 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 10%. The probability of not listening to jazz and lung cancer is 25%. The probability of listening to jazz and lung cancer is 6%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.25/0.90 = 0.29
0.29 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11892,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 68%. For people who listen to jazz, the probability of lung cancer is 79%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.79
0.79 - 0.68 = 0.11
0.11 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 68%. For people who listen to jazz, the probability of lung cancer is 79%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.79
0.79 - 0.68 = 0.11
0.11 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 68%. For people who listen to jazz, the probability of lung cancer is 79%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.79
0.79 - 0.68 = 0.11
0.11 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 7%. For people who do not listen to jazz, the probability of lung cancer is 68%. For people who listen to jazz, the probability of lung cancer is 79%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.79
0.07*0.79 - 0.93*0.68 = 0.69
0.69 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11899,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 7%. For people who do not listen to jazz, the probability of lung cancer is 68%. For people who listen to jazz, the probability of lung cancer is 79%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.79
0.07*0.79 - 0.93*0.68 = 0.69
0.69 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11900,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 7%. The probability of not listening to jazz and lung cancer is 63%. The probability of listening to jazz and lung cancer is 6%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.06
0.06/0.07 - 0.63/0.93 = 0.11
0.11 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 27%. For people who listen to jazz, the probability of lung cancer is 41%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.14
0.14 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11905,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 27%. For people who listen to jazz, the probability of lung cancer is 41%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.14
0.14 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 27%. For people who listen to jazz, the probability of lung cancer is 41%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.14
0.14 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 27%. For people who listen to jazz, the probability of lung cancer is 41%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.14
0.14 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 27%. For people who listen to jazz, the probability of lung cancer is 41%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.14
0.14 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 17%. For people who do not listen to jazz, the probability of lung cancer is 27%. For people who listen to jazz, the probability of lung cancer is 41%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.17*0.41 - 0.83*0.27 = 0.29
0.29 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11913,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 17%. The probability of not listening to jazz and lung cancer is 22%. The probability of listening to jazz and lung cancer is 7%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.07
0.07/0.17 - 0.22/0.83 = 0.14
0.14 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11916,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 52%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.52
0.52 - 0.40 = 0.12
0.12 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 52%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.52
0.52 - 0.40 = 0.12
0.12 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 52%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.52
0.52 - 0.40 = 0.12
0.12 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 52%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.52
0.52 - 0.40 = 0.12
0.12 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11923,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 14%. For people who do not listen to jazz, the probability of lung cancer is 40%. For people who listen to jazz, the probability of lung cancer is 52%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.52
0.14*0.52 - 0.86*0.40 = 0.42
0.42 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 14%. The probability of not listening to jazz and lung cancer is 34%. The probability of listening to jazz and lung cancer is 7%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.07
0.07/0.14 - 0.34/0.86 = 0.12
0.12 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11930,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 22%. For people who listen to jazz, the probability of lung cancer is 49%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.49
0.49 - 0.22 = 0.27
0.27 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11934,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 18%. For people who do not listen to jazz, the probability of lung cancer is 22%. For people who listen to jazz, the probability of lung cancer is 49%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.49
0.18*0.49 - 0.82*0.22 = 0.27
0.27 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 61%. For people who listen to jazz, the probability of lung cancer is 79%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.79
0.79 - 0.61 = 0.17
0.17 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 61%. For people who listen to jazz, the probability of lung cancer is 79%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.79
0.79 - 0.61 = 0.17
0.17 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 61%. For people who listen to jazz, the probability of lung cancer is 79%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.79
0.79 - 0.61 = 0.17
0.17 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 32%. For people who listen to jazz, the probability of lung cancer is 73%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.73
0.73 - 0.32 = 0.41
0.41 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 32%. For people who listen to jazz, the probability of lung cancer is 73%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.73
0.73 - 0.32 = 0.41
0.41 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 32%. For people who listen to jazz, the probability of lung cancer is 73%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.73
0.73 - 0.32 = 0.41
0.41 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 32%. For people who listen to jazz, the probability of lung cancer is 73%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.73
0.73 - 0.32 = 0.41
0.41 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 41%. For people who listen to jazz, the probability of lung cancer is 83%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.83
0.83 - 0.41 = 0.43
0.43 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 41%. For people who listen to jazz, the probability of lung cancer is 83%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.83
0.83 - 0.41 = 0.43
0.43 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11970,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 5%. For people who do not listen to jazz, the probability of lung cancer is 41%. For people who listen to jazz, the probability of lung cancer is 83%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.83
0.05*0.83 - 0.95*0.41 = 0.43
0.43 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 5%. For people who do not listen to jazz, the probability of lung cancer is 41%. For people who listen to jazz, the probability of lung cancer is 83%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.83
0.05*0.83 - 0.95*0.41 = 0.43
0.43 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 5%. The probability of not listening to jazz and lung cancer is 39%. The probability of listening to jazz and lung cancer is 4%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.04
0.04/0.05 - 0.39/0.95 = 0.43
0.43 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
11975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
11976,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 34%. For people who listen to jazz, the probability of lung cancer is 51%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.51
0.51 - 0.34 = 0.16
0.16 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 34%. For people who listen to jazz, the probability of lung cancer is 51%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.51
0.51 - 0.34 = 0.16
0.16 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 34%. For people who listen to jazz, the probability of lung cancer is 51%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.51
0.51 - 0.34 = 0.16
0.16 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
11983,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 11%. For people who do not listen to jazz, the probability of lung cancer is 34%. For people who listen to jazz, the probability of lung cancer is 51%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.51
0.11*0.51 - 0.89*0.34 = 0.36
0.36 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 53%. For people who listen to jazz, the probability of lung cancer is 69%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.69 - 0.53 = 0.16
0.16 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
11990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 53%. For people who listen to jazz, the probability of lung cancer is 69%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.69 - 0.53 = 0.16
0.16 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 53%. For people who listen to jazz, the probability of lung cancer is 69%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.69 - 0.53 = 0.16
0.16 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
11994,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 14%. For people who do not listen to jazz, the probability of lung cancer is 53%. For people who listen to jazz, the probability of lung cancer is 69%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.14*0.69 - 0.86*0.53 = 0.55
0.55 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 14%. For people who do not listen to jazz, the probability of lung cancer is 53%. For people who listen to jazz, the probability of lung cancer is 69%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.14*0.69 - 0.86*0.53 = 0.55
0.55 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
11997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 14%. The probability of not listening to jazz and lung cancer is 45%. The probability of listening to jazz and lung cancer is 9%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.09
0.09/0.14 - 0.45/0.86 = 0.16
0.16 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 76%. For people who listen to jazz, the probability of lung cancer is 90%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.90
0.90 - 0.76 = 0.13
0.13 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12003,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 76%. For people who listen to jazz, the probability of lung cancer is 90%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.90
0.90 - 0.76 = 0.13
0.13 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 16%. The probability of not listening to jazz and lung cancer is 64%. The probability of listening to jazz and lung cancer is 14%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.64
P(Y=1, X=1=1) = 0.14
0.14/0.16 - 0.64/0.84 = 0.13
0.13 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 43%. For people who listen to jazz, the probability of lung cancer is 64%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.64
0.64 - 0.43 = 0.21
0.21 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 43%. For people who listen to jazz, the probability of lung cancer is 64%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.64
0.64 - 0.43 = 0.21
0.21 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 10%. For people who do not listen to jazz, the probability of lung cancer is 43%. For people who listen to jazz, the probability of lung cancer is 64%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.64
0.10*0.64 - 0.90*0.43 = 0.45
0.45 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12022,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 79%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.79
0.79 - 0.52 = 0.27
0.27 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 79%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.79
0.79 - 0.52 = 0.27
0.27 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 3%. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 79%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.79
0.03*0.79 - 0.97*0.52 = 0.53
0.53 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 61%. For people who listen to jazz, the probability of lung cancer is 75%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.75
0.75 - 0.61 = 0.14
0.14 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 3%. For people who do not listen to jazz, the probability of lung cancer is 61%. For people who listen to jazz, the probability of lung cancer is 75%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.75
0.03*0.75 - 0.97*0.61 = 0.62
0.62 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 3%. The probability of not listening to jazz and lung cancer is 59%. The probability of listening to jazz and lung cancer is 2%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.59/0.97 = 0.14
0.14 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12052,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 26%. For people who listen to jazz, the probability of lung cancer is 49%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.49
0.49 - 0.26 = 0.23
0.23 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 10%. The probability of not listening to jazz and lung cancer is 24%. The probability of listening to jazz and lung cancer is 5%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.05
0.05/0.10 - 0.24/0.90 = 0.23
0.23 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 10%. The probability of not listening to jazz and lung cancer is 24%. The probability of listening to jazz and lung cancer is 5%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.05
0.05/0.10 - 0.24/0.90 = 0.23
0.23 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 35%. For people who listen to jazz, the probability of lung cancer is 46%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.46
0.46 - 0.35 = 0.10
0.10 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 35%. For people who listen to jazz, the probability of lung cancer is 46%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.46
0.46 - 0.35 = 0.10
0.10 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 18%. The probability of not listening to jazz and lung cancer is 29%. The probability of listening to jazz and lung cancer is 8%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.08
0.08/0.18 - 0.29/0.82 = 0.10
0.10 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 62%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.62
0.62 - 0.28 = 0.34
0.34 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12074,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 62%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.62
0.62 - 0.28 = 0.34
0.34 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 62%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.62
0.62 - 0.28 = 0.34
0.34 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 28%. For people who listen to jazz, the probability of lung cancer is 62%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.62
0.62 - 0.28 = 0.34
0.34 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 51%. For people who listen to jazz, the probability of lung cancer is 79%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.79
0.79 - 0.51 = 0.28
0.28 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 51%. For people who listen to jazz, the probability of lung cancer is 79%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.79
0.79 - 0.51 = 0.28
0.28 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 35%. For people who listen to jazz, the probability of lung cancer is 62%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.62
0.62 - 0.35 = 0.28
0.28 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 12%. For people who do not listen to jazz, the probability of lung cancer is 35%. For people who listen to jazz, the probability of lung cancer is 62%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.62
0.12*0.62 - 0.88*0.35 = 0.38
0.38 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12104,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 12%. The probability of not listening to jazz and lung cancer is 30%. The probability of listening to jazz and lung cancer is 8%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.08
0.08/0.12 - 0.30/0.88 = 0.28
0.28 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 12%. The probability of not listening to jazz and lung cancer is 30%. The probability of listening to jazz and lung cancer is 8%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.08
0.08/0.12 - 0.30/0.88 = 0.28
0.28 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12111,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 46%. For people who listen to jazz, the probability of lung cancer is 74%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.74
0.74 - 0.46 = 0.29
0.29 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 46%. For people who listen to jazz, the probability of lung cancer is 74%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.74
0.74 - 0.46 = 0.29
0.29 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 18%. For people who do not listen to jazz, the probability of lung cancer is 46%. For people who listen to jazz, the probability of lung cancer is 74%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.74
0.18*0.74 - 0.82*0.46 = 0.51
0.51 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 18%. The probability of not listening to jazz and lung cancer is 38%. The probability of listening to jazz and lung cancer is 13%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.13
0.13/0.18 - 0.38/0.82 = 0.29
0.29 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 90%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.90
0.90 - 0.52 = 0.39
0.39 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 90%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.90
0.90 - 0.52 = 0.39
0.39 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12125,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 90%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.90
0.90 - 0.52 = 0.39
0.39 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 12%. For people who do not listen to jazz, the probability of lung cancer is 52%. For people who listen to jazz, the probability of lung cancer is 90%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.90
0.12*0.90 - 0.88*0.52 = 0.56
0.56 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 14%. For people who listen to jazz, the probability of lung cancer is 34%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.34
0.34 - 0.14 = 0.20
0.20 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 14%. For people who listen to jazz, the probability of lung cancer is 34%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.34
0.34 - 0.14 = 0.20
0.20 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 14%. For people who listen to jazz, the probability of lung cancer is 34%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.14
P(Y=1 | X=1) = 0.34
0.34 - 0.14 = 0.20
0.20 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 12%. The probability of not listening to jazz and lung cancer is 12%. The probability of listening to jazz and lung cancer is 4%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.04
0.04/0.12 - 0.12/0.88 = 0.20
0.20 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 12%. The probability of not listening to jazz and lung cancer is 12%. The probability of listening to jazz and lung cancer is 4%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.04
0.04/0.12 - 0.12/0.88 = 0.20
0.20 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how listening to jazz correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how listening to jazz correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12143,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 30%. For people who listen to jazz, the probability of lung cancer is 55%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.55
0.55 - 0.30 = 0.25
0.25 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 30%. For people who listen to jazz, the probability of lung cancer is 55%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.55
0.55 - 0.30 = 0.25
0.25 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 3%. The probability of not listening to jazz and lung cancer is 30%. The probability of listening to jazz and lung cancer is 1%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.30/0.97 = 0.25
0.25 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 30%. For people who listen to jazz, the probability of lung cancer is 51%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.51
0.51 - 0.30 = 0.21
0.21 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 30%. For people who listen to jazz, the probability of lung cancer is 51%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.51
0.51 - 0.30 = 0.21
0.21 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 30%. For people who listen to jazz, the probability of lung cancer is 51%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.51
0.51 - 0.30 = 0.21
0.21 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 30%. For people who listen to jazz, the probability of lung cancer is 51%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.51
0.51 - 0.30 = 0.21
0.21 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12163,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 11%. For people who do not listen to jazz, the probability of lung cancer is 30%. For people who listen to jazz, the probability of lung cancer is 51%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.51
0.11*0.51 - 0.89*0.30 = 0.33
0.33 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 11%. The probability of not listening to jazz and lung cancer is 27%. The probability of listening to jazz and lung cancer is 6%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.06
0.06/0.11 - 0.27/0.89 = 0.21
0.21 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 11%. The probability of not listening to jazz and lung cancer is 27%. The probability of listening to jazz and lung cancer is 6%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.06
0.06/0.11 - 0.27/0.89 = 0.21
0.21 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
12167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how listening to jazz correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
12171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not listen to jazz, the probability of lung cancer is 10%. For people who listen to jazz, the probability of lung cancer is 41%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.41
0.41 - 0.10 = 0.31
0.31 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 17%. For people who do not listen to jazz, the probability of lung cancer is 10%. For people who listen to jazz, the probability of lung cancer is 41%.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.41
0.17*0.41 - 0.83*0.10 = 0.15
0.15 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of listening to jazz is 17%. For people who do not listen to jazz, the probability of lung cancer is 10%. For people who listen to jazz, the probability of lung cancer is 41%.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.41
0.17*0.41 - 0.83*0.10 = 0.15
0.15 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
12182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 37%. For infants with nonsmoking mothers, the probability of brown eyes is 80%. For infants with smoking mothers, the probability of brown eyes is 43%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.43
0.37*0.43 - 0.63*0.80 = 0.66
0.66 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 37%. The probability of nonsmoking mother and brown eyes is 50%. The probability of smoking mother and brown eyes is 16%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.16
0.16/0.37 - 0.50/0.63 = -0.37
-0.37 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12187,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 51%. For areas with high cigarette tax, the probability of brown eyes is 62%. For areas with low cigarette tax, the probability of smoking mother is 84%. For areas with high cigarette tax, the probability of smoking mother is 41%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.51
P(Y=1 | V2=1) = 0.62
P(X=1 | V2=0) = 0.84
P(X=1 | V2=1) = 0.41
(0.62 - 0.51) / (0.41 - 0.84) = -0.25
-0.25 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 49%. For infants with nonsmoking mothers, the probability of brown eyes is 72%. For infants with smoking mothers, the probability of brown eyes is 47%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.47
0.49*0.47 - 0.51*0.72 = 0.60
0.60 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 49%. For infants with nonsmoking mothers, the probability of brown eyes is 72%. For infants with smoking mothers, the probability of brown eyes is 47%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.47
0.49*0.47 - 0.51*0.72 = 0.60
0.60 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 49%. The probability of nonsmoking mother and brown eyes is 37%. The probability of smoking mother and brown eyes is 23%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.23
0.23/0.49 - 0.37/0.51 = -0.25
-0.25 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 15%. The probability of nonsmoking mother and brown eyes is 53%. The probability of smoking mother and brown eyes is 5%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.05
0.05/0.15 - 0.53/0.85 = -0.30
-0.30 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12202,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 43%. For infants with nonsmoking mothers, the probability of brown eyes is 86%. For infants with smoking mothers, the probability of brown eyes is 40%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.40
0.43*0.40 - 0.57*0.86 = 0.66
0.66 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 43%. For infants with nonsmoking mothers, the probability of brown eyes is 86%. For infants with smoking mothers, the probability of brown eyes is 40%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.40
0.43*0.40 - 0.57*0.86 = 0.66
0.66 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12208,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 43%. The probability of nonsmoking mother and brown eyes is 49%. The probability of smoking mother and brown eyes is 17%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.17
0.17/0.43 - 0.49/0.57 = -0.46
-0.46 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 56%. For areas with high cigarette tax, the probability of brown eyes is 67%. For areas with low cigarette tax, the probability of smoking mother is 49%. For areas with high cigarette tax, the probability of smoking mother is 20%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.56
P(Y=1 | V2=1) = 0.67
P(X=1 | V2=0) = 0.49
P(X=1 | V2=1) = 0.20
(0.67 - 0.56) / (0.20 - 0.49) = -0.39
-0.39 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 56%. For areas with high cigarette tax, the probability of brown eyes is 67%. For areas with low cigarette tax, the probability of smoking mother is 49%. For areas with high cigarette tax, the probability of smoking mother is 20%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.56
P(Y=1 | V2=1) = 0.67
P(X=1 | V2=0) = 0.49
P(X=1 | V2=1) = 0.20
(0.67 - 0.56) / (0.20 - 0.49) = -0.39
-0.39 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 21%. The probability of nonsmoking mother and brown eyes is 59%. The probability of smoking mother and brown eyes is 8%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.21
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.08
0.08/0.21 - 0.59/0.79 = -0.38
-0.38 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 54%. For areas with high cigarette tax, the probability of brown eyes is 66%. For areas with low cigarette tax, the probability of smoking mother is 55%. For areas with high cigarette tax, the probability of smoking mother is 22%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.66
P(X=1 | V2=0) = 0.55
P(X=1 | V2=1) = 0.22
(0.66 - 0.54) / (0.22 - 0.55) = -0.38
-0.38 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 54%. For areas with high cigarette tax, the probability of brown eyes is 66%. For areas with low cigarette tax, the probability of smoking mother is 55%. For areas with high cigarette tax, the probability of smoking mother is 22%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.66
P(X=1 | V2=0) = 0.55
P(X=1 | V2=1) = 0.22
(0.66 - 0.54) / (0.22 - 0.55) = -0.38
-0.38 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 29%. For infants with nonsmoking mothers, the probability of brown eyes is 74%. For infants with smoking mothers, the probability of brown eyes is 37%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.37
0.29*0.37 - 0.71*0.74 = 0.64
0.64 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 29%. The probability of nonsmoking mother and brown eyes is 53%. The probability of smoking mother and brown eyes is 11%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.29
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.11
0.11/0.29 - 0.53/0.71 = -0.37
-0.37 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 48%. For areas with high cigarette tax, the probability of brown eyes is 60%. For areas with low cigarette tax, the probability of smoking mother is 63%. For areas with high cigarette tax, the probability of smoking mother is 37%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.48
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.63
P(X=1 | V2=1) = 0.37
(0.60 - 0.48) / (0.37 - 0.63) = -0.44
-0.44 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 48%. For areas with high cigarette tax, the probability of brown eyes is 60%. For areas with low cigarette tax, the probability of smoking mother is 63%. For areas with high cigarette tax, the probability of smoking mother is 37%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.48
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.63
P(X=1 | V2=1) = 0.37
(0.60 - 0.48) / (0.37 - 0.63) = -0.44
-0.44 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 39%. For infants with nonsmoking mothers, the probability of brown eyes is 76%. For infants with smoking mothers, the probability of brown eyes is 33%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.33
0.39*0.33 - 0.61*0.76 = 0.59
0.59 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 39%. The probability of nonsmoking mother and brown eyes is 47%. The probability of smoking mother and brown eyes is 13%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.13
0.13/0.39 - 0.47/0.61 = -0.44
-0.44 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 39%. The probability of nonsmoking mother and brown eyes is 47%. The probability of smoking mother and brown eyes is 13%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.13
0.13/0.39 - 0.47/0.61 = -0.44
-0.44 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 55%. For areas with high cigarette tax, the probability of brown eyes is 66%. For areas with low cigarette tax, the probability of smoking mother is 80%. For areas with high cigarette tax, the probability of smoking mother is 43%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.55
P(Y=1 | V2=1) = 0.66
P(X=1 | V2=0) = 0.80
P(X=1 | V2=1) = 0.43
(0.66 - 0.55) / (0.43 - 0.80) = -0.32
-0.32 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 22%. For infants with nonsmoking mothers, the probability of brown eyes is 50%. For infants with smoking mothers, the probability of brown eyes is 22%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.22
0.22*0.22 - 0.78*0.50 = 0.44
0.44 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 22%. For infants with nonsmoking mothers, the probability of brown eyes is 50%. For infants with smoking mothers, the probability of brown eyes is 22%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.22
0.22*0.22 - 0.78*0.50 = 0.44
0.44 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12248,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 22%. The probability of nonsmoking mother and brown eyes is 39%. The probability of smoking mother and brown eyes is 5%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.22
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.05
0.05/0.22 - 0.39/0.78 = -0.28
-0.28 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 28%. For areas with high cigarette tax, the probability of brown eyes is 44%. For areas with low cigarette tax, the probability of smoking mother is 63%. For areas with high cigarette tax, the probability of smoking mother is 27%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.28
P(Y=1 | V2=1) = 0.44
P(X=1 | V2=0) = 0.63
P(X=1 | V2=1) = 0.27
(0.44 - 0.28) / (0.27 - 0.63) = -0.45
-0.45 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 29%. For infants with nonsmoking mothers, the probability of brown eyes is 57%. For infants with smoking mothers, the probability of brown eyes is 12%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.12
0.29*0.12 - 0.71*0.57 = 0.43
0.43 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 29%. For infants with nonsmoking mothers, the probability of brown eyes is 57%. For infants with smoking mothers, the probability of brown eyes is 12%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.12
0.29*0.12 - 0.71*0.57 = 0.43
0.43 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 29%. The probability of nonsmoking mother and brown eyes is 41%. The probability of smoking mother and brown eyes is 3%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.29
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.03
0.03/0.29 - 0.41/0.71 = -0.45
-0.45 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 29%. The probability of nonsmoking mother and brown eyes is 41%. The probability of smoking mother and brown eyes is 3%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.29
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.03
0.03/0.29 - 0.41/0.71 = -0.45
-0.45 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 36%. For areas with high cigarette tax, the probability of brown eyes is 46%. For areas with low cigarette tax, the probability of smoking mother is 59%. For areas with high cigarette tax, the probability of smoking mother is 34%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.36
P(Y=1 | V2=1) = 0.46
P(X=1 | V2=0) = 0.59
P(X=1 | V2=1) = 0.34
(0.46 - 0.36) / (0.34 - 0.59) = -0.42
-0.42 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 50%. For areas with high cigarette tax, the probability of brown eyes is 61%. For areas with low cigarette tax, the probability of smoking mother is 67%. For areas with high cigarette tax, the probability of smoking mother is 32%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.50
P(Y=1 | V2=1) = 0.61
P(X=1 | V2=0) = 0.67
P(X=1 | V2=1) = 0.32
(0.61 - 0.50) / (0.32 - 0.67) = -0.29
-0.29 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 38%. The probability of nonsmoking mother and brown eyes is 43%. The probability of smoking mother and brown eyes is 16%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.16
0.16/0.38 - 0.43/0.62 = -0.29
-0.29 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 44%. For areas with high cigarette tax, the probability of brown eyes is 61%. For areas with low cigarette tax, the probability of smoking mother is 76%. For areas with high cigarette tax, the probability of smoking mother is 49%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.44
P(Y=1 | V2=1) = 0.61
P(X=1 | V2=0) = 0.76
P(X=1 | V2=1) = 0.49
(0.61 - 0.44) / (0.49 - 0.76) = -0.61
-0.61 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 44%. For areas with high cigarette tax, the probability of brown eyes is 61%. For areas with low cigarette tax, the probability of smoking mother is 76%. For areas with high cigarette tax, the probability of smoking mother is 49%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.44
P(Y=1 | V2=1) = 0.61
P(X=1 | V2=0) = 0.76
P(X=1 | V2=1) = 0.49
(0.61 - 0.44) / (0.49 - 0.76) = -0.61
-0.61 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 49%. For areas with high cigarette tax, the probability of brown eyes is 67%. For areas with low cigarette tax, the probability of smoking mother is 68%. For areas with high cigarette tax, the probability of smoking mother is 34%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.67
P(X=1 | V2=0) = 0.68
P(X=1 | V2=1) = 0.34
(0.67 - 0.49) / (0.34 - 0.68) = -0.51
-0.51 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 35%. The probability of nonsmoking mother and brown eyes is 54%. The probability of smoking mother and brown eyes is 11%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.11
0.11/0.35 - 0.54/0.65 = -0.51
-0.51 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 38%. For infants with nonsmoking mothers, the probability of brown eyes is 59%. For infants with smoking mothers, the probability of brown eyes is 25%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.38
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.25
0.38*0.25 - 0.62*0.59 = 0.47
0.47 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 38%. The probability of nonsmoking mother and brown eyes is 37%. The probability of smoking mother and brown eyes is 9%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.09
0.09/0.38 - 0.37/0.62 = -0.34
-0.34 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 25%. For areas with high cigarette tax, the probability of brown eyes is 41%. For areas with low cigarette tax, the probability of smoking mother is 52%. For areas with high cigarette tax, the probability of smoking mother is 12%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.25
P(Y=1 | V2=1) = 0.41
P(X=1 | V2=0) = 0.52
P(X=1 | V2=1) = 0.12
(0.41 - 0.25) / (0.12 - 0.52) = -0.38
-0.38 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 59%. For areas with high cigarette tax, the probability of brown eyes is 69%. For areas with low cigarette tax, the probability of smoking mother is 70%. For areas with high cigarette tax, the probability of smoking mother is 41%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.69
P(X=1 | V2=0) = 0.70
P(X=1 | V2=1) = 0.41
(0.69 - 0.59) / (0.41 - 0.70) = -0.32
-0.32 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 59%. For areas with high cigarette tax, the probability of brown eyes is 69%. For areas with low cigarette tax, the probability of smoking mother is 70%. For areas with high cigarette tax, the probability of smoking mother is 41%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.69
P(X=1 | V2=0) = 0.70
P(X=1 | V2=1) = 0.41
(0.69 - 0.59) / (0.41 - 0.70) = -0.32
-0.32 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 44%. The probability of nonsmoking mother and brown eyes is 46%. The probability of smoking mother and brown eyes is 22%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.22
0.22/0.44 - 0.46/0.56 = -0.32
-0.32 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12315,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 32%. The probability of nonsmoking mother and brown eyes is 43%. The probability of smoking mother and brown eyes is 9%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.32
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.09
0.09/0.32 - 0.43/0.68 = -0.35
-0.35 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12323,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 48%. For areas with high cigarette tax, the probability of brown eyes is 57%. For areas with low cigarette tax, the probability of smoking mother is 74%. For areas with high cigarette tax, the probability of smoking mother is 41%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.48
P(Y=1 | V2=1) = 0.57
P(X=1 | V2=0) = 0.74
P(X=1 | V2=1) = 0.41
(0.57 - 0.48) / (0.41 - 0.74) = -0.26
-0.26 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 46%. For areas with high cigarette tax, the probability of brown eyes is 55%. For areas with low cigarette tax, the probability of smoking mother is 63%. For areas with high cigarette tax, the probability of smoking mother is 35%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.46
P(Y=1 | V2=1) = 0.55
P(X=1 | V2=0) = 0.63
P(X=1 | V2=1) = 0.35
(0.55 - 0.46) / (0.35 - 0.63) = -0.33
-0.33 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 35%. For infants with nonsmoking mothers, the probability of brown eyes is 67%. For infants with smoking mothers, the probability of brown eyes is 34%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.34
0.35*0.34 - 0.65*0.67 = 0.55
0.55 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 35%. The probability of nonsmoking mother and brown eyes is 43%. The probability of smoking mother and brown eyes is 12%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.12
0.12/0.35 - 0.43/0.65 = -0.33
-0.33 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12348,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 49%. For areas with high cigarette tax, the probability of brown eyes is 68%. For areas with low cigarette tax, the probability of smoking mother is 94%. For areas with high cigarette tax, the probability of smoking mother is 42%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.68
P(X=1 | V2=0) = 0.94
P(X=1 | V2=1) = 0.42
(0.68 - 0.49) / (0.42 - 0.94) = -0.35
-0.35 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12349,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 49%. For areas with high cigarette tax, the probability of brown eyes is 68%. For areas with low cigarette tax, the probability of smoking mother is 94%. For areas with high cigarette tax, the probability of smoking mother is 42%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.68
P(X=1 | V2=0) = 0.94
P(X=1 | V2=1) = 0.42
(0.68 - 0.49) / (0.42 - 0.94) = -0.35
-0.35 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12350,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 48%. For infants with nonsmoking mothers, the probability of brown eyes is 83%. For infants with smoking mothers, the probability of brown eyes is 47%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.47
0.48*0.47 - 0.52*0.83 = 0.65
0.65 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 48%. For infants with nonsmoking mothers, the probability of brown eyes is 83%. For infants with smoking mothers, the probability of brown eyes is 47%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.47
0.48*0.47 - 0.52*0.83 = 0.65
0.65 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 49%. For infants with nonsmoking mothers, the probability of brown eyes is 58%. For infants with smoking mothers, the probability of brown eyes is 26%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.26
0.49*0.26 - 0.51*0.58 = 0.42
0.42 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 49%. For infants with nonsmoking mothers, the probability of brown eyes is 77%. For infants with smoking mothers, the probability of brown eyes is 50%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.50
0.49*0.50 - 0.51*0.77 = 0.64
0.64 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 49%. The probability of nonsmoking mother and brown eyes is 40%. The probability of smoking mother and brown eyes is 24%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.24
0.24/0.49 - 0.40/0.51 = -0.27
-0.27 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12369,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 49%. The probability of nonsmoking mother and brown eyes is 40%. The probability of smoking mother and brown eyes is 24%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.24
0.24/0.49 - 0.40/0.51 = -0.27
-0.27 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 45%. For areas with high cigarette tax, the probability of brown eyes is 58%. For areas with low cigarette tax, the probability of smoking mother is 63%. For areas with high cigarette tax, the probability of smoking mother is 27%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.45
P(Y=1 | V2=1) = 0.58
P(X=1 | V2=0) = 0.63
P(X=1 | V2=1) = 0.27
(0.58 - 0.45) / (0.27 - 0.63) = -0.38
-0.38 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 32%. For infants with nonsmoking mothers, the probability of brown eyes is 69%. For infants with smoking mothers, the probability of brown eyes is 31%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.31
0.32*0.31 - 0.68*0.69 = 0.57
0.57 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12378,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 21%. The probability of nonsmoking mother and brown eyes is 61%. The probability of smoking mother and brown eyes is 7%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.21
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.07
0.07/0.21 - 0.61/0.79 = -0.44
-0.44 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look directly at how maternal smoking status correlates with brown eyes in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 63%. For infants with nonsmoking mothers, the probability of brown eyes is 88%. For infants with smoking mothers, the probability of brown eyes is 31%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.31
0.63*0.31 - 0.37*0.88 = 0.53
0.53 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 63%. The probability of nonsmoking mother and brown eyes is 32%. The probability of smoking mother and brown eyes is 19%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.19
0.19/0.63 - 0.32/0.37 = -0.57
-0.57 < 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
12404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 47%. For areas with high cigarette tax, the probability of brown eyes is 57%. For areas with low cigarette tax, the probability of smoking mother is 42%. For areas with high cigarette tax, the probability of smoking mother is 11%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.47
P(Y=1 | V2=1) = 0.57
P(X=1 | V2=0) = 0.42
P(X=1 | V2=1) = 0.11
(0.57 - 0.47) / (0.11 - 0.42) = -0.30
-0.30 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 17%. For infants with nonsmoking mothers, the probability of brown eyes is 60%. For infants with smoking mothers, the probability of brown eyes is 30%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.30
0.17*0.30 - 0.83*0.60 = 0.55
0.55 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 17%. For infants with nonsmoking mothers, the probability of brown eyes is 60%. For infants with smoking mothers, the probability of brown eyes is 30%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.30
0.17*0.30 - 0.83*0.60 = 0.55
0.55 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12411,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. Method 1: We look at how maternal smoking status correlates with brown eyes case by case according to unobserved confounders. Method 2: We look directly at how maternal smoking status correlates with brown eyes in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
12413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of brown eyes is 34%. For areas with high cigarette tax, the probability of brown eyes is 51%. For areas with low cigarette tax, the probability of smoking mother is 57%. For areas with high cigarette tax, the probability of smoking mother is 22%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.34
P(Y=1 | V2=1) = 0.51
P(X=1 | V2=0) = 0.57
P(X=1 | V2=1) = 0.22
(0.51 - 0.34) / (0.22 - 0.57) = -0.48
-0.48 < 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. The overall probability of smoking mother is 23%. For infants with nonsmoking mothers, the probability of brown eyes is 61%. For infants with smoking mothers, the probability of brown eyes is 12%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.12
0.23*0.12 - 0.77*0.61 = 0.50
0.50 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
12420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 73%. For people served by a global water company, the probability of cholera contraction is 65%. For people served by a local water company, the probability of liking spicy food is 28%. For people served by a global water company, the probability of liking spicy food is 61%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.73
P(Y=1 | V2=1) = 0.65
P(X=1 | V2=0) = 0.28
P(X=1 | V2=1) = 0.61
(0.65 - 0.73) / (0.61 - 0.28) = -0.26
-0.26 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 42%. For people who do not like spicy food, the probability of cholera contraction is 74%. For people who like spicy food, the probability of cholera contraction is 36%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.36
0.42*0.36 - 0.58*0.74 = 0.58
0.58 > 0",IV,water_cholera,1,marginal,P(Y)
12431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 42%. For people who do not like spicy food, the probability of cholera contraction is 74%. For people who like spicy food, the probability of cholera contraction is 36%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.36
0.42*0.36 - 0.58*0.74 = 0.58
0.58 > 0",IV,water_cholera,1,marginal,P(Y)
12433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 42%. The probability of not liking spicy food and cholera contraction is 43%. The probability of liking spicy food and cholera contraction is 15%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.15
0.15/0.42 - 0.43/0.58 = -0.37
-0.37 < 0",IV,water_cholera,1,correlation,P(Y | X)
12437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 74%. For people served by a global water company, the probability of cholera contraction is 60%. For people served by a local water company, the probability of liking spicy food is 9%. For people served by a global water company, the probability of liking spicy food is 52%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.74
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.09
P(X=1 | V2=1) = 0.52
(0.60 - 0.74) / (0.52 - 0.09) = -0.32
-0.32 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 29%. For people who do not like spicy food, the probability of cholera contraction is 78%. For people who like spicy food, the probability of cholera contraction is 44%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.44
0.29*0.44 - 0.71*0.78 = 0.68
0.68 > 0",IV,water_cholera,1,marginal,P(Y)
12446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 59%. For people who do not like spicy food, the probability of cholera contraction is 77%. For people who like spicy food, the probability of cholera contraction is 40%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.40
0.59*0.40 - 0.41*0.77 = 0.55
0.55 > 0",IV,water_cholera,1,marginal,P(Y)
12451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look at how liking spicy food correlates with cholera case by case according to poverty. Method 2: We look directly at how liking spicy food correlates with cholera in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 72%. For people served by a global water company, the probability of cholera contraction is 64%. For people served by a local water company, the probability of liking spicy food is 20%. For people served by a global water company, the probability of liking spicy food is 53%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.72
P(Y=1 | V2=1) = 0.64
P(X=1 | V2=0) = 0.20
P(X=1 | V2=1) = 0.53
(0.64 - 0.72) / (0.53 - 0.20) = -0.26
-0.26 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 36%. For people who do not like spicy food, the probability of cholera contraction is 77%. For people who like spicy food, the probability of cholera contraction is 51%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.51
0.36*0.51 - 0.64*0.77 = 0.68
0.68 > 0",IV,water_cholera,1,marginal,P(Y)
12456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 36%. The probability of not liking spicy food and cholera contraction is 50%. The probability of liking spicy food and cholera contraction is 18%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.36
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.18
0.18/0.36 - 0.50/0.64 = -0.26
-0.26 < 0",IV,water_cholera,1,correlation,P(Y | X)
12461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 58%. For people served by a global water company, the probability of cholera contraction is 60%. For people served by a local water company, the probability of liking spicy food is 56%. For people served by a global water company, the probability of liking spicy food is 45%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.58
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.56
P(X=1 | V2=1) = 0.45
(0.60 - 0.58) / (0.45 - 0.56) = -0.28
-0.28 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 55%. For people who do not like spicy food, the probability of cholera contraction is 80%. For people who like spicy food, the probability of cholera contraction is 40%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.40
0.55*0.40 - 0.45*0.80 = 0.58
0.58 > 0",IV,water_cholera,1,marginal,P(Y)
12463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 55%. For people who do not like spicy food, the probability of cholera contraction is 80%. For people who like spicy food, the probability of cholera contraction is 40%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.40
0.55*0.40 - 0.45*0.80 = 0.58
0.58 > 0",IV,water_cholera,1,marginal,P(Y)
12464,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 55%. The probability of not liking spicy food and cholera contraction is 36%. The probability of liking spicy food and cholera contraction is 22%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.22
0.22/0.55 - 0.36/0.45 = -0.40
-0.40 < 0",IV,water_cholera,1,correlation,P(Y | X)
12467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look at how liking spicy food correlates with cholera case by case according to poverty. Method 2: We look directly at how liking spicy food correlates with cholera in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 61%. For people served by a global water company, the probability of cholera contraction is 50%. For people served by a local water company, the probability of liking spicy food is 14%. For people served by a global water company, the probability of liking spicy food is 45%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.14
P(X=1 | V2=1) = 0.45
(0.50 - 0.61) / (0.45 - 0.14) = -0.34
-0.34 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 32%. For people who do not like spicy food, the probability of cholera contraction is 67%. For people who like spicy food, the probability of cholera contraction is 29%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.29
0.32*0.29 - 0.68*0.67 = 0.55
0.55 > 0",IV,water_cholera,1,marginal,P(Y)
12471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 32%. For people who do not like spicy food, the probability of cholera contraction is 67%. For people who like spicy food, the probability of cholera contraction is 29%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.29
0.32*0.29 - 0.68*0.67 = 0.55
0.55 > 0",IV,water_cholera,1,marginal,P(Y)
12477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 29%. For people served by a global water company, the probability of cholera contraction is 33%. For people served by a local water company, the probability of liking spicy food is 83%. For people served by a global water company, the probability of liking spicy food is 68%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.29
P(Y=1 | V2=1) = 0.33
P(X=1 | V2=0) = 0.83
P(X=1 | V2=1) = 0.68
(0.33 - 0.29) / (0.68 - 0.83) = -0.32
-0.32 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 81%. For people who do not like spicy food, the probability of cholera contraction is 65%. For people who like spicy food, the probability of cholera contraction is 21%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.21
0.81*0.21 - 0.19*0.65 = 0.30
0.30 > 0",IV,water_cholera,1,marginal,P(Y)
12480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 81%. The probability of not liking spicy food and cholera contraction is 13%. The probability of liking spicy food and cholera contraction is 17%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.17
0.17/0.81 - 0.13/0.19 = -0.44
-0.44 < 0",IV,water_cholera,1,correlation,P(Y | X)
12481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 81%. The probability of not liking spicy food and cholera contraction is 13%. The probability of liking spicy food and cholera contraction is 17%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.17
0.17/0.81 - 0.13/0.19 = -0.44
-0.44 < 0",IV,water_cholera,1,correlation,P(Y | X)
12483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look at how liking spicy food correlates with cholera case by case according to poverty. Method 2: We look directly at how liking spicy food correlates with cholera in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 72%. For people served by a global water company, the probability of cholera contraction is 61%. For people served by a local water company, the probability of liking spicy food is 6%. For people served by a global water company, the probability of liking spicy food is 42%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.72
P(Y=1 | V2=1) = 0.61
P(X=1 | V2=0) = 0.06
P(X=1 | V2=1) = 0.42
(0.61 - 0.72) / (0.42 - 0.06) = -0.29
-0.29 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12492,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 49%. For people served by a global water company, the probability of cholera contraction is 49%. For people served by a local water company, the probability of liking spicy food is 52%. For people served by a global water company, the probability of liking spicy food is 53%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.52
P(X=1 | V2=1) = 0.53
(0.49 - 0.49) / (0.53 - 0.52) = -0.25
-0.25 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 52%. For people who do not like spicy food, the probability of cholera contraction is 68%. For people who like spicy food, the probability of cholera contraction is 33%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.33
0.52*0.33 - 0.48*0.68 = 0.49
0.49 > 0",IV,water_cholera,1,marginal,P(Y)
12501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 72%. For people served by a global water company, the probability of cholera contraction is 66%. For people served by a local water company, the probability of liking spicy food is 12%. For people served by a global water company, the probability of liking spicy food is 36%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.72
P(Y=1 | V2=1) = 0.66
P(X=1 | V2=0) = 0.12
P(X=1 | V2=1) = 0.36
(0.66 - 0.72) / (0.36 - 0.12) = -0.22
-0.22 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 26%. For people who do not like spicy food, the probability of cholera contraction is 75%. For people who like spicy food, the probability of cholera contraction is 52%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.52
0.26*0.52 - 0.74*0.75 = 0.69
0.69 > 0",IV,water_cholera,1,marginal,P(Y)
12503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 26%. For people who do not like spicy food, the probability of cholera contraction is 75%. For people who like spicy food, the probability of cholera contraction is 52%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.52
0.26*0.52 - 0.74*0.75 = 0.69
0.69 > 0",IV,water_cholera,1,marginal,P(Y)
12505,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 26%. The probability of not liking spicy food and cholera contraction is 56%. The probability of liking spicy food and cholera contraction is 13%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.56
P(Y=1, X=1=1) = 0.13
0.13/0.26 - 0.56/0.74 = -0.23
-0.23 < 0",IV,water_cholera,1,correlation,P(Y | X)
12506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 49%. For people who do not like spicy food, the probability of cholera contraction is 90%. For people who like spicy food, the probability of cholera contraction is 38%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.38
0.49*0.38 - 0.51*0.90 = 0.65
0.65 > 0",IV,water_cholera,1,marginal,P(Y)
12513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 49%. The probability of not liking spicy food and cholera contraction is 45%. The probability of liking spicy food and cholera contraction is 19%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.19
0.19/0.49 - 0.45/0.51 = -0.52
-0.52 < 0",IV,water_cholera,1,correlation,P(Y | X)
12515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look at how liking spicy food correlates with cholera case by case according to poverty. Method 2: We look directly at how liking spicy food correlates with cholera in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 80%. For people served by a global water company, the probability of cholera contraction is 69%. For people served by a local water company, the probability of liking spicy food is 26%. For people served by a global water company, the probability of liking spicy food is 62%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.80
P(Y=1 | V2=1) = 0.69
P(X=1 | V2=0) = 0.26
P(X=1 | V2=1) = 0.62
(0.69 - 0.80) / (0.62 - 0.26) = -0.30
-0.30 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 46%. For people who do not like spicy food, the probability of cholera contraction is 88%. For people who like spicy food, the probability of cholera contraction is 57%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.57
0.46*0.57 - 0.54*0.88 = 0.74
0.74 > 0",IV,water_cholera,1,marginal,P(Y)
12520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 46%. The probability of not liking spicy food and cholera contraction is 48%. The probability of liking spicy food and cholera contraction is 26%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.26
0.26/0.46 - 0.48/0.54 = -0.32
-0.32 < 0",IV,water_cholera,1,correlation,P(Y | X)
12524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 54%. For people served by a global water company, the probability of cholera contraction is 53%. For people served by a local water company, the probability of liking spicy food is 54%. For people served by a global water company, the probability of liking spicy food is 57%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.53
P(X=1 | V2=0) = 0.54
P(X=1 | V2=1) = 0.57
(0.53 - 0.54) / (0.57 - 0.54) = -0.36
-0.36 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 54%. For people who do not like spicy food, the probability of cholera contraction is 79%. For people who like spicy food, the probability of cholera contraction is 32%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.54
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.32
0.54*0.32 - 0.46*0.79 = 0.54
0.54 > 0",IV,water_cholera,1,marginal,P(Y)
12534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 33%. For people who do not like spicy food, the probability of cholera contraction is 79%. For people who like spicy food, the probability of cholera contraction is 43%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.33
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.43
0.33*0.43 - 0.67*0.79 = 0.67
0.67 > 0",IV,water_cholera,1,marginal,P(Y)
12536,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 33%. The probability of not liking spicy food and cholera contraction is 53%. The probability of liking spicy food and cholera contraction is 14%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.33
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.14
0.14/0.33 - 0.53/0.67 = -0.36
-0.36 < 0",IV,water_cholera,1,correlation,P(Y | X)
12539,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look at how liking spicy food correlates with cholera case by case according to poverty. Method 2: We look directly at how liking spicy food correlates with cholera in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 64%. For people served by a global water company, the probability of cholera contraction is 66%. For people served by a local water company, the probability of liking spicy food is 50%. For people served by a global water company, the probability of liking spicy food is 45%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.64
P(Y=1 | V2=1) = 0.66
P(X=1 | V2=0) = 0.50
P(X=1 | V2=1) = 0.45
(0.66 - 0.64) / (0.45 - 0.50) = -0.39
-0.39 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 50%. The probability of not liking spicy food and cholera contraction is 44%. The probability of liking spicy food and cholera contraction is 20%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.20
0.20/0.50 - 0.44/0.50 = -0.46
-0.46 < 0",IV,water_cholera,1,correlation,P(Y | X)
12550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 28%. For people who do not like spicy food, the probability of cholera contraction is 84%. For people who like spicy food, the probability of cholera contraction is 46%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.28
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.46
0.28*0.46 - 0.72*0.84 = 0.73
0.73 > 0",IV,water_cholera,1,marginal,P(Y)
12552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 28%. The probability of not liking spicy food and cholera contraction is 60%. The probability of liking spicy food and cholera contraction is 13%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.28
P(Y=1, X=0=1) = 0.60
P(Y=1, X=1=1) = 0.13
0.13/0.28 - 0.60/0.72 = -0.38
-0.38 < 0",IV,water_cholera,1,correlation,P(Y | X)
12555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look at how liking spicy food correlates with cholera case by case according to poverty. Method 2: We look directly at how liking spicy food correlates with cholera in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 59%. For people served by a global water company, the probability of cholera contraction is 60%. For people served by a local water company, the probability of liking spicy food is 33%. For people served by a global water company, the probability of liking spicy food is 30%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.33
P(X=1 | V2=1) = 0.30
(0.60 - 0.59) / (0.30 - 0.33) = -0.29
-0.29 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 33%. The probability of not liking spicy food and cholera contraction is 49%. The probability of liking spicy food and cholera contraction is 9%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.33
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.09
0.09/0.33 - 0.49/0.67 = -0.46
-0.46 < 0",IV,water_cholera,1,correlation,P(Y | X)
12562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 61%. For people served by a global water company, the probability of cholera contraction is 55%. For people served by a local water company, the probability of liking spicy food is 26%. For people served by a global water company, the probability of liking spicy food is 53%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.55
P(X=1 | V2=0) = 0.26
P(X=1 | V2=1) = 0.53
(0.55 - 0.61) / (0.53 - 0.26) = -0.23
-0.23 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 54%. For people served by a global water company, the probability of cholera contraction is 54%. For people served by a local water company, the probability of liking spicy food is 39%. For people served by a global water company, the probability of liking spicy food is 39%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.39
P(X=1 | V2=1) = 0.39
(0.54 - 0.54) / (0.39 - 0.39) = -0.25
-0.25 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 54%. For people served by a global water company, the probability of cholera contraction is 54%. For people served by a local water company, the probability of liking spicy food is 39%. For people served by a global water company, the probability of liking spicy food is 39%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.39
P(X=1 | V2=1) = 0.39
(0.54 - 0.54) / (0.39 - 0.39) = -0.25
-0.25 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 39%. For people who do not like spicy food, the probability of cholera contraction is 67%. For people who like spicy food, the probability of cholera contraction is 33%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.33
0.39*0.33 - 0.61*0.67 = 0.54
0.54 > 0",IV,water_cholera,1,marginal,P(Y)
12575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 39%. For people who do not like spicy food, the probability of cholera contraction is 67%. For people who like spicy food, the probability of cholera contraction is 33%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.33
0.39*0.33 - 0.61*0.67 = 0.54
0.54 > 0",IV,water_cholera,1,marginal,P(Y)
12578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 37%. For people who do not like spicy food, the probability of cholera contraction is 84%. For people who like spicy food, the probability of cholera contraction is 50%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.50
0.37*0.50 - 0.63*0.84 = 0.71
0.71 > 0",IV,water_cholera,1,marginal,P(Y)
12583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 37%. For people who do not like spicy food, the probability of cholera contraction is 84%. For people who like spicy food, the probability of cholera contraction is 50%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.50
0.37*0.50 - 0.63*0.84 = 0.71
0.71 > 0",IV,water_cholera,1,marginal,P(Y)
12586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 52%. For people who do not like spicy food, the probability of cholera contraction is 68%. For people who like spicy food, the probability of cholera contraction is 31%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.31
0.52*0.31 - 0.48*0.68 = 0.50
0.50 > 0",IV,water_cholera,1,marginal,P(Y)
12592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 52%. The probability of not liking spicy food and cholera contraction is 33%. The probability of liking spicy food and cholera contraction is 16%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.16
0.16/0.52 - 0.33/0.48 = -0.37
-0.37 < 0",IV,water_cholera,1,correlation,P(Y | X)
12595,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look at how liking spicy food correlates with cholera case by case according to poverty. Method 2: We look directly at how liking spicy food correlates with cholera in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 38%. For people who do not like spicy food, the probability of cholera contraction is 75%. For people who like spicy food, the probability of cholera contraction is 44%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.38
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.44
0.38*0.44 - 0.62*0.75 = 0.63
0.63 > 0",IV,water_cholera,1,marginal,P(Y)
12601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 38%. The probability of not liking spicy food and cholera contraction is 47%. The probability of liking spicy food and cholera contraction is 17%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.17
0.17/0.38 - 0.47/0.62 = -0.31
-0.31 < 0",IV,water_cholera,1,correlation,P(Y | X)
12608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 40%. The probability of not liking spicy food and cholera contraction is 56%. The probability of liking spicy food and cholera contraction is 11%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.56
P(Y=1, X=1=1) = 0.11
0.11/0.40 - 0.56/0.60 = -0.66
-0.66 < 0",IV,water_cholera,1,correlation,P(Y | X)
12610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 77%. For people served by a global water company, the probability of cholera contraction is 70%. For people served by a local water company, the probability of liking spicy food is 14%. For people served by a global water company, the probability of liking spicy food is 38%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.77
P(Y=1 | V2=1) = 0.70
P(X=1 | V2=0) = 0.14
P(X=1 | V2=1) = 0.38
(0.70 - 0.77) / (0.38 - 0.14) = -0.30
-0.30 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12620,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 46%. For people served by a global water company, the probability of cholera contraction is 47%. For people served by a local water company, the probability of liking spicy food is 66%. For people served by a global water company, the probability of liking spicy food is 60%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.46
P(Y=1 | V2=1) = 0.47
P(X=1 | V2=0) = 0.66
P(X=1 | V2=1) = 0.60
(0.47 - 0.46) / (0.60 - 0.66) = -0.23
-0.23 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12625,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 65%. The probability of not liking spicy food and cholera contraction is 24%. The probability of liking spicy food and cholera contraction is 23%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.23
0.23/0.65 - 0.24/0.35 = -0.33
-0.33 < 0",IV,water_cholera,1,correlation,P(Y | X)
12626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 55%. For people served by a global water company, the probability of cholera contraction is 43%. For people served by a local water company, the probability of liking spicy food is 12%. For people served by a global water company, the probability of liking spicy food is 65%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.55
P(Y=1 | V2=1) = 0.43
P(X=1 | V2=0) = 0.12
P(X=1 | V2=1) = 0.65
(0.43 - 0.55) / (0.65 - 0.12) = -0.21
-0.21 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 55%. For people served by a global water company, the probability of cholera contraction is 43%. For people served by a local water company, the probability of liking spicy food is 12%. For people served by a global water company, the probability of liking spicy food is 65%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.55
P(Y=1 | V2=1) = 0.43
P(X=1 | V2=0) = 0.12
P(X=1 | V2=1) = 0.65
(0.43 - 0.55) / (0.65 - 0.12) = -0.21
-0.21 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12630,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 41%. For people who do not like spicy food, the probability of cholera contraction is 59%. For people who like spicy food, the probability of cholera contraction is 33%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.33
0.41*0.33 - 0.59*0.59 = 0.48
0.48 > 0",IV,water_cholera,1,marginal,P(Y)
12633,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 41%. The probability of not liking spicy food and cholera contraction is 34%. The probability of liking spicy food and cholera contraction is 14%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.14
0.14/0.41 - 0.34/0.59 = -0.25
-0.25 < 0",IV,water_cholera,1,correlation,P(Y | X)
12636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 47%. For people served by a global water company, the probability of cholera contraction is 43%. For people served by a local water company, the probability of liking spicy food is 34%. For people served by a global water company, the probability of liking spicy food is 49%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.47
P(Y=1 | V2=1) = 0.43
P(X=1 | V2=0) = 0.34
P(X=1 | V2=1) = 0.49
(0.43 - 0.47) / (0.49 - 0.34) = -0.29
-0.29 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look at how liking spicy food correlates with cholera case by case according to poverty. Method 2: We look directly at how liking spicy food correlates with cholera in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 83%. For people served by a global water company, the probability of cholera contraction is 75%. For people served by a local water company, the probability of liking spicy food is 21%. For people served by a global water company, the probability of liking spicy food is 52%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.83
P(Y=1 | V2=1) = 0.75
P(X=1 | V2=0) = 0.21
P(X=1 | V2=1) = 0.52
(0.75 - 0.83) / (0.52 - 0.21) = -0.25
-0.25 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12646,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 34%. For people who do not like spicy food, the probability of cholera contraction is 89%. For people who like spicy food, the probability of cholera contraction is 61%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.34
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.61
0.34*0.61 - 0.66*0.89 = 0.80
0.80 > 0",IV,water_cholera,1,marginal,P(Y)
12650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. Method 1: We look directly at how liking spicy food correlates with cholera in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
12652,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 43%. For people served by a global water company, the probability of cholera contraction is 40%. For people served by a local water company, the probability of liking spicy food is 62%. For people served by a global water company, the probability of liking spicy food is 76%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.43
P(Y=1 | V2=1) = 0.40
P(X=1 | V2=0) = 0.62
P(X=1 | V2=1) = 0.76
(0.40 - 0.43) / (0.76 - 0.62) = -0.23
-0.23 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. For people served by a local water company, the probability of cholera contraction is 43%. For people served by a global water company, the probability of cholera contraction is 40%. For people served by a local water company, the probability of liking spicy food is 62%. For people served by a global water company, the probability of liking spicy food is 76%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.43
P(Y=1 | V2=1) = 0.40
P(X=1 | V2=0) = 0.62
P(X=1 | V2=1) = 0.76
(0.40 - 0.43) / (0.76 - 0.62) = -0.23
-0.23 < 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 63%. For people who do not like spicy food, the probability of cholera contraction is 65%. For people who like spicy food, the probability of cholera contraction is 30%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.30
0.63*0.30 - 0.37*0.65 = 0.43
0.43 > 0",IV,water_cholera,1,marginal,P(Y)
12656,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 63%. The probability of not liking spicy food and cholera contraction is 24%. The probability of liking spicy food and cholera contraction is 19%.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.19
0.19/0.63 - 0.24/0.37 = -0.35
-0.35 < 0",IV,water_cholera,1,correlation,P(Y | X)
12657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. The overall probability of liking spicy food is 63%. The probability of not liking spicy food and cholera contraction is 24%. The probability of liking spicy food and cholera contraction is 19%.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.19
0.19/0.63 - 0.24/0.37 = -0.35
-0.35 < 0",IV,water_cholera,1,correlation,P(Y | X)
12662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 74%. For people who have a brother, the probability of ringing alarm is 22%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.22
0.22 - 0.74 = -0.52
-0.52 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 6%. The probability of not having a brother and ringing alarm is 70%. The probability of having a brother and ringing alarm is 1%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.70
P(Y=1, X=1=1) = 0.01
0.01/0.06 - 0.70/0.94 = -0.52
-0.52 < 0",mediation,alarm,1,correlation,P(Y | X)
12673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 78%. For people who have a brother, the probability of ringing alarm is 32%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.32
0.32 - 0.78 = -0.46
-0.46 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 98%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 49%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 67%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 14%. For people who do not have a brother, the probability of alarm set by wife is 41%. For people who have a brother, the probability of alarm set by wife is 67%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.67
P(Y=1 | X=1, V2=1) = 0.14
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.67
0.41 * (0.14 - 0.67) + 0.67 * (0.49 - 0.98) = -0.32
-0.32 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 4%. The probability of not having a brother and ringing alarm is 74%. The probability of having a brother and ringing alarm is 1%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.74
P(Y=1, X=1=1) = 0.01
0.01/0.04 - 0.74/0.96 = -0.46
-0.46 < 0",mediation,alarm,1,correlation,P(Y | X)
12688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 90%. For people who have a brother, the probability of ringing alarm is 31%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.31
0.31 - 0.90 = -0.58
-0.58 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 90%. For people who have a brother, the probability of ringing alarm is 31%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.31
0.31 - 0.90 = -0.58
-0.58 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12692,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 90%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 58%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 1%. For people who have a brother, the probability of alarm set by wife is 57%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.01
P(V2=1 | X=1) = 0.57
0.57 * (0.45 - 0.90)+ 0.01 * (0.11 - 0.58)= -0.25
-0.25 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 90%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 58%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 1%. For people who have a brother, the probability of alarm set by wife is 57%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.01
P(V2=1 | X=1) = 0.57
0.01 * (0.11 - 0.58) + 0.57 * (0.45 - 0.90) = -0.32
-0.32 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 90%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 58%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 1%. For people who have a brother, the probability of alarm set by wife is 57%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.01
P(V2=1 | X=1) = 0.57
0.01 * (0.11 - 0.58) + 0.57 * (0.45 - 0.90) = -0.32
-0.32 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 4%. For people who do not have a brother, the probability of ringing alarm is 90%. For people who have a brother, the probability of ringing alarm is 31%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.31
0.04*0.31 - 0.96*0.90 = 0.88
0.88 > 0",mediation,alarm,1,marginal,P(Y)
12698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 4%. The probability of not having a brother and ringing alarm is 86%. The probability of having a brother and ringing alarm is 1%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.86
P(Y=1, X=1=1) = 0.01
0.01/0.04 - 0.86/0.96 = -0.58
-0.58 < 0",mediation,alarm,1,correlation,P(Y | X)
12701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 17%. For people who do not have a brother, the probability of ringing alarm is 84%. For people who have a brother, the probability of ringing alarm is 20%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.20
0.17*0.20 - 0.83*0.84 = 0.73
0.73 > 0",mediation,alarm,1,marginal,P(Y)
12713,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 17%. The probability of not having a brother and ringing alarm is 69%. The probability of having a brother and ringing alarm is 3%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.69
P(Y=1, X=1=1) = 0.03
0.03/0.17 - 0.69/0.83 = -0.64
-0.64 < 0",mediation,alarm,1,correlation,P(Y | X)
12715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 71%. For people who have a brother, the probability of ringing alarm is 10%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.10
0.10 - 0.71 = -0.61
-0.61 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 71%. For people who have a brother, the probability of ringing alarm is 10%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.10
0.10 - 0.71 = -0.61
-0.61 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 90%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 42%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 9%. For people who do not have a brother, the probability of alarm set by wife is 39%. For people who have a brother, the probability of alarm set by wife is 98%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.09
P(V2=1 | X=0) = 0.39
P(V2=1 | X=1) = 0.98
0.39 * (0.09 - 0.55) + 0.98 * (0.42 - 0.90) = -0.34
-0.34 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 17%. For people who do not have a brother, the probability of ringing alarm is 71%. For people who have a brother, the probability of ringing alarm is 10%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.10
0.17*0.10 - 0.83*0.71 = 0.60
0.60 > 0",mediation,alarm,1,marginal,P(Y)
12729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 83%. For people who have a brother, the probability of ringing alarm is 27%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.27
0.27 - 0.83 = -0.56
-0.56 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12733,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 83%. For people who have a brother, the probability of ringing alarm is 27%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.27
0.27 - 0.83 = -0.56
-0.56 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 95%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 42%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 62%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 3%. For people who do not have a brother, the probability of alarm set by wife is 22%. For people who have a brother, the probability of alarm set by wife is 58%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.62
P(Y=1 | X=1, V2=1) = 0.03
P(V2=1 | X=0) = 0.22
P(V2=1 | X=1) = 0.58
0.22 * (0.03 - 0.62) + 0.58 * (0.42 - 0.95) = -0.34
-0.34 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 2%. For people who do not have a brother, the probability of ringing alarm is 83%. For people who have a brother, the probability of ringing alarm is 27%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.27
0.02*0.27 - 0.98*0.83 = 0.82
0.82 > 0",mediation,alarm,1,marginal,P(Y)
12741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 2%. The probability of not having a brother and ringing alarm is 81%. The probability of having a brother and ringing alarm is 1%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.81
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.81/0.98 = -0.56
-0.56 < 0",mediation,alarm,1,correlation,P(Y | X)
12745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 86%. For people who have a brother, the probability of ringing alarm is 34%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.34
0.34 - 0.86 = -0.52
-0.52 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 86%. For people who have a brother, the probability of ringing alarm is 34%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.34
0.34 - 0.86 = -0.52
-0.52 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 86%. For people who have a brother, the probability of ringing alarm is 34%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.34
0.34 - 0.86 = -0.52
-0.52 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 95%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 52%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 63%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 13%. For people who do not have a brother, the probability of alarm set by wife is 23%. For people who have a brother, the probability of alarm set by wife is 59%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.13
P(V2=1 | X=0) = 0.23
P(V2=1 | X=1) = 0.59
0.59 * (0.52 - 0.95)+ 0.23 * (0.13 - 0.63)= -0.16
-0.16 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 95%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 52%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 63%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 13%. For people who do not have a brother, the probability of alarm set by wife is 23%. For people who have a brother, the probability of alarm set by wife is 59%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.13
P(V2=1 | X=0) = 0.23
P(V2=1 | X=1) = 0.59
0.23 * (0.13 - 0.63) + 0.59 * (0.52 - 0.95) = -0.34
-0.34 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 95%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 52%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 63%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 13%. For people who do not have a brother, the probability of alarm set by wife is 23%. For people who have a brother, the probability of alarm set by wife is 59%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.13
P(V2=1 | X=0) = 0.23
P(V2=1 | X=1) = 0.59
0.23 * (0.13 - 0.63) + 0.59 * (0.52 - 0.95) = -0.34
-0.34 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12753,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 6%. For people who do not have a brother, the probability of ringing alarm is 86%. For people who have a brother, the probability of ringing alarm is 34%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.34
0.06*0.34 - 0.94*0.86 = 0.83
0.83 > 0",mediation,alarm,1,marginal,P(Y)
12754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 6%. The probability of not having a brother and ringing alarm is 81%. The probability of having a brother and ringing alarm is 2%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.81
P(Y=1, X=1=1) = 0.02
0.02/0.06 - 0.81/0.94 = -0.52
-0.52 < 0",mediation,alarm,1,correlation,P(Y | X)
12756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 24%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.24
0.24 - 0.72 = -0.48
-0.48 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 24%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.24
0.24 - 0.72 = -0.48
-0.48 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 24%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.24
0.24 - 0.72 = -0.48
-0.48 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 94%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 43%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 43%. For people who have a brother, the probability of alarm set by wife is 69%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.43
P(V2=1 | X=1) = 0.69
0.69 * (0.43 - 0.94)+ 0.43 * (0.11 - 0.55)= -0.14
-0.14 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 94%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 43%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 43%. For people who have a brother, the probability of alarm set by wife is 69%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.43
P(V2=1 | X=1) = 0.69
0.69 * (0.43 - 0.94)+ 0.43 * (0.11 - 0.55)= -0.14
-0.14 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12764,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 94%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 43%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 43%. For people who have a brother, the probability of alarm set by wife is 69%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.43
P(V2=1 | X=1) = 0.69
0.43 * (0.11 - 0.55) + 0.69 * (0.43 - 0.94) = -0.36
-0.36 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 94%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 43%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 43%. For people who have a brother, the probability of alarm set by wife is 69%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.43
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.43
P(V2=1 | X=1) = 0.69
0.43 * (0.11 - 0.55) + 0.69 * (0.43 - 0.94) = -0.36
-0.36 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 13%. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 24%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.24
0.13*0.24 - 0.87*0.72 = 0.66
0.66 > 0",mediation,alarm,1,marginal,P(Y)
12768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 13%. The probability of not having a brother and ringing alarm is 63%. The probability of having a brother and ringing alarm is 3%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.03
0.03/0.13 - 0.63/0.87 = -0.48
-0.48 < 0",mediation,alarm,1,correlation,P(Y | X)
12771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 82%. For people who have a brother, the probability of ringing alarm is 28%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.28
0.28 - 0.82 = -0.54
-0.54 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12777,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 88%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 39%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 50%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 2%. For people who do not have a brother, the probability of alarm set by wife is 13%. For people who have a brother, the probability of alarm set by wife is 47%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.39
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.02
P(V2=1 | X=0) = 0.13
P(V2=1 | X=1) = 0.47
0.47 * (0.39 - 0.88)+ 0.13 * (0.02 - 0.50)= -0.17
-0.17 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 88%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 39%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 50%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 2%. For people who do not have a brother, the probability of alarm set by wife is 13%. For people who have a brother, the probability of alarm set by wife is 47%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.39
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.02
P(V2=1 | X=0) = 0.13
P(V2=1 | X=1) = 0.47
0.13 * (0.02 - 0.50) + 0.47 * (0.39 - 0.88) = -0.38
-0.38 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 14%. For people who do not have a brother, the probability of ringing alarm is 82%. For people who have a brother, the probability of ringing alarm is 28%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.28
0.14*0.28 - 0.86*0.82 = 0.74
0.74 > 0",mediation,alarm,1,marginal,P(Y)
12781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 14%. For people who do not have a brother, the probability of ringing alarm is 82%. For people who have a brother, the probability of ringing alarm is 28%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.28
0.14*0.28 - 0.86*0.82 = 0.74
0.74 > 0",mediation,alarm,1,marginal,P(Y)
12784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 17%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.17
0.17 - 0.72 = -0.54
-0.54 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 17%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.17
0.17 - 0.72 = -0.54
-0.54 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 17%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.17
0.17 - 0.72 = -0.54
-0.54 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12790,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 91%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 40%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 53%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 3%. For people who do not have a brother, the probability of alarm set by wife is 38%. For people who have a brother, the probability of alarm set by wife is 71%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.91
P(Y=1 | X=0, V2=1) = 0.40
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.03
P(V2=1 | X=0) = 0.38
P(V2=1 | X=1) = 0.71
0.71 * (0.40 - 0.91)+ 0.38 * (0.03 - 0.53)= -0.17
-0.17 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12794,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 9%. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 17%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.17
0.09*0.17 - 0.91*0.72 = 0.67
0.67 > 0",mediation,alarm,1,marginal,P(Y)
12797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 9%. The probability of not having a brother and ringing alarm is 65%. The probability of having a brother and ringing alarm is 2%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.02
0.02/0.09 - 0.65/0.91 = -0.54
-0.54 < 0",mediation,alarm,1,correlation,P(Y | X)
12798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 81%. For people who have a brother, the probability of ringing alarm is 20%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.20
0.20 - 0.81 = -0.61
-0.61 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 81%. For people who have a brother, the probability of ringing alarm is 20%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.20
0.20 - 0.81 = -0.61
-0.61 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 98%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 51%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 63%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 17%. For people who do not have a brother, the probability of alarm set by wife is 36%. For people who have a brother, the probability of alarm set by wife is 93%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.36
P(V2=1 | X=1) = 0.93
0.93 * (0.51 - 0.98)+ 0.36 * (0.17 - 0.63)= -0.26
-0.26 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 98%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 51%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 63%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 17%. For people who do not have a brother, the probability of alarm set by wife is 36%. For people who have a brother, the probability of alarm set by wife is 93%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.36
P(V2=1 | X=1) = 0.93
0.36 * (0.17 - 0.63) + 0.93 * (0.51 - 0.98) = -0.34
-0.34 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 98%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 51%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 63%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 17%. For people who do not have a brother, the probability of alarm set by wife is 36%. For people who have a brother, the probability of alarm set by wife is 93%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.36
P(V2=1 | X=1) = 0.93
0.36 * (0.17 - 0.63) + 0.93 * (0.51 - 0.98) = -0.34
-0.34 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 10%. The probability of not having a brother and ringing alarm is 73%. The probability of having a brother and ringing alarm is 2%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.73
P(Y=1, X=1=1) = 0.02
0.02/0.10 - 0.73/0.90 = -0.61
-0.61 < 0",mediation,alarm,1,correlation,P(Y | X)
12811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 10%. The probability of not having a brother and ringing alarm is 73%. The probability of having a brother and ringing alarm is 2%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.73
P(Y=1, X=1=1) = 0.02
0.02/0.10 - 0.73/0.90 = -0.61
-0.61 < 0",mediation,alarm,1,correlation,P(Y | X)
12812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12815,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 82%. For people who have a brother, the probability of ringing alarm is 24%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.24
0.24 - 0.82 = -0.58
-0.58 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 82%. For people who have a brother, the probability of ringing alarm is 24%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.24
0.24 - 0.82 = -0.58
-0.58 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 82%. For people who have a brother, the probability of ringing alarm is 24%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.24
0.24 - 0.82 = -0.58
-0.58 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 15%. For people who do not have a brother, the probability of ringing alarm is 82%. For people who have a brother, the probability of ringing alarm is 24%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.24
0.15*0.24 - 0.85*0.82 = 0.73
0.73 > 0",mediation,alarm,1,marginal,P(Y)
12826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12831,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 64%. For people who have a brother, the probability of ringing alarm is 24%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.24
0.24 - 0.64 = -0.40
-0.40 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 81%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 35%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 46%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 0%. For people who do not have a brother, the probability of alarm set by wife is 37%. For people who have a brother, the probability of alarm set by wife is 48%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.81
P(Y=1 | X=0, V2=1) = 0.35
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.00
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.48
0.48 * (0.35 - 0.81)+ 0.37 * (0.00 - 0.46)= -0.05
-0.05 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 9%. For people who do not have a brother, the probability of ringing alarm is 64%. For people who have a brother, the probability of ringing alarm is 24%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.24
0.09*0.24 - 0.91*0.64 = 0.60
0.60 > 0",mediation,alarm,1,marginal,P(Y)
12837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 9%. For people who do not have a brother, the probability of ringing alarm is 64%. For people who have a brother, the probability of ringing alarm is 24%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.24
0.09*0.24 - 0.91*0.64 = 0.60
0.60 > 0",mediation,alarm,1,marginal,P(Y)
12840,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 80%. For people who have a brother, the probability of ringing alarm is 26%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.26
0.26 - 0.80 = -0.54
-0.54 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 87%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 40%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 9%. For people who do not have a brother, the probability of alarm set by wife is 16%. For people who have a brother, the probability of alarm set by wife is 62%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.87
P(Y=1 | X=0, V2=1) = 0.40
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.09
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.62
0.62 * (0.40 - 0.87)+ 0.16 * (0.09 - 0.55)= -0.22
-0.22 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 72%. For people who have a brother, the probability of ringing alarm is 26%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.26
0.26 - 0.72 = -0.47
-0.47 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12871,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 80%. For people who have a brother, the probability of ringing alarm is 34%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.34
0.34 - 0.80 = -0.46
-0.46 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 93%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 48%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 63%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 15%. For people who do not have a brother, the probability of alarm set by wife is 30%. For people who have a brother, the probability of alarm set by wife is 61%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.93
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.15
P(V2=1 | X=0) = 0.30
P(V2=1 | X=1) = 0.61
0.61 * (0.48 - 0.93)+ 0.30 * (0.15 - 0.63)= -0.14
-0.14 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 2%. For people who do not have a brother, the probability of ringing alarm is 80%. For people who have a brother, the probability of ringing alarm is 34%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.34
0.02*0.34 - 0.98*0.80 = 0.79
0.79 > 0",mediation,alarm,1,marginal,P(Y)
12880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 2%. The probability of not having a brother and ringing alarm is 78%. The probability of having a brother and ringing alarm is 1%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.78
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.78/0.98 = -0.46
-0.46 < 0",mediation,alarm,1,correlation,P(Y | X)
12882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12883,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 69%. For people who have a brother, the probability of ringing alarm is 25%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.25
0.25 - 0.69 = -0.45
-0.45 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12900,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 74%. For people who have a brother, the probability of ringing alarm is 21%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.21
0.21 - 0.74 = -0.52
-0.52 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12901,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 74%. For people who have a brother, the probability of ringing alarm is 21%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.21
0.21 - 0.74 = -0.52
-0.52 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 86%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 42%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 54%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 7%. For people who do not have a brother, the probability of alarm set by wife is 27%. For people who have a brother, the probability of alarm set by wife is 69%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.86
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.07
P(V2=1 | X=0) = 0.27
P(V2=1 | X=1) = 0.69
0.69 * (0.42 - 0.86)+ 0.27 * (0.07 - 0.54)= -0.18
-0.18 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 86%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 42%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 54%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 7%. For people who do not have a brother, the probability of alarm set by wife is 27%. For people who have a brother, the probability of alarm set by wife is 69%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.86
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.07
P(V2=1 | X=0) = 0.27
P(V2=1 | X=1) = 0.69
0.27 * (0.07 - 0.54) + 0.69 * (0.42 - 0.86) = -0.33
-0.33 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12907,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 1%. For people who do not have a brother, the probability of ringing alarm is 74%. For people who have a brother, the probability of ringing alarm is 21%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.21
0.01*0.21 - 0.99*0.74 = 0.73
0.73 > 0",mediation,alarm,1,marginal,P(Y)
12909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 1%. The probability of not having a brother and ringing alarm is 73%. The probability of having a brother and ringing alarm is 0%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.73
P(Y=1, X=1=1) = 0.00
0.00/0.01 - 0.73/0.99 = -0.52
-0.52 < 0",mediation,alarm,1,correlation,P(Y | X)
12918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 89%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 44%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 59%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 45%. For people who have a brother, the probability of alarm set by wife is 94%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.89
P(Y=1 | X=0, V2=1) = 0.44
P(Y=1 | X=1, V2=0) = 0.59
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.45
P(V2=1 | X=1) = 0.94
0.45 * (0.11 - 0.59) + 0.94 * (0.44 - 0.89) = -0.32
-0.32 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12923,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 18%. The probability of not having a brother and ringing alarm is 56%. The probability of having a brother and ringing alarm is 3%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.56
P(Y=1, X=1=1) = 0.03
0.03/0.18 - 0.56/0.82 = -0.55
-0.55 < 0",mediation,alarm,1,correlation,P(Y | X)
12925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 91%. For people who have a brother, the probability of ringing alarm is 23%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.23
0.23 - 0.91 = -0.68
-0.68 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12933,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 99%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 52%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 66%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 17%. For people who do not have a brother, the probability of alarm set by wife is 16%. For people who have a brother, the probability of alarm set by wife is 88%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.99
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.88
0.16 * (0.17 - 0.66) + 0.88 * (0.52 - 0.99) = -0.33
-0.33 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12934,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 13%. For people who do not have a brother, the probability of ringing alarm is 91%. For people who have a brother, the probability of ringing alarm is 23%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.23
0.13*0.23 - 0.87*0.91 = 0.82
0.82 > 0",mediation,alarm,1,marginal,P(Y)
12935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 13%. For people who do not have a brother, the probability of ringing alarm is 91%. For people who have a brother, the probability of ringing alarm is 23%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.23
0.13*0.23 - 0.87*0.91 = 0.82
0.82 > 0",mediation,alarm,1,marginal,P(Y)
12938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 79%. For people who have a brother, the probability of ringing alarm is 31%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.31
0.31 - 0.79 = -0.48
-0.48 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 79%. For people who have a brother, the probability of ringing alarm is 31%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.31
0.31 - 0.79 = -0.48
-0.48 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 79%. For people who have a brother, the probability of ringing alarm is 31%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.31
0.31 - 0.79 = -0.48
-0.48 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 94%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 49%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 64%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 14%. For people who do not have a brother, the probability of alarm set by wife is 34%. For people who have a brother, the probability of alarm set by wife is 65%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.49
P(Y=1 | X=1, V2=0) = 0.64
P(Y=1 | X=1, V2=1) = 0.14
P(V2=1 | X=0) = 0.34
P(V2=1 | X=1) = 0.65
0.65 * (0.49 - 0.94)+ 0.34 * (0.14 - 0.64)= -0.14
-0.14 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 4%. For people who do not have a brother, the probability of ringing alarm is 79%. For people who have a brother, the probability of ringing alarm is 31%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.31
0.04*0.31 - 0.96*0.79 = 0.77
0.77 > 0",mediation,alarm,1,marginal,P(Y)
12951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 4%. The probability of not having a brother and ringing alarm is 76%. The probability of having a brother and ringing alarm is 1%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.01
0.01/0.04 - 0.76/0.96 = -0.48
-0.48 < 0",mediation,alarm,1,correlation,P(Y | X)
12953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 65%. For people who have a brother, the probability of ringing alarm is 17%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.17
0.17 - 0.65 = -0.48
-0.48 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 89%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 36%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 46%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 3%. For people who do not have a brother, the probability of alarm set by wife is 46%. For people who have a brother, the probability of alarm set by wife is 67%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.89
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.03
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.67
0.67 * (0.36 - 0.89)+ 0.46 * (0.03 - 0.46)= -0.11
-0.11 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 89%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 36%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 46%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 3%. For people who do not have a brother, the probability of alarm set by wife is 46%. For people who have a brother, the probability of alarm set by wife is 67%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.89
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.03
P(V2=1 | X=0) = 0.46
P(V2=1 | X=1) = 0.67
0.46 * (0.03 - 0.46) + 0.67 * (0.36 - 0.89) = -0.38
-0.38 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
12963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 1%. For people who do not have a brother, the probability of ringing alarm is 65%. For people who have a brother, the probability of ringing alarm is 17%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.17
0.01*0.17 - 0.99*0.65 = 0.64
0.64 > 0",mediation,alarm,1,marginal,P(Y)
12964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 1%. The probability of not having a brother and ringing alarm is 64%. The probability of having a brother and ringing alarm is 0%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.64
P(Y=1, X=1=1) = 0.00
0.00/0.01 - 0.64/0.99 = -0.48
-0.48 < 0",mediation,alarm,1,correlation,P(Y | X)
12965,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 1%. The probability of not having a brother and ringing alarm is 64%. The probability of having a brother and ringing alarm is 0%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.64
P(Y=1, X=1=1) = 0.00
0.00/0.01 - 0.64/0.99 = -0.48
-0.48 < 0",mediation,alarm,1,correlation,P(Y | X)
12967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 81%. For people who have a brother, the probability of ringing alarm is 18%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.18
0.18 - 0.81 = -0.64
-0.64 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 90%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 34%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 52%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 1%. For people who do not have a brother, the probability of alarm set by wife is 16%. For people who have a brother, the probability of alarm set by wife is 68%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.34
P(Y=1 | X=1, V2=0) = 0.52
P(Y=1 | X=1, V2=1) = 0.01
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.68
0.68 * (0.34 - 0.90)+ 0.16 * (0.01 - 0.52)= -0.30
-0.30 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12976,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 17%. For people who do not have a brother, the probability of ringing alarm is 81%. For people who have a brother, the probability of ringing alarm is 18%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.18
0.17*0.18 - 0.83*0.81 = 0.70
0.70 > 0",mediation,alarm,1,marginal,P(Y)
12978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 17%. The probability of not having a brother and ringing alarm is 67%. The probability of having a brother and ringing alarm is 3%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.67
P(Y=1, X=1=1) = 0.03
0.03/0.17 - 0.67/0.83 = -0.64
-0.64 < 0",mediation,alarm,1,correlation,P(Y | X)
12980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
12982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 77%. For people who have a brother, the probability of ringing alarm is 25%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.25
0.25 - 0.77 = -0.52
-0.52 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 77%. For people who have a brother, the probability of ringing alarm is 25%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.25
0.25 - 0.77 = -0.52
-0.52 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 77%. For people who have a brother, the probability of ringing alarm is 25%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.25
0.25 - 0.77 = -0.52
-0.52 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
12986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 95%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 50%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 62%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 14%. For people who do not have a brother, the probability of alarm set by wife is 40%. For people who have a brother, the probability of alarm set by wife is 77%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.62
P(Y=1 | X=1, V2=1) = 0.14
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.77
0.77 * (0.50 - 0.95)+ 0.40 * (0.14 - 0.62)= -0.17
-0.17 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12987,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 95%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 50%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 62%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 14%. For people who do not have a brother, the probability of alarm set by wife is 40%. For people who have a brother, the probability of alarm set by wife is 77%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.62
P(Y=1 | X=1, V2=1) = 0.14
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.77
0.77 * (0.50 - 0.95)+ 0.40 * (0.14 - 0.62)= -0.17
-0.17 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
12990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 7%. For people who do not have a brother, the probability of ringing alarm is 77%. For people who have a brother, the probability of ringing alarm is 25%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.25
0.07*0.25 - 0.93*0.77 = 0.73
0.73 > 0",mediation,alarm,1,marginal,P(Y)
12991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 7%. For people who do not have a brother, the probability of ringing alarm is 77%. For people who have a brother, the probability of ringing alarm is 25%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.25
0.07*0.25 - 0.93*0.77 = 0.73
0.73 > 0",mediation,alarm,1,marginal,P(Y)
12993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 7%. The probability of not having a brother and ringing alarm is 71%. The probability of having a brother and ringing alarm is 2%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.71
P(Y=1, X=1=1) = 0.02
0.02/0.07 - 0.71/0.93 = -0.52
-0.52 < 0",mediation,alarm,1,correlation,P(Y | X)
12996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 84%. For people who have a brother, the probability of ringing alarm is 29%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.29
0.29 - 0.84 = -0.55
-0.55 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
12997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 84%. For people who have a brother, the probability of ringing alarm is 29%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.29
0.29 - 0.84 = -0.55
-0.55 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 88%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 58%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 13%. For people who do not have a brother, the probability of alarm set by wife is 9%. For people who have a brother, the probability of alarm set by wife is 64%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.13
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.64
0.64 * (0.45 - 0.88)+ 0.09 * (0.13 - 0.58)= -0.24
-0.24 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
13001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 88%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 58%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 13%. For people who do not have a brother, the probability of alarm set by wife is 9%. For people who have a brother, the probability of alarm set by wife is 64%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.13
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.64
0.64 * (0.45 - 0.88)+ 0.09 * (0.13 - 0.58)= -0.24
-0.24 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
13002,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 88%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 58%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 13%. For people who do not have a brother, the probability of alarm set by wife is 9%. For people who have a brother, the probability of alarm set by wife is 64%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.13
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.64
0.09 * (0.13 - 0.58) + 0.64 * (0.45 - 0.88) = -0.31
-0.31 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
13003,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 88%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 58%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 13%. For people who do not have a brother, the probability of alarm set by wife is 9%. For people who have a brother, the probability of alarm set by wife is 64%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.13
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.64
0.09 * (0.13 - 0.58) + 0.64 * (0.45 - 0.88) = -0.31
-0.31 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
13010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 75%. For people who have a brother, the probability of ringing alarm is 16%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.16
0.16 - 0.75 = -0.59
-0.59 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 85%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 36%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 47%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 6%. For people who do not have a brother, the probability of alarm set by wife is 20%. For people who have a brother, the probability of alarm set by wife is 75%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.85
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.06
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.75
0.20 * (0.06 - 0.47) + 0.75 * (0.36 - 0.85) = -0.36
-0.36 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
13018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 8%. For people who do not have a brother, the probability of ringing alarm is 75%. For people who have a brother, the probability of ringing alarm is 16%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.16
0.08*0.16 - 0.92*0.75 = 0.70
0.70 > 0",mediation,alarm,1,marginal,P(Y)
13020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 8%. The probability of not having a brother and ringing alarm is 69%. The probability of having a brother and ringing alarm is 1%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.69
P(Y=1, X=1=1) = 0.01
0.01/0.08 - 0.69/0.92 = -0.59
-0.59 < 0",mediation,alarm,1,correlation,P(Y | X)
13025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 74%. For people who have a brother, the probability of ringing alarm is 22%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.22
0.22 - 0.74 = -0.52
-0.52 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 3%. For people who do not have a brother, the probability of ringing alarm is 74%. For people who have a brother, the probability of ringing alarm is 22%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.22
0.03*0.22 - 0.97*0.74 = 0.72
0.72 > 0",mediation,alarm,1,marginal,P(Y)
13036,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look at how having a brother correlates with alarm clock case by case according to wife. Method 2: We look directly at how having a brother correlates with alarm clock in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
13039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 79%. For people who have a brother, the probability of ringing alarm is 30%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.30
0.30 - 0.79 = -0.49
-0.49 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 89%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 44%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 58%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 11%. For people who do not have a brother, the probability of alarm set by wife is 22%. For people who have a brother, the probability of alarm set by wife is 59%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.89
P(Y=1 | X=0, V2=1) = 0.44
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.11
P(V2=1 | X=0) = 0.22
P(V2=1 | X=1) = 0.59
0.59 * (0.44 - 0.89)+ 0.22 * (0.11 - 0.58)= -0.17
-0.17 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
13046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 1%. For people who do not have a brother, the probability of ringing alarm is 79%. For people who have a brother, the probability of ringing alarm is 30%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.30
0.01*0.30 - 0.99*0.79 = 0.78
0.78 > 0",mediation,alarm,1,marginal,P(Y)
13047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 1%. For people who do not have a brother, the probability of ringing alarm is 79%. For people who have a brother, the probability of ringing alarm is 30%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.30
0.01*0.30 - 0.99*0.79 = 0.78
0.78 > 0",mediation,alarm,1,marginal,P(Y)
13051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
13052,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 90%. For people who have a brother, the probability of ringing alarm is 25%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.25
0.25 - 0.90 = -0.65
-0.65 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 90%. For people who have a brother, the probability of ringing alarm is 25%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.25
0.25 - 0.90 = -0.65
-0.65 < 0",mediation,alarm,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 90%. For people who have a brother, the probability of ringing alarm is 25%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.25
0.25 - 0.90 = -0.65
-0.65 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13055,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother, the probability of ringing alarm is 90%. For people who have a brother, the probability of ringing alarm is 25%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.25
0.25 - 0.90 = -0.65
-0.65 < 0",mediation,alarm,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 94%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 62%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 6%. For people who do not have a brother, the probability of alarm set by wife is 9%. For people who have a brother, the probability of alarm set by wife is 66%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.62
P(Y=1 | X=1, V2=1) = 0.06
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.66
0.66 * (0.45 - 0.94)+ 0.09 * (0.06 - 0.62)= -0.28
-0.28 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
13057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 94%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 62%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 6%. For people who do not have a brother, the probability of alarm set by wife is 9%. For people who have a brother, the probability of alarm set by wife is 66%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.62
P(Y=1 | X=1, V2=1) = 0.06
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.66
0.66 * (0.45 - 0.94)+ 0.09 * (0.06 - 0.62)= -0.28
-0.28 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
13059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 94%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 45%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 62%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 6%. For people who do not have a brother, the probability of alarm set by wife is 9%. For people who have a brother, the probability of alarm set by wife is 66%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.62
P(Y=1 | X=1, V2=1) = 0.06
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.66
0.09 * (0.06 - 0.62) + 0.66 * (0.45 - 0.94) = -0.33
-0.33 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
13070,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 87%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 42%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 9%. For people who do not have a brother, the probability of alarm set by wife is 62%. For people who have a brother, the probability of alarm set by wife is 75%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.87
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.09
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.75
0.75 * (0.42 - 0.87)+ 0.62 * (0.09 - 0.55)= -0.06
-0.06 < 0",mediation,alarm,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
13072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. For people who do not have a brother and wives that don't set the alarm, the probability of ringing alarm is 87%. For people who do not have a brother and wives that set the alarm, the probability of ringing alarm is 42%. For people who have a brother and wives that don't set the alarm, the probability of ringing alarm is 55%. For people who have a brother and wives that set the alarm, the probability of ringing alarm is 9%. For people who do not have a brother, the probability of alarm set by wife is 62%. For people who have a brother, the probability of alarm set by wife is 75%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.87
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.09
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.75
0.62 * (0.09 - 0.55) + 0.75 * (0.42 - 0.87) = -0.32
-0.32 < 0",mediation,alarm,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
13075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 0%. For people who do not have a brother, the probability of ringing alarm is 59%. For people who have a brother, the probability of ringing alarm is 21%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.00
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.21
0.00*0.21 - 1.00*0.59 = 0.59
0.59 > 0",mediation,alarm,1,marginal,P(Y)
13076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 0%. The probability of not having a brother and ringing alarm is 59%. The probability of having a brother and ringing alarm is 0%.",no,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.00
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.00
0.00/0.00 - 0.59/1.00 = -0.38
-0.38 < 0",mediation,alarm,1,correlation,P(Y | X)
13077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. The overall probability of having a brother is 0%. The probability of not having a brother and ringing alarm is 59%. The probability of having a brother and ringing alarm is 0%.",yes,"Let X = having a brother; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.00
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.00
0.00/0.00 - 0.59/1.00 = -0.38
-0.38 < 0",mediation,alarm,1,correlation,P(Y | X)
13079,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. Method 1: We look directly at how having a brother correlates with alarm clock in general. Method 2: We look at this correlation case by case according to wife.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,alarm,2,backadj,[backdoor adjustment set for Y given X]
13082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 86%. For people who drink coffee, the probability of dark room is 55%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.55
0.55 - 0.86 = -0.31
-0.31 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 7%. For people who do not drink coffee, the probability of dark room is 86%. For people who drink coffee, the probability of dark room is 55%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.55
0.07*0.55 - 0.93*0.86 = 0.84
0.84 > 0",fork,candle,1,marginal,P(Y)
13087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 7%. The probability of not drinking coffee and dark room is 80%. The probability of drinking coffee and dark room is 4%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.80
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.80/0.93 = -0.31
-0.31 < 0",fork,candle,1,correlation,P(Y | X)
13090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 87%. For people who drink coffee, the probability of dark room is 55%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.55
0.55 - 0.87 = -0.31
-0.31 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 9%. The probability of not drinking coffee and dark room is 79%. The probability of drinking coffee and dark room is 5%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.79
P(Y=1, X=1=1) = 0.05
0.05/0.09 - 0.79/0.91 = -0.31
-0.31 < 0",fork,candle,1,correlation,P(Y | X)
13099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 50%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.50
0.50 - 0.84 = -0.34
-0.34 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13103,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 50%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.50
0.50 - 0.84 = -0.34
-0.34 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13104,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 5%. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 50%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.50
0.05*0.50 - 0.95*0.84 = 0.82
0.82 > 0",fork,candle,1,marginal,P(Y)
13109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 91%. For people who drink coffee, the probability of dark room is 52%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.52
0.52 - 0.91 = -0.39
-0.39 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 83%. For people who drink coffee, the probability of dark room is 46%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.46
0.46 - 0.83 = -0.37
-0.37 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 17%. For people who do not drink coffee, the probability of dark room is 83%. For people who drink coffee, the probability of dark room is 46%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.46
0.17*0.46 - 0.83*0.83 = 0.76
0.76 > 0",fork,candle,1,marginal,P(Y)
13126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 17%. The probability of not drinking coffee and dark room is 69%. The probability of drinking coffee and dark room is 8%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.69
P(Y=1, X=1=1) = 0.08
0.08/0.17 - 0.69/0.83 = -0.37
-0.37 < 0",fork,candle,1,correlation,P(Y | X)
13127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 17%. The probability of not drinking coffee and dark room is 69%. The probability of drinking coffee and dark room is 8%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.69
P(Y=1, X=1=1) = 0.08
0.08/0.17 - 0.69/0.83 = -0.37
-0.37 < 0",fork,candle,1,correlation,P(Y | X)
13130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 58%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.58
0.58 - 0.89 = -0.30
-0.30 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 58%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.58
0.58 - 0.89 = -0.30
-0.30 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 58%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.58
0.58 - 0.89 = -0.30
-0.30 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 58%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.58
0.58 - 0.89 = -0.30
-0.30 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 20%. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 58%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.58
0.20*0.58 - 0.80*0.89 = 0.83
0.83 > 0",fork,candle,1,marginal,P(Y)
13137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 20%. The probability of not drinking coffee and dark room is 71%. The probability of drinking coffee and dark room is 11%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.71
P(Y=1, X=1=1) = 0.11
0.11/0.20 - 0.71/0.80 = -0.30
-0.30 < 0",fork,candle,1,correlation,P(Y | X)
13138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 96%. For people who drink coffee, the probability of dark room is 61%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.96
P(Y=1 | X=1) = 0.61
0.61 - 0.96 = -0.35
-0.35 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 3%. The probability of not drinking coffee and dark room is 93%. The probability of drinking coffee and dark room is 2%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.93
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.93/0.97 = -0.35
-0.35 < 0",fork,candle,1,correlation,P(Y | X)
13148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 57%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.57
0.57 - 0.89 = -0.32
-0.32 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 57%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.57
0.57 - 0.89 = -0.32
-0.32 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 20%. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 57%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.57
0.20*0.57 - 0.80*0.89 = 0.83
0.83 > 0",fork,candle,1,marginal,P(Y)
13159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13163,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 57%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.57
0.57 - 0.88 = -0.31
-0.31 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 12%. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 57%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.57
0.12*0.57 - 0.88*0.88 = 0.84
0.84 > 0",fork,candle,1,marginal,P(Y)
13165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 12%. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 57%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.57
0.12*0.57 - 0.88*0.88 = 0.84
0.84 > 0",fork,candle,1,marginal,P(Y)
13171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 85%. For people who drink coffee, the probability of dark room is 52%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.52
0.52 - 0.85 = -0.34
-0.34 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 85%. For people who drink coffee, the probability of dark room is 52%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.52
0.52 - 0.85 = -0.34
-0.34 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 3%. For people who do not drink coffee, the probability of dark room is 85%. For people who drink coffee, the probability of dark room is 52%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.52
0.03*0.52 - 0.97*0.85 = 0.84
0.84 > 0",fork,candle,1,marginal,P(Y)
13176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 3%. The probability of not drinking coffee and dark room is 83%. The probability of drinking coffee and dark room is 2%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.83
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.83/0.97 = -0.34
-0.34 < 0",fork,candle,1,correlation,P(Y | X)
13181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 56%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.56
0.56 - 0.88 = -0.32
-0.32 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 56%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.56
0.56 - 0.88 = -0.32
-0.32 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 16%. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 56%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.56
0.16*0.56 - 0.84*0.88 = 0.83
0.83 > 0",fork,candle,1,marginal,P(Y)
13185,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 16%. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 56%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.56
0.16*0.56 - 0.84*0.88 = 0.83
0.83 > 0",fork,candle,1,marginal,P(Y)
13186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 16%. The probability of not drinking coffee and dark room is 74%. The probability of drinking coffee and dark room is 9%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.74
P(Y=1, X=1=1) = 0.09
0.09/0.16 - 0.74/0.84 = -0.32
-0.32 < 0",fork,candle,1,correlation,P(Y | X)
13187,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 16%. The probability of not drinking coffee and dark room is 74%. The probability of drinking coffee and dark room is 9%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.74
P(Y=1, X=1=1) = 0.09
0.09/0.16 - 0.74/0.84 = -0.32
-0.32 < 0",fork,candle,1,correlation,P(Y | X)
13190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 82%. For people who drink coffee, the probability of dark room is 47%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.47
0.47 - 0.82 = -0.35
-0.35 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13192,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 82%. For people who drink coffee, the probability of dark room is 47%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.47
0.47 - 0.82 = -0.35
-0.35 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 20%. The probability of not drinking coffee and dark room is 66%. The probability of drinking coffee and dark room is 9%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.09
0.09/0.20 - 0.66/0.80 = -0.35
-0.35 < 0",fork,candle,1,correlation,P(Y | X)
13199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 93%. For people who drink coffee, the probability of dark room is 62%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.62
0.62 - 0.93 = -0.30
-0.30 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13203,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 93%. For people who drink coffee, the probability of dark room is 62%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.62
0.62 - 0.93 = -0.30
-0.30 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 17%. For people who do not drink coffee, the probability of dark room is 93%. For people who drink coffee, the probability of dark room is 62%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.62
0.17*0.62 - 0.83*0.93 = 0.88
0.88 > 0",fork,candle,1,marginal,P(Y)
13206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 17%. The probability of not drinking coffee and dark room is 77%. The probability of drinking coffee and dark room is 11%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.77
P(Y=1, X=1=1) = 0.11
0.11/0.17 - 0.77/0.83 = -0.30
-0.30 < 0",fork,candle,1,correlation,P(Y | X)
13210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 98%. For people who drink coffee, the probability of dark room is 55%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.98
P(Y=1 | X=1) = 0.55
0.55 - 0.98 = -0.43
-0.43 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 20%. The probability of not drinking coffee and dark room is 79%. The probability of drinking coffee and dark room is 11%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.79
P(Y=1, X=1=1) = 0.11
0.11/0.20 - 0.79/0.80 = -0.43
-0.43 < 0",fork,candle,1,correlation,P(Y | X)
13217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 20%. The probability of not drinking coffee and dark room is 79%. The probability of drinking coffee and dark room is 11%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.79
P(Y=1, X=1=1) = 0.11
0.11/0.20 - 0.79/0.80 = -0.43
-0.43 < 0",fork,candle,1,correlation,P(Y | X)
13218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 86%. For people who drink coffee, the probability of dark room is 56%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.56
0.56 - 0.86 = -0.31
-0.31 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 5%. The probability of not drinking coffee and dark room is 82%. The probability of drinking coffee and dark room is 3%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.82
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.82/0.95 = -0.31
-0.31 < 0",fork,candle,1,correlation,P(Y | X)
13227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 5%. The probability of not drinking coffee and dark room is 82%. The probability of drinking coffee and dark room is 3%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.82
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.82/0.95 = -0.31
-0.31 < 0",fork,candle,1,correlation,P(Y | X)
13230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 49%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.49
0.49 - 0.84 = -0.35
-0.35 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 49%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.49
0.49 - 0.84 = -0.35
-0.35 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 49%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.49
0.49 - 0.84 = -0.35
-0.35 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 10%. The probability of not drinking coffee and dark room is 75%. The probability of drinking coffee and dark room is 5%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.75
P(Y=1, X=1=1) = 0.05
0.05/0.10 - 0.75/0.90 = -0.35
-0.35 < 0",fork,candle,1,correlation,P(Y | X)
13237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 10%. The probability of not drinking coffee and dark room is 75%. The probability of drinking coffee and dark room is 5%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.75
P(Y=1, X=1=1) = 0.05
0.05/0.10 - 0.75/0.90 = -0.35
-0.35 < 0",fork,candle,1,correlation,P(Y | X)
13239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 54%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.54
0.54 - 0.88 = -0.34
-0.34 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 55%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.55
0.55 - 0.88 = -0.32
-0.32 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 55%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.55
0.55 - 0.88 = -0.32
-0.32 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 2%. For people who do not drink coffee, the probability of dark room is 88%. For people who drink coffee, the probability of dark room is 55%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.55
0.02*0.55 - 0.98*0.88 = 0.87
0.87 > 0",fork,candle,1,marginal,P(Y)
13259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 83%. For people who drink coffee, the probability of dark room is 49%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.49
0.49 - 0.83 = -0.35
-0.35 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 15%. For people who do not drink coffee, the probability of dark room is 83%. For people who drink coffee, the probability of dark room is 49%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.49
0.15*0.49 - 0.85*0.83 = 0.78
0.78 > 0",fork,candle,1,marginal,P(Y)
13265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 15%. For people who do not drink coffee, the probability of dark room is 83%. For people who drink coffee, the probability of dark room is 49%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.49
0.15*0.49 - 0.85*0.83 = 0.78
0.78 > 0",fork,candle,1,marginal,P(Y)
13268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 94%. For people who drink coffee, the probability of dark room is 60%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.60
0.60 - 0.94 = -0.34
-0.34 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 14%. For people who do not drink coffee, the probability of dark room is 94%. For people who drink coffee, the probability of dark room is 60%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.60
0.14*0.60 - 0.86*0.94 = 0.89
0.89 > 0",fork,candle,1,marginal,P(Y)
13276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 14%. The probability of not drinking coffee and dark room is 81%. The probability of drinking coffee and dark room is 8%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.81
P(Y=1, X=1=1) = 0.08
0.08/0.14 - 0.81/0.86 = -0.34
-0.34 < 0",fork,candle,1,correlation,P(Y | X)
13283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 80%. For people who drink coffee, the probability of dark room is 49%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.49
0.49 - 0.80 = -0.30
-0.30 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 18%. The probability of not drinking coffee and dark room is 65%. The probability of drinking coffee and dark room is 9%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.09
0.09/0.18 - 0.65/0.82 = -0.30
-0.30 < 0",fork,candle,1,correlation,P(Y | X)
13288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 7%. For people who do not drink coffee, the probability of dark room is 78%. For people who drink coffee, the probability of dark room is 45%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.45
0.07*0.45 - 0.93*0.78 = 0.76
0.76 > 0",fork,candle,1,marginal,P(Y)
13298,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 5%. For people who do not drink coffee, the probability of dark room is 89%. For people who drink coffee, the probability of dark room is 56%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.56
0.05*0.56 - 0.95*0.89 = 0.87
0.87 > 0",fork,candle,1,marginal,P(Y)
13308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 52%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.52
0.52 - 0.84 = -0.32
-0.32 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13324,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 15%. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 52%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.52
0.15*0.52 - 0.85*0.84 = 0.79
0.79 > 0",fork,candle,1,marginal,P(Y)
13325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 15%. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 52%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.52
0.15*0.52 - 0.85*0.84 = 0.79
0.79 > 0",fork,candle,1,marginal,P(Y)
13328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 49%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.49
0.49 - 0.84 = -0.35
-0.35 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 49%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.49
0.49 - 0.84 = -0.35
-0.35 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 3%. For people who do not drink coffee, the probability of dark room is 84%. For people who drink coffee, the probability of dark room is 49%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.49
0.03*0.49 - 0.97*0.84 = 0.83
0.83 > 0",fork,candle,1,marginal,P(Y)
13336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 3%. The probability of not drinking coffee and dark room is 82%. The probability of drinking coffee and dark room is 1%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.82
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.82/0.97 = -0.35
-0.35 < 0",fork,candle,1,correlation,P(Y | X)
13337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 3%. The probability of not drinking coffee and dark room is 82%. The probability of drinking coffee and dark room is 1%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.82
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.82/0.97 = -0.35
-0.35 < 0",fork,candle,1,correlation,P(Y | X)
13341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 92%. For people who drink coffee, the probability of dark room is 58%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.58
0.58 - 0.92 = -0.34
-0.34 < 0",fork,candle,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 92%. For people who drink coffee, the probability of dark room is 58%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.58
0.58 - 0.92 = -0.34
-0.34 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 92%. For people who drink coffee, the probability of dark room is 58%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.58
0.58 - 0.92 = -0.34
-0.34 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 18%. The probability of not drinking coffee and dark room is 76%. The probability of drinking coffee and dark room is 10%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.10
0.10/0.18 - 0.76/0.82 = -0.34
-0.34 < 0",fork,candle,1,correlation,P(Y | X)
13349,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look directly at how drinking coffee correlates with room in general. Method 2: We look at this correlation case by case according to the candle.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 87%. For people who drink coffee, the probability of dark room is 54%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.54
0.54 - 0.87 = -0.33
-0.33 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 18%. For people who do not drink coffee, the probability of dark room is 87%. For people who drink coffee, the probability of dark room is 54%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.54
0.18*0.54 - 0.82*0.87 = 0.81
0.81 > 0",fork,candle,1,marginal,P(Y)
13355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 18%. For people who do not drink coffee, the probability of dark room is 87%. For people who drink coffee, the probability of dark room is 54%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.54
0.18*0.54 - 0.82*0.87 = 0.81
0.81 > 0",fork,candle,1,marginal,P(Y)
13357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 18%. The probability of not drinking coffee and dark room is 71%. The probability of drinking coffee and dark room is 10%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.71
P(Y=1, X=1=1) = 0.10
0.10/0.18 - 0.71/0.82 = -0.33
-0.33 < 0",fork,candle,1,correlation,P(Y | X)
13362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 86%. For people who drink coffee, the probability of dark room is 54%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.54
0.54 - 0.86 = -0.32
-0.32 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 86%. For people who drink coffee, the probability of dark room is 54%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.54
0.54 - 0.86 = -0.32
-0.32 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13364,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 15%. For people who do not drink coffee, the probability of dark room is 86%. For people who drink coffee, the probability of dark room is 54%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.54
0.15*0.54 - 0.85*0.86 = 0.81
0.81 > 0",fork,candle,1,marginal,P(Y)
13368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. Method 1: We look at how drinking coffee correlates with room case by case according to the candle. Method 2: We look directly at how drinking coffee correlates with room in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,candle,2,backadj,[backdoor adjustment set for Y given X]
13373,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. For people who do not drink coffee, the probability of dark room is 92%. For people who drink coffee, the probability of dark room is 59%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.59
0.59 - 0.92 = -0.33
-0.33 < 0",fork,candle,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 14%. For people who do not drink coffee, the probability of dark room is 92%. For people who drink coffee, the probability of dark room is 59%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.59
0.14*0.59 - 0.86*0.92 = 0.88
0.88 > 0",fork,candle,1,marginal,P(Y)
13375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 14%. For people who do not drink coffee, the probability of dark room is 92%. For people who drink coffee, the probability of dark room is 59%.",no,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.59
0.14*0.59 - 0.86*0.92 = 0.88
0.88 > 0",fork,candle,1,marginal,P(Y)
13377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on room. The candle has a direct effect on room. The overall probability of drinking coffee is 14%. The probability of not drinking coffee and dark room is 79%. The probability of drinking coffee and dark room is 8%.",yes,"Let V2 = the candle; X = drinking coffee; Y = room.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.79
P(Y=1, X=1=1) = 0.08
0.08/0.14 - 0.79/0.86 = -0.33
-0.33 < 0",fork,candle,1,correlation,P(Y | X)
13382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 83%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 50%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 50%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 15%. For managers who don't sign termination letters, the probability of director signing the termination letter is 7%. For managers who sign termination letters, the probability of director signing the termination letter is 13%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.15
P(V3=1 | X=0) = 0.07
P(V3=1 | X=1) = 0.13
0.13 * (0.15 - 0.50) + 0.07 * (0.50 - 0.83) = -0.33
-0.33 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 29%. For managers who don't sign termination letters, the probability of large feet is 81%. For managers who sign termination letters, the probability of large feet is 46%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.46
0.29*0.46 - 0.71*0.81 = 0.70
0.70 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 29%. The probability of manager not signing the termination letter and large feet is 57%. The probability of manager signing the termination letter and large feet is 13%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.29
P(Y=1, X=0=1) = 0.57
P(Y=1, X=1=1) = 0.13
0.13/0.29 - 0.57/0.71 = -0.35
-0.35 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13390,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 46%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 8%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 69%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 34%. The overall probability of CEO's decision to fire the employee is 98%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.46
P(Y=1 | V1=0, X=1) = 0.08
P(Y=1 | V1=1, X=0) = 0.69
P(Y=1 | V1=1, X=1) = 0.34
P(V1=1) = 0.98
0.02 * (0.08 - 0.46) 0.98 * (0.34 - 0.69) = -0.36
-0.36 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13392,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 83%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 44%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 48%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 6%. For managers who don't sign termination letters, the probability of director signing the termination letter is 35%. For managers who sign termination letters, the probability of director signing the termination letter is 38%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.06
P(V3=1 | X=0) = 0.35
P(V3=1 | X=1) = 0.38
0.38 * (0.06 - 0.48) + 0.35 * (0.44 - 0.83) = -0.36
-0.36 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 25%. For managers who don't sign termination letters, the probability of large feet is 69%. For managers who sign termination letters, the probability of large feet is 32%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.25
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.32
0.25*0.32 - 0.75*0.69 = 0.60
0.60 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 25%. For managers who don't sign termination letters, the probability of large feet is 69%. For managers who sign termination letters, the probability of large feet is 32%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.25
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.32
0.25*0.32 - 0.75*0.69 = 0.60
0.60 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 25%. The probability of manager not signing the termination letter and large feet is 52%. The probability of manager signing the termination letter and large feet is 8%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.08
0.08/0.25 - 0.52/0.75 = -0.37
-0.37 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 71%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 25%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 88%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 45%. The overall probability of CEO's decision to fire the employee is 91%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.71
P(Y=1 | V1=0, X=1) = 0.25
P(Y=1 | V1=1, X=0) = 0.88
P(Y=1 | V1=1, X=1) = 0.45
P(V1=1) = 0.91
0.09 * (0.25 - 0.71) 0.91 * (0.45 - 0.88) = -0.43
-0.43 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 96%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 62%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 54%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 16%. For managers who don't sign termination letters, the probability of director signing the termination letter is 26%. For managers who sign termination letters, the probability of director signing the termination letter is 34%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0) = 0.26
P(V3=1 | X=1) = 0.34
0.34 * (0.16 - 0.54) + 0.26 * (0.62 - 0.96) = -0.43
-0.43 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 34%. The probability of manager not signing the termination letter and large feet is 57%. The probability of manager signing the termination letter and large feet is 14%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.34
P(Y=1, X=0=1) = 0.57
P(Y=1, X=1=1) = 0.14
0.14/0.34 - 0.57/0.66 = -0.46
-0.46 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 84%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 49%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 45%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 13%. For managers who don't sign termination letters, the probability of director signing the termination letter is 32%. For managers who sign termination letters, the probability of director signing the termination letter is 62%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.13
P(V3=1 | X=0) = 0.32
P(V3=1 | X=1) = 0.62
0.62 * (0.13 - 0.45) + 0.32 * (0.49 - 0.84) = -0.37
-0.37 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 30%. For managers who don't sign termination letters, the probability of large feet is 73%. For managers who sign termination letters, the probability of large feet is 25%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.30
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.25
0.30*0.25 - 0.70*0.73 = 0.58
0.58 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13416,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 30%. The probability of manager not signing the termination letter and large feet is 51%. The probability of manager signing the termination letter and large feet is 7%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.51
P(Y=1, X=1=1) = 0.07
0.07/0.30 - 0.51/0.70 = -0.48
-0.48 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13419,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 19%. The probability of manager not signing the termination letter and large feet is 60%. The probability of manager signing the termination letter and large feet is 7%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.60
P(Y=1, X=1=1) = 0.07
0.07/0.19 - 0.60/0.81 = -0.36
-0.36 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 81%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 46%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 49%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 10%. For managers who don't sign termination letters, the probability of director signing the termination letter is 15%. For managers who sign termination letters, the probability of director signing the termination letter is 39%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.81
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.10
P(V3=1 | X=0) = 0.15
P(V3=1 | X=1) = 0.39
0.39 * (0.10 - 0.49) + 0.15 * (0.46 - 0.81) = -0.34
-0.34 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13434,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 20%. For managers who don't sign termination letters, the probability of large feet is 76%. For managers who sign termination letters, the probability of large feet is 34%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.34
0.20*0.34 - 0.80*0.76 = 0.67
0.67 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 20%. The probability of manager not signing the termination letter and large feet is 61%. The probability of manager signing the termination letter and large feet is 7%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.07
0.07/0.20 - 0.61/0.80 = -0.42
-0.42 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 52%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 14%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 71%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 32%. The overall probability of CEO's decision to fire the employee is 98%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.52
P(Y=1 | V1=0, X=1) = 0.14
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.32
P(V1=1) = 0.98
0.02 * (0.14 - 0.52) 0.98 * (0.32 - 0.71) = -0.40
-0.40 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 90%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 44%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 48%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 7%. For managers who don't sign termination letters, the probability of director signing the termination letter is 40%. For managers who sign termination letters, the probability of director signing the termination letter is 45%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.90
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.07
P(V3=1 | X=0) = 0.40
P(V3=1 | X=1) = 0.45
0.45 * (0.07 - 0.48) + 0.40 * (0.44 - 0.90) = -0.39
-0.39 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 54%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 14%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 70%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 27%. The overall probability of CEO's decision to fire the employee is 87%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.54
P(Y=1 | V1=0, X=1) = 0.14
P(Y=1 | V1=1, X=0) = 0.70
P(Y=1 | V1=1, X=1) = 0.27
P(V1=1) = 0.87
0.13 * (0.14 - 0.54) 0.87 * (0.27 - 0.70) = -0.43
-0.43 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 43%. For managers who don't sign termination letters, the probability of large feet is 70%. For managers who sign termination letters, the probability of large feet is 23%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.23
0.43*0.23 - 0.57*0.70 = 0.49
0.49 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 54%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 21%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 79%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 46%. The overall probability of CEO's decision to fire the employee is 92%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.54
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.79
P(Y=1 | V1=1, X=1) = 0.46
P(V1=1) = 0.92
0.08 * (0.21 - 0.54) 0.92 * (0.46 - 0.79) = -0.33
-0.33 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 54%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 21%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 79%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 46%. The overall probability of CEO's decision to fire the employee is 92%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.54
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.79
P(Y=1 | V1=1, X=1) = 0.46
P(V1=1) = 0.92
0.08 * (0.21 - 0.54) 0.92 * (0.46 - 0.79) = -0.33
-0.33 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 85%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 50%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 51%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 17%. For managers who don't sign termination letters, the probability of director signing the termination letter is 17%. For managers who sign termination letters, the probability of director signing the termination letter is 32%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.17
P(V3=1 | X=0) = 0.17
P(V3=1 | X=1) = 0.32
0.32 * (0.17 - 0.51) + 0.17 * (0.50 - 0.85) = -0.33
-0.33 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13464,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 23%. For managers who don't sign termination letters, the probability of large feet is 79%. For managers who sign termination letters, the probability of large feet is 40%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.40
0.23*0.40 - 0.77*0.79 = 0.70
0.70 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 52%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 20%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 77%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 47%. The overall probability of CEO's decision to fire the employee is 91%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.52
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.47
P(V1=1) = 0.91
0.09 * (0.20 - 0.52) 0.91 * (0.47 - 0.77) = -0.31
-0.31 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 52%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 20%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 77%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 47%. The overall probability of CEO's decision to fire the employee is 91%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.52
P(Y=1 | V1=0, X=1) = 0.20
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.47
P(V1=1) = 0.91
0.09 * (0.20 - 0.52) 0.91 * (0.47 - 0.77) = -0.31
-0.31 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13473,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 86%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 48%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 55%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 16%. For managers who don't sign termination letters, the probability of director signing the termination letter is 25%. For managers who sign termination letters, the probability of director signing the termination letter is 35%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.86
P(Y=1 | X=0, V3=1) = 0.48
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0) = 0.25
P(V3=1 | X=1) = 0.35
0.35 * (0.16 - 0.55) + 0.25 * (0.48 - 0.86) = -0.31
-0.31 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 35%. For managers who don't sign termination letters, the probability of large feet is 76%. For managers who sign termination letters, the probability of large feet is 42%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.42
0.35*0.42 - 0.65*0.76 = 0.64
0.64 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13475,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 35%. For managers who don't sign termination letters, the probability of large feet is 76%. For managers who sign termination letters, the probability of large feet is 42%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.42
0.35*0.42 - 0.65*0.76 = 0.64
0.64 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 44%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 9%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 70%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 34%. The overall probability of CEO's decision to fire the employee is 83%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.44
P(Y=1 | V1=0, X=1) = 0.09
P(Y=1 | V1=1, X=0) = 0.70
P(Y=1 | V1=1, X=1) = 0.34
P(V1=1) = 0.83
0.17 * (0.09 - 0.44) 0.83 * (0.34 - 0.70) = -0.35
-0.35 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 84%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 44%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 49%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 8%. For managers who don't sign termination letters, the probability of director signing the termination letter is 37%. For managers who sign termination letters, the probability of director signing the termination letter is 67%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.44
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.08
P(V3=1 | X=0) = 0.37
P(V3=1 | X=1) = 0.67
0.67 * (0.08 - 0.49) + 0.37 * (0.44 - 0.84) = -0.35
-0.35 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13486,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 32%. The probability of manager not signing the termination letter and large feet is 47%. The probability of manager signing the termination letter and large feet is 7%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.32
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.07
0.07/0.32 - 0.47/0.68 = -0.48
-0.48 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13491,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 61%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 24%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 77%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 42%. The overall probability of CEO's decision to fire the employee is 95%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.61
P(Y=1 | V1=0, X=1) = 0.24
P(Y=1 | V1=1, X=0) = 0.77
P(Y=1 | V1=1, X=1) = 0.42
P(V1=1) = 0.95
0.05 * (0.24 - 0.61) 0.95 * (0.42 - 0.77) = -0.35
-0.35 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 44%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 7%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 76%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 34%. The overall probability of CEO's decision to fire the employee is 89%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.44
P(Y=1 | V1=0, X=1) = 0.07
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.34
P(V1=1) = 0.89
0.11 * (0.07 - 0.44) 0.89 * (0.34 - 0.76) = -0.41
-0.41 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 44%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 7%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 76%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 34%. The overall probability of CEO's decision to fire the employee is 89%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.44
P(Y=1 | V1=0, X=1) = 0.07
P(Y=1 | V1=1, X=0) = 0.76
P(Y=1 | V1=1, X=1) = 0.34
P(V1=1) = 0.89
0.11 * (0.07 - 0.44) 0.89 * (0.34 - 0.76) = -0.41
-0.41 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 80%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 43%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 37%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 6%. For managers who don't sign termination letters, the probability of director signing the termination letter is 14%. For managers who sign termination letters, the probability of director signing the termination letter is 45%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.43
P(Y=1 | X=1, V3=0) = 0.37
P(Y=1 | X=1, V3=1) = 0.06
P(V3=1 | X=0) = 0.14
P(V3=1 | X=1) = 0.45
0.45 * (0.06 - 0.37) + 0.14 * (0.43 - 0.80) = -0.40
-0.40 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13505,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 24%. For managers who don't sign termination letters, the probability of large feet is 75%. For managers who sign termination letters, the probability of large feet is 23%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.23
0.24*0.23 - 0.76*0.75 = 0.62
0.62 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 24%. The probability of manager not signing the termination letter and large feet is 57%. The probability of manager signing the termination letter and large feet is 6%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.57
P(Y=1, X=1=1) = 0.06
0.06/0.24 - 0.57/0.76 = -0.52
-0.52 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 73%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 31%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 90%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 47%. The overall probability of CEO's decision to fire the employee is 91%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.73
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.90
P(Y=1 | V1=1, X=1) = 0.47
P(V1=1) = 0.91
0.09 * (0.31 - 0.73) 0.91 * (0.47 - 0.90) = -0.43
-0.43 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 73%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 31%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 90%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 47%. The overall probability of CEO's decision to fire the employee is 91%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.73
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.90
P(Y=1 | V1=1, X=1) = 0.47
P(V1=1) = 0.91
0.09 * (0.31 - 0.73) 0.91 * (0.47 - 0.90) = -0.43
-0.43 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 27%. For managers who don't sign termination letters, the probability of large feet is 89%. For managers who sign termination letters, the probability of large feet is 42%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.27
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.42
0.27*0.42 - 0.73*0.89 = 0.77
0.77 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 27%. The probability of manager not signing the termination letter and large feet is 65%. The probability of manager signing the termination letter and large feet is 11%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.27
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.11
0.11/0.27 - 0.65/0.73 = -0.47
-0.47 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 96%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 59%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 50%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 13%. For managers who don't sign termination letters, the probability of director signing the termination letter is 8%. For managers who sign termination letters, the probability of director signing the termination letter is 19%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.13
P(V3=1 | X=0) = 0.08
P(V3=1 | X=1) = 0.19
0.19 * (0.13 - 0.50) + 0.08 * (0.59 - 0.96) = -0.46
-0.46 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 96%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 59%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 50%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 13%. For managers who don't sign termination letters, the probability of director signing the termination letter is 8%. For managers who sign termination letters, the probability of director signing the termination letter is 19%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.13
P(V3=1 | X=0) = 0.08
P(V3=1 | X=1) = 0.19
0.19 * (0.13 - 0.50) + 0.08 * (0.59 - 0.96) = -0.46
-0.46 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 46%. For managers who don't sign termination letters, the probability of large feet is 93%. For managers who sign termination letters, the probability of large feet is 43%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.43
0.46*0.43 - 0.54*0.93 = 0.70
0.70 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 46%. For managers who don't sign termination letters, the probability of large feet is 93%. For managers who sign termination letters, the probability of large feet is 43%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.43
0.46*0.43 - 0.54*0.93 = 0.70
0.70 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 53%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 22%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 73%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 42%. The overall probability of CEO's decision to fire the employee is 81%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.53
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.73
P(Y=1 | V1=1, X=1) = 0.42
P(V1=1) = 0.81
0.19 * (0.22 - 0.53) 0.81 * (0.42 - 0.73) = -0.32
-0.32 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 53%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 22%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 73%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 42%. The overall probability of CEO's decision to fire the employee is 81%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.53
P(Y=1 | V1=0, X=1) = 0.22
P(Y=1 | V1=1, X=0) = 0.73
P(Y=1 | V1=1, X=1) = 0.42
P(V1=1) = 0.81
0.19 * (0.22 - 0.53) 0.81 * (0.42 - 0.73) = -0.32
-0.32 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13537,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 33%. The probability of manager not signing the termination letter and large feet is 48%. The probability of manager signing the termination letter and large feet is 11%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.33
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.11
0.11/0.33 - 0.48/0.67 = -0.38
-0.38 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13539,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 49%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 8%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 63%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 25%. The overall probability of CEO's decision to fire the employee is 82%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.49
P(Y=1 | V1=0, X=1) = 0.08
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.25
P(V1=1) = 0.82
0.18 * (0.08 - 0.49) 0.82 * (0.25 - 0.63) = -0.39
-0.39 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 49%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 8%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 63%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 25%. The overall probability of CEO's decision to fire the employee is 82%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.49
P(Y=1 | V1=0, X=1) = 0.08
P(Y=1 | V1=1, X=0) = 0.63
P(Y=1 | V1=1, X=1) = 0.25
P(V1=1) = 0.82
0.18 * (0.08 - 0.49) 0.82 * (0.25 - 0.63) = -0.39
-0.39 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13548,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 63%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 21%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 84%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 46%. The overall probability of CEO's decision to fire the employee is 90%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.63
P(Y=1 | V1=0, X=1) = 0.21
P(Y=1 | V1=1, X=0) = 0.84
P(Y=1 | V1=1, X=1) = 0.46
P(V1=1) = 0.90
0.10 * (0.21 - 0.63) 0.90 * (0.46 - 0.84) = -0.39
-0.39 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 100%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 54%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 64%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 11%. For managers who don't sign termination letters, the probability of director signing the termination letter is 35%. For managers who sign termination letters, the probability of director signing the termination letter is 45%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 1.00
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.11
P(V3=1 | X=0) = 0.35
P(V3=1 | X=1) = 0.45
0.45 * (0.11 - 0.64) + 0.35 * (0.54 - 1.00) = -0.39
-0.39 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 66%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 19%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 81%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 37%. The overall probability of CEO's decision to fire the employee is 88%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.66
P(Y=1 | V1=0, X=1) = 0.19
P(Y=1 | V1=1, X=0) = 0.81
P(Y=1 | V1=1, X=1) = 0.37
P(V1=1) = 0.88
0.12 * (0.19 - 0.66) 0.88 * (0.37 - 0.81) = -0.45
-0.45 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 87%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 52%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 44%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 3%. For managers who don't sign termination letters, the probability of director signing the termination letter is 20%. For managers who sign termination letters, the probability of director signing the termination letter is 40%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.87
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.03
P(V3=1 | X=0) = 0.20
P(V3=1 | X=1) = 0.40
0.40 * (0.03 - 0.44) + 0.20 * (0.52 - 0.87) = -0.46
-0.46 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13570,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 72%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 28%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 94%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 51%. The overall probability of CEO's decision to fire the employee is 88%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.72
P(Y=1 | V1=0, X=1) = 0.28
P(Y=1 | V1=1, X=0) = 0.94
P(Y=1 | V1=1, X=1) = 0.51
P(V1=1) = 0.88
0.12 * (0.28 - 0.72) 0.88 * (0.51 - 0.94) = -0.43
-0.43 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 99%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 65%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 56%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 20%. For managers who don't sign termination letters, the probability of director signing the termination letter is 17%. For managers who sign termination letters, the probability of director signing the termination letter is 39%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.20
P(V3=1 | X=0) = 0.17
P(V3=1 | X=1) = 0.39
0.39 * (0.20 - 0.56) + 0.17 * (0.65 - 0.99) = -0.43
-0.43 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 26%. For managers who don't sign termination letters, the probability of large feet is 93%. For managers who sign termination letters, the probability of large feet is 42%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.42
0.26*0.42 - 0.74*0.93 = 0.80
0.80 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 26%. The probability of manager not signing the termination letter and large feet is 68%. The probability of manager signing the termination letter and large feet is 11%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.68
P(Y=1, X=1=1) = 0.11
0.11/0.26 - 0.68/0.74 = -0.51
-0.51 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 26%. The probability of manager not signing the termination letter and large feet is 68%. The probability of manager signing the termination letter and large feet is 11%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.68
P(Y=1, X=1=1) = 0.11
0.11/0.26 - 0.68/0.74 = -0.51
-0.51 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 98%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 63%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 66%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 25%. For managers who don't sign termination letters, the probability of director signing the termination letter is 17%. For managers who sign termination letters, the probability of director signing the termination letter is 41%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.25
P(V3=1 | X=0) = 0.17
P(V3=1 | X=1) = 0.41
0.41 * (0.25 - 0.66) + 0.17 * (0.63 - 0.98) = -0.34
-0.34 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 28%. For managers who don't sign termination letters, the probability of large feet is 92%. For managers who sign termination letters, the probability of large feet is 49%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.28
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.49
0.28*0.49 - 0.72*0.92 = 0.80
0.80 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 28%. The probability of manager not signing the termination letter and large feet is 66%. The probability of manager signing the termination letter and large feet is 14%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.28
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.14
0.14/0.28 - 0.66/0.72 = -0.43
-0.43 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 28%. The probability of manager not signing the termination letter and large feet is 66%. The probability of manager signing the termination letter and large feet is 14%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.28
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.14
0.14/0.28 - 0.66/0.72 = -0.43
-0.43 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 71%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 31%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 85%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 47%. The overall probability of CEO's decision to fire the employee is 91%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.71
P(Y=1 | V1=0, X=1) = 0.31
P(Y=1 | V1=1, X=0) = 0.85
P(Y=1 | V1=1, X=1) = 0.47
P(V1=1) = 0.91
0.09 * (0.31 - 0.71) 0.91 * (0.47 - 0.85) = -0.38
-0.38 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 17%. The probability of manager not signing the termination letter and large feet is 70%. The probability of manager signing the termination letter and large feet is 7%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.70
P(Y=1, X=1=1) = 0.07
0.07/0.17 - 0.70/0.83 = -0.44
-0.44 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13597,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 17%. The probability of manager not signing the termination letter and large feet is 70%. The probability of manager signing the termination letter and large feet is 7%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.70
P(Y=1, X=1=1) = 0.07
0.07/0.17 - 0.70/0.83 = -0.44
-0.44 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13600,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 60%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 10%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 80%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 33%. The overall probability of CEO's decision to fire the employee is 89%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.60
P(Y=1 | V1=0, X=1) = 0.10
P(Y=1 | V1=1, X=0) = 0.80
P(Y=1 | V1=1, X=1) = 0.33
P(V1=1) = 0.89
0.11 * (0.10 - 0.60) 0.89 * (0.33 - 0.80) = -0.47
-0.47 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 25%. The probability of manager not signing the termination letter and large feet is 59%. The probability of manager signing the termination letter and large feet is 6%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.06
0.06/0.25 - 0.59/0.75 = -0.54
-0.54 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 54%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 12%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 71%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 25%. The overall probability of CEO's decision to fire the employee is 90%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.54
P(Y=1 | V1=0, X=1) = 0.12
P(Y=1 | V1=1, X=0) = 0.71
P(Y=1 | V1=1, X=1) = 0.25
P(V1=1) = 0.90
0.10 * (0.12 - 0.54) 0.90 * (0.25 - 0.71) = -0.45
-0.45 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 86%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 47%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 37%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 6%. For managers who don't sign termination letters, the probability of director signing the termination letter is 40%. For managers who sign termination letters, the probability of director signing the termination letter is 52%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.86
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.37
P(Y=1 | X=1, V3=1) = 0.06
P(V3=1 | X=0) = 0.40
P(V3=1 | X=1) = 0.52
0.52 * (0.06 - 0.37) + 0.40 * (0.47 - 0.86) = -0.45
-0.45 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 30%. For managers who don't sign termination letters, the probability of large feet is 73%. For managers who sign termination letters, the probability of large feet is 36%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.30
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.36
0.30*0.36 - 0.70*0.73 = 0.62
0.62 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13625,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 30%. For managers who don't sign termination letters, the probability of large feet is 73%. For managers who sign termination letters, the probability of large feet is 36%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.30
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.36
0.30*0.36 - 0.70*0.73 = 0.62
0.62 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 69%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 30%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 94%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 54%. The overall probability of CEO's decision to fire the employee is 100%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.69
P(Y=1 | V1=0, X=1) = 0.30
P(Y=1 | V1=1, X=0) = 0.94
P(Y=1 | V1=1, X=1) = 0.54
P(V1=1) = 1.00
0.00 * (0.30 - 0.69) 1.00 * (0.54 - 0.94) = -0.40
-0.40 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 99%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 57%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 58%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 19%. For managers who don't sign termination letters, the probability of director signing the termination letter is 12%. For managers who sign termination letters, the probability of director signing the termination letter is 13%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0) = 0.12
P(V3=1 | X=1) = 0.13
0.13 * (0.19 - 0.58) + 0.12 * (0.57 - 0.99) = -0.40
-0.40 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13638,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 25%. For managers who don't sign termination letters, the probability of large feet is 74%. For managers who sign termination letters, the probability of large feet is 35%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.25
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.35
0.25*0.35 - 0.75*0.74 = 0.64
0.64 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 25%. The probability of manager not signing the termination letter and large feet is 55%. The probability of manager signing the termination letter and large feet is 9%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.55
P(Y=1, X=1=1) = 0.09
0.09/0.25 - 0.55/0.75 = -0.39
-0.39 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For managers who don't sign termination letters and directors who don't sign termination letters, the probability of large feet is 96%. For managers who don't sign termination letters and directors who sign termination letters, the probability of large feet is 57%. For managers who sign termination letters and directors who don't sign termination letters, the probability of large feet is 52%. For managers who sign termination letters and directors who sign termination letters, the probability of large feet is 10%. For managers who don't sign termination letters, the probability of director signing the termination letter is 30%. For managers who sign termination letters, the probability of director signing the termination letter is 36%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v} P(V3=v|X=1)*[P(Y=1|X=1,V3=v) - P(Y=1|X=0,V3=v)]
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.10
P(V3=1 | X=0) = 0.30
P(V3=1 | X=1) = 0.36
0.36 * (0.10 - 0.52) + 0.30 * (0.57 - 0.96) = -0.45
-0.45 < 0",diamondcut,firing_employee,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 57%. The probability of manager not signing the termination letter and large feet is 37%. The probability of manager signing the termination letter and large feet is 21%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.21
0.21/0.57 - 0.37/0.43 = -0.47
-0.47 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look at how manager correlates with foot size case by case according to director. Method 2: We look directly at how manager correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 62%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 15%. For CEOs who fire employees and managers who don't sign termination letters, the probability of large feet is 83%. For CEOs who fire employees and managers who sign termination letters, the probability of large feet is 35%. The overall probability of CEO's decision to fire the employee is 94%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.62
P(Y=1 | V1=0, X=1) = 0.15
P(Y=1 | V1=1, X=0) = 0.83
P(Y=1 | V1=1, X=1) = 0.35
P(V1=1) = 0.94
0.06 * (0.15 - 0.62) 0.94 * (0.35 - 0.83) = -0.48
-0.48 < 0",diamondcut,firing_employee,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 14%. For managers who don't sign termination letters, the probability of large feet is 83%. For managers who sign termination letters, the probability of large feet is 29%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.29
0.14*0.29 - 0.86*0.83 = 0.75
0.75 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 14%. For managers who don't sign termination letters, the probability of large feet is 83%. For managers who sign termination letters, the probability of large feet is 29%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.29
0.14*0.29 - 0.86*0.83 = 0.75
0.75 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 14%. The probability of manager not signing the termination letter and large feet is 71%. The probability of manager signing the termination letter and large feet is 4%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.71
P(Y=1, X=1=1) = 0.04
0.04/0.14 - 0.71/0.86 = -0.54
-0.54 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 14%. The probability of manager not signing the termination letter and large feet is 71%. The probability of manager signing the termination letter and large feet is 4%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.71
P(Y=1, X=1=1) = 0.04
0.04/0.14 - 0.71/0.86 = -0.54
-0.54 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. Method 1: We look directly at how manager correlates with foot size in general. Method 2: We look at this correlation case by case according to director.",no,"nan
nan
nan
nan
nan
nan
nan",diamondcut,firing_employee,2,backadj,[backdoor adjustment set for Y given X]
13674,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 17%. For managers who don't sign termination letters, the probability of large feet is 93%. For managers who sign termination letters, the probability of large feet is 36%.",yes,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.36
0.17*0.36 - 0.83*0.93 = 0.83
0.83 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 17%. For managers who don't sign termination letters, the probability of large feet is 93%. For managers who sign termination letters, the probability of large feet is 36%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.36
0.17*0.36 - 0.83*0.93 = 0.83
0.83 > 0",diamondcut,firing_employee,1,marginal,P(Y)
13676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and manager. Manager has a direct effect on foot size. Director has a direct effect on foot size. The overall probability of manager signing the termination letter is 17%. The probability of manager not signing the termination letter and large feet is 76%. The probability of manager signing the termination letter and large feet is 6%.",no,"Let V1 = CEO; V3 = director; X = manager; Y = foot size.
V1->V3,V1->X,X->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.06
0.06/0.17 - 0.76/0.83 = -0.56
-0.56 < 0",diamondcut,firing_employee,1,correlation,P(Y | X)
13680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 40%. For people who have visited England, the probability of the prisoner's death is 78%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.78
0.78 - 0.40 = 0.38
0.38 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 40%. For people who have visited England, the probability of the prisoner's death is 78%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.78
0.78 - 0.40 = 0.38
0.38 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 40%. For people who have visited England, the probability of the prisoner's death is 78%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.78
0.78 - 0.40 = 0.38
0.38 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 40%. For people who have visited England, the probability of the prisoner's death is 78%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.78
0.78 - 0.40 = 0.38
0.38 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13692,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 22%. For people who have visited England, the probability of the prisoner's death is 68%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.68
0.68 - 0.22 = 0.46
0.46 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 22%. For people who have visited England, the probability of the prisoner's death is 68%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.68
0.68 - 0.22 = 0.46
0.46 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 22%. For people who have visited England, the probability of the prisoner's death is 68%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.68
0.68 - 0.22 = 0.46
0.46 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 34%. For people who have visited England, the probability of the prisoner's death is 73%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.73
0.73 - 0.34 = 0.39
0.39 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 34%. For people who have visited England, the probability of the prisoner's death is 73%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.73
0.73 - 0.34 = 0.39
0.39 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 34%. For people who have visited England, the probability of the prisoner's death is 73%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.73
0.73 - 0.34 = 0.39
0.39 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 13%. For people who have not visited England, the probability of the prisoner's death is 34%. For people who have visited England, the probability of the prisoner's death is 73%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.73
0.13*0.73 - 0.87*0.34 = 0.40
0.40 > 0",diamond,firing_squad,1,marginal,P(Y)
13711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 13%. For people who have not visited England, the probability of the prisoner's death is 34%. For people who have visited England, the probability of the prisoner's death is 73%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.73
0.13*0.73 - 0.87*0.34 = 0.40
0.40 > 0",diamond,firing_squad,1,marginal,P(Y)
13714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 31%. For people who have visited England, the probability of the prisoner's death is 66%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.66
0.66 - 0.31 = 0.36
0.36 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 28%. For people who have visited England, the probability of the prisoner's death is 75%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.75
0.75 - 0.28 = 0.47
0.47 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13736,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 16%. The probability of not having visited England and the prisoner's death is 24%. The probability of having visited England and the prisoner's death is 12%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.12
0.12/0.16 - 0.24/0.84 = 0.47
0.47 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 16%. The probability of not having visited England and the prisoner's death is 24%. The probability of having visited England and the prisoner's death is 12%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.12
0.12/0.16 - 0.24/0.84 = 0.47
0.47 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 21%. For people who have visited England, the probability of the prisoner's death is 66%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.21
P(Y=1 | X=1) = 0.66
0.66 - 0.21 = 0.45
0.45 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 57%. The probability of not having visited England and the prisoner's death is 9%. The probability of having visited England and the prisoner's death is 38%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.38
0.38/0.57 - 0.09/0.43 = 0.45
0.45 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 33%. For people who have visited England, the probability of the prisoner's death is 81%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.81
0.81 - 0.33 = 0.48
0.48 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 33%. For people who have visited England, the probability of the prisoner's death is 81%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.81
0.81 - 0.33 = 0.48
0.48 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 18%. For people who have not visited England, the probability of the prisoner's death is 33%. For people who have visited England, the probability of the prisoner's death is 81%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.81
0.18*0.81 - 0.82*0.33 = 0.42
0.42 > 0",diamond,firing_squad,1,marginal,P(Y)
13761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 18%. The probability of not having visited England and the prisoner's death is 27%. The probability of having visited England and the prisoner's death is 15%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.15
0.15/0.18 - 0.27/0.82 = 0.48
0.48 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 24%. For people who have visited England, the probability of the prisoner's death is 74%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.74
0.74 - 0.24 = 0.50
0.50 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 24%. For people who have visited England, the probability of the prisoner's death is 74%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.74
0.74 - 0.24 = 0.50
0.50 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 80%. For people who have not visited England, the probability of the prisoner's death is 24%. For people who have visited England, the probability of the prisoner's death is 74%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.74
0.80*0.74 - 0.20*0.24 = 0.63
0.63 > 0",diamond,firing_squad,1,marginal,P(Y)
13774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 32%. For people who have visited England, the probability of the prisoner's death is 75%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.75
0.75 - 0.32 = 0.43
0.43 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 32%. For people who have visited England, the probability of the prisoner's death is 75%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.75
0.75 - 0.32 = 0.43
0.43 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 32%. For people who have visited England, the probability of the prisoner's death is 75%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.75
0.75 - 0.32 = 0.43
0.43 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 32%. For people who have visited England, the probability of the prisoner's death is 75%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.75
0.75 - 0.32 = 0.43
0.43 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 19%. For people who have not visited England, the probability of the prisoner's death is 32%. For people who have visited England, the probability of the prisoner's death is 75%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.75
0.19*0.75 - 0.81*0.32 = 0.40
0.40 > 0",diamond,firing_squad,1,marginal,P(Y)
13785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 19%. The probability of not having visited England and the prisoner's death is 26%. The probability of having visited England and the prisoner's death is 14%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.14
0.14/0.19 - 0.26/0.81 = 0.43
0.43 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 28%. For people who have visited England, the probability of the prisoner's death is 62%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.62
0.62 - 0.28 = 0.34
0.34 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 28%. For people who have visited England, the probability of the prisoner's death is 62%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.62
0.62 - 0.28 = 0.34
0.34 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 28%. For people who have visited England, the probability of the prisoner's death is 62%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.62
0.62 - 0.28 = 0.34
0.34 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 78%. The probability of not having visited England and the prisoner's death is 6%. The probability of having visited England and the prisoner's death is 49%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.78
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.49
0.49/0.78 - 0.06/0.22 = 0.34
0.34 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 78%. The probability of not having visited England and the prisoner's death is 6%. The probability of having visited England and the prisoner's death is 49%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.78
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.49
0.49/0.78 - 0.06/0.22 = 0.34
0.34 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 11%. For people who have visited England, the probability of the prisoner's death is 55%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.55
0.55 - 0.11 = 0.43
0.43 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 11%. For people who have visited England, the probability of the prisoner's death is 55%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.55
0.55 - 0.11 = 0.43
0.43 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 11%. For people who have visited England, the probability of the prisoner's death is 55%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.55
0.55 - 0.11 = 0.43
0.43 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 11%. For people who have visited England, the probability of the prisoner's death is 55%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.55
0.55 - 0.11 = 0.43
0.43 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 7%. For people who have not visited England, the probability of the prisoner's death is 11%. For people who have visited England, the probability of the prisoner's death is 55%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.55
0.07*0.55 - 0.93*0.11 = 0.15
0.15 > 0",diamond,firing_squad,1,marginal,P(Y)
13811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 49%. The probability of not having visited England and the prisoner's death is 6%. The probability of having visited England and the prisoner's death is 30%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.30
0.30/0.49 - 0.06/0.51 = 0.50
0.50 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 36%. For people who have visited England, the probability of the prisoner's death is 72%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.72
0.72 - 0.36 = 0.36
0.36 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 36%. For people who have visited England, the probability of the prisoner's death is 72%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.72
0.72 - 0.36 = 0.36
0.36 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 36%. For people who have visited England, the probability of the prisoner's death is 72%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.72
0.72 - 0.36 = 0.36
0.36 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 20%. For people who have visited England, the probability of the prisoner's death is 74%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.74
0.74 - 0.20 = 0.53
0.53 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 20%. For people who have visited England, the probability of the prisoner's death is 74%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.74
0.74 - 0.20 = 0.53
0.53 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 43%. For people who have not visited England, the probability of the prisoner's death is 20%. For people who have visited England, the probability of the prisoner's death is 74%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.74
0.43*0.74 - 0.57*0.20 = 0.43
0.43 > 0",diamond,firing_squad,1,marginal,P(Y)
13843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 43%. For people who have not visited England, the probability of the prisoner's death is 20%. For people who have visited England, the probability of the prisoner's death is 74%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.74
0.43*0.74 - 0.57*0.20 = 0.43
0.43 > 0",diamond,firing_squad,1,marginal,P(Y)
13844,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 43%. The probability of not having visited England and the prisoner's death is 12%. The probability of having visited England and the prisoner's death is 31%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.31
0.31/0.43 - 0.12/0.57 = 0.53
0.53 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 43%. The probability of not having visited England and the prisoner's death is 12%. The probability of having visited England and the prisoner's death is 31%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.31
0.31/0.43 - 0.12/0.57 = 0.53
0.53 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 19%. For people who have visited England, the probability of the prisoner's death is 73%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.73
0.73 - 0.19 = 0.54
0.54 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 19%. For people who have visited England, the probability of the prisoner's death is 73%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.73
0.73 - 0.19 = 0.54
0.54 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 19%. For people who have not visited England, the probability of the prisoner's death is 19%. For people who have visited England, the probability of the prisoner's death is 73%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.73
0.19*0.73 - 0.81*0.19 = 0.29
0.29 > 0",diamond,firing_squad,1,marginal,P(Y)
13858,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13862,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 12%. For people who have visited England, the probability of the prisoner's death is 57%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.57
0.57 - 0.12 = 0.45
0.45 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 12%. For people who have visited England, the probability of the prisoner's death is 57%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.57
0.57 - 0.12 = 0.45
0.45 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 48%. The probability of not having visited England and the prisoner's death is 6%. The probability of having visited England and the prisoner's death is 28%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.28
0.28/0.48 - 0.06/0.52 = 0.45
0.45 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13871,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 36%. For people who have visited England, the probability of the prisoner's death is 83%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.83
0.83 - 0.36 = 0.47
0.47 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13873,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 36%. For people who have visited England, the probability of the prisoner's death is 83%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.83
0.83 - 0.36 = 0.47
0.47 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 36%. For people who have visited England, the probability of the prisoner's death is 83%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.83
0.83 - 0.36 = 0.47
0.47 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13877,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 36%. For people who have visited England, the probability of the prisoner's death is 83%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.83
0.83 - 0.36 = 0.47
0.47 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13878,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 12%. For people who have not visited England, the probability of the prisoner's death is 36%. For people who have visited England, the probability of the prisoner's death is 83%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.83
0.12*0.83 - 0.88*0.36 = 0.42
0.42 > 0",diamond,firing_squad,1,marginal,P(Y)
13880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 12%. The probability of not having visited England and the prisoner's death is 32%. The probability of having visited England and the prisoner's death is 10%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.10
0.10/0.12 - 0.32/0.88 = 0.47
0.47 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 30%. For people who have visited England, the probability of the prisoner's death is 69%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.69
0.69 - 0.30 = 0.39
0.39 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 30%. For people who have visited England, the probability of the prisoner's death is 69%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.69
0.69 - 0.30 = 0.39
0.39 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 30%. For people who have visited England, the probability of the prisoner's death is 69%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.69
0.69 - 0.30 = 0.39
0.39 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 30%. For people who have visited England, the probability of the prisoner's death is 69%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.69
0.69 - 0.30 = 0.39
0.39 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13892,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 66%. The probability of not having visited England and the prisoner's death is 10%. The probability of having visited England and the prisoner's death is 45%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.45
0.45/0.66 - 0.10/0.34 = 0.39
0.39 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 66%. The probability of not having visited England and the prisoner's death is 10%. The probability of having visited England and the prisoner's death is 45%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.45
0.45/0.66 - 0.10/0.34 = 0.39
0.39 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13897,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 33%. For people who have visited England, the probability of the prisoner's death is 89%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.89
0.89 - 0.33 = 0.56
0.56 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13900,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 33%. For people who have visited England, the probability of the prisoner's death is 89%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.89
0.89 - 0.33 = 0.56
0.56 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 14%. For people who have not visited England, the probability of the prisoner's death is 33%. For people who have visited England, the probability of the prisoner's death is 89%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.89
0.14*0.89 - 0.86*0.33 = 0.41
0.41 > 0",diamond,firing_squad,1,marginal,P(Y)
13906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 20%. For people who have visited England, the probability of the prisoner's death is 60%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.60
0.60 - 0.20 = 0.40
0.40 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13913,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 20%. For people who have visited England, the probability of the prisoner's death is 60%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.60
0.60 - 0.20 = 0.40
0.40 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 32%. For people who have visited England, the probability of the prisoner's death is 86%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.86
0.86 - 0.32 = 0.55
0.55 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13929,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 8%. The probability of not having visited England and the prisoner's death is 29%. The probability of having visited England and the prisoner's death is 7%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.07
0.07/0.08 - 0.29/0.92 = 0.55
0.55 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13934,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 31%. For people who have visited England, the probability of the prisoner's death is 68%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.68
0.68 - 0.31 = 0.37
0.37 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 69%. The probability of not having visited England and the prisoner's death is 10%. The probability of having visited England and the prisoner's death is 47%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.69
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.47
0.47/0.69 - 0.10/0.31 = 0.37
0.37 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 29%. For people who have visited England, the probability of the prisoner's death is 81%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.81
0.81 - 0.29 = 0.51
0.51 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 29%. For people who have visited England, the probability of the prisoner's death is 81%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.81
0.81 - 0.29 = 0.51
0.51 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 16%. For people who have not visited England, the probability of the prisoner's death is 29%. For people who have visited England, the probability of the prisoner's death is 81%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.81
0.16*0.81 - 0.84*0.29 = 0.37
0.37 > 0",diamond,firing_squad,1,marginal,P(Y)
13951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 16%. For people who have not visited England, the probability of the prisoner's death is 29%. For people who have visited England, the probability of the prisoner's death is 81%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.81
0.16*0.81 - 0.84*0.29 = 0.37
0.37 > 0",diamond,firing_squad,1,marginal,P(Y)
13956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 23%. For people who have visited England, the probability of the prisoner's death is 64%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.64
0.64 - 0.23 = 0.41
0.41 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 23%. For people who have visited England, the probability of the prisoner's death is 64%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.64
0.64 - 0.23 = 0.41
0.41 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 23%. For people who have visited England, the probability of the prisoner's death is 64%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.64
0.64 - 0.23 = 0.41
0.41 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 23%. For people who have visited England, the probability of the prisoner's death is 64%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.64
0.64 - 0.23 = 0.41
0.41 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
13962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 69%. For people who have not visited England, the probability of the prisoner's death is 23%. For people who have visited England, the probability of the prisoner's death is 64%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.69
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.64
0.69*0.64 - 0.31*0.23 = 0.51
0.51 > 0",diamond,firing_squad,1,marginal,P(Y)
13963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 69%. For people who have not visited England, the probability of the prisoner's death is 23%. For people who have visited England, the probability of the prisoner's death is 64%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.69
P(Y=1 | X=0) = 0.23
P(Y=1 | X=1) = 0.64
0.69*0.64 - 0.31*0.23 = 0.51
0.51 > 0",diamond,firing_squad,1,marginal,P(Y)
13966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13970,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 34%. For people who have visited England, the probability of the prisoner's death is 79%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.79
0.79 - 0.34 = 0.45
0.45 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13974,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 13%. For people who have not visited England, the probability of the prisoner's death is 34%. For people who have visited England, the probability of the prisoner's death is 79%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.79
0.13*0.79 - 0.87*0.34 = 0.40
0.40 > 0",diamond,firing_squad,1,marginal,P(Y)
13978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 27%. For people who have visited England, the probability of the prisoner's death is 63%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.63
0.63 - 0.27 = 0.36
0.36 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
13982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 27%. For people who have visited England, the probability of the prisoner's death is 63%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.63
0.63 - 0.27 = 0.36
0.36 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
13986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 53%. For people who have not visited England, the probability of the prisoner's death is 27%. For people who have visited England, the probability of the prisoner's death is 63%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.63
0.53*0.63 - 0.47*0.27 = 0.46
0.46 > 0",diamond,firing_squad,1,marginal,P(Y)
13988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 53%. The probability of not having visited England and the prisoner's death is 13%. The probability of having visited England and the prisoner's death is 33%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.33
0.33/0.53 - 0.13/0.47 = 0.36
0.36 > 0",diamond,firing_squad,1,correlation,P(Y | X)
13991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
13996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 29%. For people who have visited England, the probability of the prisoner's death is 73%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.73
0.73 - 0.29 = 0.44
0.44 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 8%. The probability of not having visited England and the prisoner's death is 27%. The probability of having visited England and the prisoner's death is 6%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.06
0.06/0.08 - 0.27/0.92 = 0.44
0.44 > 0",diamond,firing_squad,1,correlation,P(Y | X)
14003,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look directly at how having visited England correlates with prisoner in general. Method 2: We look at this correlation case by case according to the private.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
14005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 31%. For people who have visited England, the probability of the prisoner's death is 72%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.72
0.72 - 0.31 = 0.41
0.41 > 0",diamond,firing_squad,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14006,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 31%. For people who have visited England, the probability of the prisoner's death is 72%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.72
0.72 - 0.31 = 0.41
0.41 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 31%. For people who have visited England, the probability of the prisoner's death is 72%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.72
0.72 - 0.31 = 0.41
0.41 > 0",diamond,firing_squad,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 71%. For people who have not visited England, the probability of the prisoner's death is 31%. For people who have visited England, the probability of the prisoner's death is 72%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.72
0.71*0.72 - 0.29*0.31 = 0.60
0.60 > 0",diamond,firing_squad,1,marginal,P(Y)
14014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
14018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. For people who have not visited England, the probability of the prisoner's death is 7%. For people who have visited England, the probability of the prisoner's death is 47%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.47
0.47 - 0.07 = 0.40
0.40 > 0",diamond,firing_squad,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14022,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 80%. For people who have not visited England, the probability of the prisoner's death is 7%. For people who have visited England, the probability of the prisoner's death is 47%.",no,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.47
0.80*0.47 - 0.20*0.07 = 0.39
0.39 > 0",diamond,firing_squad,1,marginal,P(Y)
14023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 80%. For people who have not visited England, the probability of the prisoner's death is 7%. For people who have visited England, the probability of the prisoner's death is 47%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.47
0.80*0.47 - 0.20*0.07 = 0.39
0.39 > 0",diamond,firing_squad,1,marginal,P(Y)
14035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. The overall probability of having visited England is 17%. For people who have not visited England, the probability of the prisoner's death is 37%. For people who have visited England, the probability of the prisoner's death is 69%.",yes,"Let X = having visited England; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.69
0.17*0.69 - 0.83*0.37 = 0.43
0.43 > 0",diamond,firing_squad,1,marginal,P(Y)
14038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. Method 1: We look at how having visited England correlates with prisoner case by case according to the private. Method 2: We look directly at how having visited England correlates with prisoner in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,firing_squad,2,backadj,[backdoor adjustment set for Y given X]
14040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 34%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.34
0.34 - 0.46 = -0.12
-0.12 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 34%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.34
0.34 - 0.46 = -0.12
-0.12 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 34%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.34
0.34 - 0.46 = -0.12
-0.12 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 80%. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 34%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.34
0.80*0.34 - 0.20*0.46 = 0.37
0.37 > 0",diamond,floor_wet,1,marginal,P(Y)
14047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 80%. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 34%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.34
0.80*0.34 - 0.20*0.46 = 0.37
0.37 > 0",diamond,floor_wet,1,marginal,P(Y)
14049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 80%. The probability of dry season and high rainfall is 9%. The probability of rainy season and high rainfall is 28%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.80
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.28
0.28/0.80 - 0.09/0.20 = -0.12
-0.12 < 0",diamond,floor_wet,1,correlation,P(Y | X)
14050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14052,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 40%. For in the rainy season, the probability of high rainfall is 50%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.50
0.50 - 0.40 = 0.10
0.10 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 40%. For in the rainy season, the probability of high rainfall is 50%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.50
0.50 - 0.40 = 0.10
0.10 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 40%. For in the rainy season, the probability of high rainfall is 50%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.50
0.50 - 0.40 = 0.10
0.10 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 89%. The probability of dry season and high rainfall is 5%. The probability of rainy season and high rainfall is 44%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.44
0.44/0.89 - 0.05/0.11 = 0.10
0.10 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 55%. For in the rainy season, the probability of high rainfall is 54%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.54
0.54 - 0.55 = -0.02
-0.02 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14070,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 85%. For people in the dry season, the probability of high rainfall is 55%. For in the rainy season, the probability of high rainfall is 54%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.54
0.85*0.54 - 0.15*0.55 = 0.54
0.54 > 0",diamond,floor_wet,1,marginal,P(Y)
14071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 85%. For people in the dry season, the probability of high rainfall is 55%. For in the rainy season, the probability of high rainfall is 54%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.54
0.85*0.54 - 0.15*0.55 = 0.54
0.54 > 0",diamond,floor_wet,1,marginal,P(Y)
14080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 62%. For in the rainy season, the probability of high rainfall is 69%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.69
0.69 - 0.62 = 0.07
0.07 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 93%. For people in the dry season, the probability of high rainfall is 62%. For in the rainy season, the probability of high rainfall is 69%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.69
0.93*0.69 - 0.07*0.62 = 0.68
0.68 > 0",diamond,floor_wet,1,marginal,P(Y)
14083,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 93%. For people in the dry season, the probability of high rainfall is 62%. For in the rainy season, the probability of high rainfall is 69%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.69
0.93*0.69 - 0.07*0.62 = 0.68
0.68 > 0",diamond,floor_wet,1,marginal,P(Y)
14084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 93%. The probability of dry season and high rainfall is 5%. The probability of rainy season and high rainfall is 64%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.64
0.64/0.93 - 0.05/0.07 = 0.07
0.07 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14086,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 38%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.38
0.38 - 0.41 = -0.03
-0.03 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 38%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.38
0.38 - 0.41 = -0.03
-0.03 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14092,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 38%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.38
0.38 - 0.41 = -0.03
-0.03 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14093,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 38%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.38
0.38 - 0.41 = -0.03
-0.03 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14094,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 98%. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 38%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.38
0.98*0.38 - 0.02*0.41 = 0.38
0.38 > 0",diamond,floor_wet,1,marginal,P(Y)
14095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 98%. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 38%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.38
0.98*0.38 - 0.02*0.41 = 0.38
0.38 > 0",diamond,floor_wet,1,marginal,P(Y)
14096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 98%. The probability of dry season and high rainfall is 1%. The probability of rainy season and high rainfall is 37%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.37
0.37/0.98 - 0.01/0.02 = -0.03
-0.03 < 0",diamond,floor_wet,1,correlation,P(Y | X)
14097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 98%. The probability of dry season and high rainfall is 1%. The probability of rainy season and high rainfall is 37%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.37
0.37/0.98 - 0.01/0.02 = -0.03
-0.03 < 0",diamond,floor_wet,1,correlation,P(Y | X)
14103,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 44%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.44
0.44 - 0.46 = -0.02
-0.02 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 86%. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 44%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.44
0.86*0.44 - 0.14*0.46 = 0.45
0.45 > 0",diamond,floor_wet,1,marginal,P(Y)
14113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 55%. For in the rainy season, the probability of high rainfall is 60%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.60
0.60 - 0.55 = 0.05
0.05 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 87%. For people in the dry season, the probability of high rainfall is 55%. For in the rainy season, the probability of high rainfall is 60%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.60
0.87*0.60 - 0.13*0.55 = 0.59
0.59 > 0",diamond,floor_wet,1,marginal,P(Y)
14119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 87%. For people in the dry season, the probability of high rainfall is 55%. For in the rainy season, the probability of high rainfall is 60%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.60
0.87*0.60 - 0.13*0.55 = 0.59
0.59 > 0",diamond,floor_wet,1,marginal,P(Y)
14122,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 45%. For in the rainy season, the probability of high rainfall is 47%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.47
0.47 - 0.45 = 0.02
0.02 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 51%. For in the rainy season, the probability of high rainfall is 51%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.51
0.51 - 0.51 = 0.01
0.01 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 51%. For in the rainy season, the probability of high rainfall is 51%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.51
0.51 - 0.51 = 0.01
0.01 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 51%. For in the rainy season, the probability of high rainfall is 51%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.51
0.51 - 0.51 = 0.01
0.01 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14143,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 90%. For people in the dry season, the probability of high rainfall is 51%. For in the rainy season, the probability of high rainfall is 51%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.51
0.90*0.51 - 0.10*0.51 = 0.51
0.51 > 0",diamond,floor_wet,1,marginal,P(Y)
14144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 90%. The probability of dry season and high rainfall is 5%. The probability of rainy season and high rainfall is 46%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.46
0.46/0.90 - 0.05/0.10 = 0.01
0.01 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 65%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.65
0.65 - 0.54 = 0.11
0.11 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 90%. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 65%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.65
0.90*0.65 - 0.10*0.54 = 0.64
0.64 > 0",diamond,floor_wet,1,marginal,P(Y)
14159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14162,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 57%. For in the rainy season, the probability of high rainfall is 58%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.58
0.58 - 0.57 = 0.01
0.01 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 57%. For in the rainy season, the probability of high rainfall is 58%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.58
0.58 - 0.57 = 0.01
0.01 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 90%. For people in the dry season, the probability of high rainfall is 57%. For in the rainy season, the probability of high rainfall is 58%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.58
0.90*0.58 - 0.10*0.57 = 0.58
0.58 > 0",diamond,floor_wet,1,marginal,P(Y)
14169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 90%. The probability of dry season and high rainfall is 6%. The probability of rainy season and high rainfall is 53%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.53
0.53/0.90 - 0.06/0.10 = 0.01
0.01 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 96%. The probability of dry season and high rainfall is 1%. The probability of rainy season and high rainfall is 38%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.38
0.38/0.96 - 0.01/0.04 = -0.01
-0.01 < 0",diamond,floor_wet,1,correlation,P(Y | X)
14182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 52%. For in the rainy season, the probability of high rainfall is 58%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.58
0.58 - 0.52 = 0.06
0.06 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 52%. For in the rainy season, the probability of high rainfall is 58%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.58
0.58 - 0.52 = 0.06
0.06 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14192,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 87%. The probability of dry season and high rainfall is 7%. The probability of rainy season and high rainfall is 50%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.87
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.50
0.50/0.87 - 0.07/0.13 = 0.06
0.06 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14197,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 47%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.47
0.47 - 0.46 = 0.01
0.01 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 47%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.47
0.47 - 0.46 = 0.01
0.01 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14209,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 43%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.43
0.43 - 0.54 = -0.11
-0.11 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14211,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 43%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.43
0.43 - 0.54 = -0.11
-0.11 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 43%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.43
0.43 - 0.54 = -0.11
-0.11 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 43%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.43
0.43 - 0.54 = -0.11
-0.11 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 84%. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 43%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.43
0.84*0.43 - 0.16*0.54 = 0.45
0.45 > 0",diamond,floor_wet,1,marginal,P(Y)
14215,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 84%. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 43%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.43
0.84*0.43 - 0.16*0.54 = 0.45
0.45 > 0",diamond,floor_wet,1,marginal,P(Y)
14216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 84%. The probability of dry season and high rainfall is 9%. The probability of rainy season and high rainfall is 36%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.36
0.36/0.84 - 0.09/0.16 = -0.11
-0.11 < 0",diamond,floor_wet,1,correlation,P(Y | X)
14222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 36%. For in the rainy season, the probability of high rainfall is 35%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.35
0.35 - 0.36 = -0.01
-0.01 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 87%. For people in the dry season, the probability of high rainfall is 36%. For in the rainy season, the probability of high rainfall is 35%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.35
0.87*0.35 - 0.13*0.36 = 0.35
0.35 > 0",diamond,floor_wet,1,marginal,P(Y)
14230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 50%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.50
0.50 - 0.41 = 0.09
0.09 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 50%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.50
0.50 - 0.41 = 0.09
0.09 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 50%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.50
0.50 - 0.41 = 0.09
0.09 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 50%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.50
0.50 - 0.41 = 0.09
0.09 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 89%. For people in the dry season, the probability of high rainfall is 41%. For in the rainy season, the probability of high rainfall is 50%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.50
0.89*0.50 - 0.11*0.41 = 0.49
0.49 > 0",diamond,floor_wet,1,marginal,P(Y)
14240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 89%. The probability of dry season and high rainfall is 4%. The probability of rainy season and high rainfall is 45%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.45
0.45/0.89 - 0.04/0.11 = 0.09
0.09 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 43%. For in the rainy season, the probability of high rainfall is 53%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.53
0.53 - 0.43 = 0.09
0.09 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 64%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.64
0.64 - 0.46 = 0.18
0.18 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 64%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.64
0.64 - 0.46 = 0.18
0.18 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 64%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.64
0.64 - 0.46 = 0.18
0.18 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 64%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.64
0.64 - 0.46 = 0.18
0.18 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 64%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.64
0.64 - 0.46 = 0.18
0.18 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14262,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 95%. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 64%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.64
0.95*0.64 - 0.05*0.46 = 0.63
0.63 > 0",diamond,floor_wet,1,marginal,P(Y)
14267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 40%. For in the rainy season, the probability of high rainfall is 41%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.41
0.41 - 0.40 = 0.01
0.01 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 40%. For in the rainy season, the probability of high rainfall is 41%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.41
0.41 - 0.40 = 0.01
0.01 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 40%. For in the rainy season, the probability of high rainfall is 41%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.41
0.41 - 0.40 = 0.01
0.01 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 85%. For people in the dry season, the probability of high rainfall is 40%. For in the rainy season, the probability of high rainfall is 41%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.41
0.85*0.41 - 0.15*0.40 = 0.41
0.41 > 0",diamond,floor_wet,1,marginal,P(Y)
14277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 85%. The probability of dry season and high rainfall is 6%. The probability of rainy season and high rainfall is 35%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.35
0.35/0.85 - 0.06/0.15 = 0.01
0.01 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14280,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 57%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.57
0.57 - 0.46 = 0.11
0.11 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14282,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 57%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.57
0.57 - 0.46 = 0.11
0.11 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 57%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.57
0.57 - 0.46 = 0.11
0.11 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 46%. For in the rainy season, the probability of high rainfall is 57%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.57
0.57 - 0.46 = 0.11
0.11 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 99%. The probability of dry season and high rainfall is 1%. The probability of rainy season and high rainfall is 57%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.57
0.57/0.99 - 0.01/0.01 = 0.11
0.11 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 99%. The probability of dry season and high rainfall is 1%. The probability of rainy season and high rainfall is 57%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.57
0.57/0.99 - 0.01/0.01 = 0.11
0.11 > 0",diamond,floor_wet,1,correlation,P(Y | X)
14290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 66%. For in the rainy season, the probability of high rainfall is 62%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.62
0.62 - 0.66 = -0.04
-0.04 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 66%. For in the rainy season, the probability of high rainfall is 62%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.62
0.62 - 0.66 = -0.04
-0.04 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 66%. For in the rainy season, the probability of high rainfall is 62%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.62
0.62 - 0.66 = -0.04
-0.04 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 66%. For in the rainy season, the probability of high rainfall is 62%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.62
0.62 - 0.66 = -0.04
-0.04 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 66%. For in the rainy season, the probability of high rainfall is 62%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.62
0.62 - 0.66 = -0.04
-0.04 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14298,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 96%. For people in the dry season, the probability of high rainfall is 66%. For in the rainy season, the probability of high rainfall is 62%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.62
0.96*0.62 - 0.04*0.66 = 0.62
0.62 > 0",diamond,floor_wet,1,marginal,P(Y)
14304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 36%. For in the rainy season, the probability of high rainfall is 38%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.38
0.38 - 0.36 = 0.02
0.02 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 36%. For in the rainy season, the probability of high rainfall is 38%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.38
0.38 - 0.36 = 0.02
0.02 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 36%. For in the rainy season, the probability of high rainfall is 38%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.38
0.38 - 0.36 = 0.02
0.02 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 36%. For in the rainy season, the probability of high rainfall is 38%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.38
0.38 - 0.36 = 0.02
0.02 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14310,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 97%. For people in the dry season, the probability of high rainfall is 36%. For in the rainy season, the probability of high rainfall is 38%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.38
0.97*0.38 - 0.03*0.36 = 0.38
0.38 > 0",diamond,floor_wet,1,marginal,P(Y)
14316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 43%. For in the rainy season, the probability of high rainfall is 39%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.39
0.39 - 0.43 = -0.04
-0.04 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 95%. The probability of dry season and high rainfall is 2%. The probability of rainy season and high rainfall is 37%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.37
0.37/0.95 - 0.02/0.05 = -0.04
-0.04 < 0",diamond,floor_wet,1,correlation,P(Y | X)
14327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 50%. For in the rainy season, the probability of high rainfall is 51%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.51
0.51 - 0.50 = 0.01
0.01 > 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 50%. For in the rainy season, the probability of high rainfall is 51%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.51
0.51 - 0.50 = 0.01
0.01 > 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 50%. For in the rainy season, the probability of high rainfall is 51%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.51
0.51 - 0.50 = 0.01
0.01 > 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14335,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 83%. For people in the dry season, the probability of high rainfall is 50%. For in the rainy season, the probability of high rainfall is 51%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.51
0.83*0.51 - 0.17*0.50 = 0.51
0.51 > 0",diamond,floor_wet,1,marginal,P(Y)
14339,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 52%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.52
0.52 - 0.56 = -0.04
-0.04 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 52%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.52
0.52 - 0.56 = -0.04
-0.04 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 52%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.52
0.52 - 0.56 = -0.04
-0.04 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 52%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.52
0.52 - 0.56 = -0.04
-0.04 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 45%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.45
0.45 - 0.56 = -0.11
-0.11 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 45%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.45
0.45 - 0.56 = -0.11
-0.11 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 45%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.45
0.45 - 0.56 = -0.11
-0.11 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14360,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 82%. The probability of dry season and high rainfall is 10%. The probability of rainy season and high rainfall is 37%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.37
0.37/0.82 - 0.10/0.18 = -0.11
-0.11 < 0",diamond,floor_wet,1,correlation,P(Y | X)
14362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14365,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 43%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.43
0.43 - 0.56 = -0.13
-0.13 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 43%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.43
0.43 - 0.56 = -0.13
-0.13 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 43%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.43
0.43 - 0.56 = -0.13
-0.13 < 0",diamond,floor_wet,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 43%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.43
0.43 - 0.56 = -0.13
-0.13 < 0",diamond,floor_wet,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
14370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 93%. For people in the dry season, the probability of high rainfall is 56%. For in the rainy season, the probability of high rainfall is 43%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.43
0.93*0.43 - 0.07*0.56 = 0.44
0.44 > 0",diamond,floor_wet,1,marginal,P(Y)
14374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 49%. For in the rainy season, the probability of high rainfall is 49%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.49 - 0.49 = -0.00
0.00 = 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 49%. For in the rainy season, the probability of high rainfall is 49%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.49 - 0.49 = -0.00
0.00 = 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 95%. For people in the dry season, the probability of high rainfall is 49%. For in the rainy season, the probability of high rainfall is 49%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.95*0.49 - 0.05*0.49 = 0.49
0.49 > 0",diamond,floor_wet,1,marginal,P(Y)
14385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 95%. The probability of dry season and high rainfall is 2%. The probability of rainy season and high rainfall is 46%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.46
0.46/0.95 - 0.02/0.05 = -0.00
0.00 = 0",diamond,floor_wet,1,correlation,P(Y | X)
14386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look at how season correlates with rainfall case by case according to sprinkler. Method 2: We look directly at how season correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. For people in the dry season, the probability of high rainfall is 54%. For in the rainy season, the probability of high rainfall is 54%.",no,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.54
0.54 - 0.54 = -0.01
-0.01 < 0",diamond,floor_wet,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. The overall probability of rainy season is 85%. The probability of dry season and high rainfall is 8%. The probability of rainy season and high rainfall is 45%.",yes,"Let X = season; V3 = sprinkler; V2 = weather; Y = rainfall.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.45
0.45/0.85 - 0.08/0.15 = -0.01
-0.01 < 0",diamond,floor_wet,1,correlation,P(Y | X)
14399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Season has a direct effect on sprinkler and weather. Weather has a direct effect on rainfall. Sprinkler has a direct effect on rainfall. Method 1: We look directly at how season correlates with rainfall in general. Method 2: We look at this correlation case by case according to sprinkler.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,floor_wet,2,backadj,[backdoor adjustment set for Y given X]
14402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 70%. For people who speak english, the probability of the forest on fire is 55%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.55
0.55 - 0.70 = -0.15
-0.15 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 90%. The probability of not speaking english and the forest on fire is 7%. The probability of speaking english and the forest on fire is 50%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.50
0.50/0.90 - 0.07/0.10 = -0.15
-0.15 < 0",fork,forest_fire,1,correlation,P(Y | X)
14407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 90%. The probability of not speaking english and the forest on fire is 7%. The probability of speaking english and the forest on fire is 50%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.50
0.50/0.90 - 0.07/0.10 = -0.15
-0.15 < 0",fork,forest_fire,1,correlation,P(Y | X)
14411,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 83%. For people who speak english, the probability of the forest on fire is 51%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.51
0.51 - 0.83 = -0.32
-0.32 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 83%. For people who speak english, the probability of the forest on fire is 51%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.51
0.51 - 0.83 = -0.32
-0.32 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14416,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 90%. The probability of not speaking english and the forest on fire is 8%. The probability of speaking english and the forest on fire is 46%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.46
0.46/0.90 - 0.08/0.10 = -0.32
-0.32 < 0",fork,forest_fire,1,correlation,P(Y | X)
14427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 96%. The probability of not speaking english and the forest on fire is 3%. The probability of speaking english and the forest on fire is 62%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.62
0.62/0.96 - 0.03/0.04 = -0.17
-0.17 < 0",fork,forest_fire,1,correlation,P(Y | X)
14428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how ability to speak english correlates with the forest case by case according to the smoker. Method 2: We look directly at how ability to speak english correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 98%. The probability of not speaking english and the forest on fire is 2%. The probability of speaking english and the forest on fire is 48%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.48
0.48/0.98 - 0.02/0.02 = -0.35
-0.35 < 0",fork,forest_fire,1,correlation,P(Y | X)
14441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 69%. For people who speak english, the probability of the forest on fire is 52%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.52
0.52 - 0.69 = -0.17
-0.17 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 69%. For people who speak english, the probability of the forest on fire is 52%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.52
0.52 - 0.69 = -0.17
-0.17 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 94%. For people who do not speak english, the probability of the forest on fire is 69%. For people who speak english, the probability of the forest on fire is 52%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.52
0.94*0.52 - 0.06*0.69 = 0.53
0.53 > 0",fork,forest_fire,1,marginal,P(Y)
14450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 95%. For people who speak english, the probability of the forest on fire is 60%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.60
0.60 - 0.95 = -0.35
-0.35 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 95%. For people who speak english, the probability of the forest on fire is 60%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.60
0.60 - 0.95 = -0.35
-0.35 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 95%. For people who speak english, the probability of the forest on fire is 60%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.60
0.60 - 0.95 = -0.35
-0.35 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. For people who do not speak english, the probability of the forest on fire is 95%. For people who speak english, the probability of the forest on fire is 60%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.60
0.99*0.60 - 0.01*0.95 = 0.60
0.60 > 0",fork,forest_fire,1,marginal,P(Y)
14457,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. The probability of not speaking english and the forest on fire is 1%. The probability of speaking english and the forest on fire is 59%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.59
0.59/0.99 - 0.01/0.01 = -0.35
-0.35 < 0",fork,forest_fire,1,correlation,P(Y | X)
14458,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how ability to speak english correlates with the forest case by case according to the smoker. Method 2: We look directly at how ability to speak english correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 82%. For people who speak english, the probability of the forest on fire is 63%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.63
0.63 - 0.82 = -0.19
-0.19 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 97%. The probability of not speaking english and the forest on fire is 3%. The probability of speaking english and the forest on fire is 61%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.61
0.61/0.97 - 0.03/0.03 = -0.19
-0.19 < 0",fork,forest_fire,1,correlation,P(Y | X)
14470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 89%. For people who speak english, the probability of the forest on fire is 55%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.55
0.55 - 0.89 = -0.33
-0.33 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 89%. For people who speak english, the probability of the forest on fire is 55%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.55
0.55 - 0.89 = -0.33
-0.33 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14473,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 89%. For people who speak english, the probability of the forest on fire is 55%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.55
0.55 - 0.89 = -0.33
-0.33 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14475,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. For people who do not speak english, the probability of the forest on fire is 89%. For people who speak english, the probability of the forest on fire is 55%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.55
0.95*0.55 - 0.05*0.89 = 0.57
0.57 > 0",fork,forest_fire,1,marginal,P(Y)
14476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. The probability of not speaking english and the forest on fire is 4%. The probability of speaking english and the forest on fire is 52%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.52
0.52/0.95 - 0.04/0.05 = -0.33
-0.33 < 0",fork,forest_fire,1,correlation,P(Y | X)
14477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. The probability of not speaking english and the forest on fire is 4%. The probability of speaking english and the forest on fire is 52%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.52
0.52/0.95 - 0.04/0.05 = -0.33
-0.33 < 0",fork,forest_fire,1,correlation,P(Y | X)
14480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 75%. For people who speak english, the probability of the forest on fire is 59%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.59
0.59 - 0.75 = -0.16
-0.16 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 75%. For people who speak english, the probability of the forest on fire is 59%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.59
0.59 - 0.75 = -0.16
-0.16 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 94%. For people who do not speak english, the probability of the forest on fire is 75%. For people who speak english, the probability of the forest on fire is 59%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.59
0.94*0.59 - 0.06*0.75 = 0.60
0.60 > 0",fork,forest_fire,1,marginal,P(Y)
14489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 83%. For people who speak english, the probability of the forest on fire is 45%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.45
0.45 - 0.83 = -0.39
-0.39 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 97%. For people who do not speak english, the probability of the forest on fire is 83%. For people who speak english, the probability of the forest on fire is 45%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.45
0.97*0.45 - 0.03*0.83 = 0.46
0.46 > 0",fork,forest_fire,1,marginal,P(Y)
14496,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 97%. The probability of not speaking english and the forest on fire is 3%. The probability of speaking english and the forest on fire is 43%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.43
0.43/0.97 - 0.03/0.03 = -0.39
-0.39 < 0",fork,forest_fire,1,correlation,P(Y | X)
14498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how ability to speak english correlates with the forest case by case according to the smoker. Method 2: We look directly at how ability to speak english correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 73%. For people who speak english, the probability of the forest on fire is 57%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.57
0.57 - 0.73 = -0.17
-0.17 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 73%. For people who speak english, the probability of the forest on fire is 57%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.57
0.57 - 0.73 = -0.17
-0.17 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 73%. For people who speak english, the probability of the forest on fire is 57%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.57
0.57 - 0.73 = -0.17
-0.17 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 97%. For people who do not speak english, the probability of the forest on fire is 73%. For people who speak english, the probability of the forest on fire is 57%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.57
0.97*0.57 - 0.03*0.73 = 0.57
0.57 > 0",fork,forest_fire,1,marginal,P(Y)
14506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 97%. The probability of not speaking english and the forest on fire is 2%. The probability of speaking english and the forest on fire is 55%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.55
0.55/0.97 - 0.02/0.03 = -0.17
-0.17 < 0",fork,forest_fire,1,correlation,P(Y | X)
14509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 81%. For people who speak english, the probability of the forest on fire is 43%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.43
0.43 - 0.81 = -0.38
-0.38 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 86%. For people who speak english, the probability of the forest on fire is 72%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.72
0.72 - 0.86 = -0.13
-0.13 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 86%. For people who speak english, the probability of the forest on fire is 72%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.72
0.72 - 0.86 = -0.13
-0.13 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 91%. For people who do not speak english, the probability of the forest on fire is 86%. For people who speak english, the probability of the forest on fire is 72%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.72
0.91*0.72 - 0.09*0.86 = 0.73
0.73 > 0",fork,forest_fire,1,marginal,P(Y)
14526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 91%. The probability of not speaking english and the forest on fire is 8%. The probability of speaking english and the forest on fire is 66%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.66
0.66/0.91 - 0.08/0.09 = -0.13
-0.13 < 0",fork,forest_fire,1,correlation,P(Y | X)
14528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how ability to speak english correlates with the forest case by case according to the smoker. Method 2: We look directly at how ability to speak english correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 83%. For people who speak english, the probability of the forest on fire is 48%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.48
0.48 - 0.83 = -0.34
-0.34 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14533,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 83%. For people who speak english, the probability of the forest on fire is 48%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.48
0.48 - 0.83 = -0.34
-0.34 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14535,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. For people who do not speak english, the probability of the forest on fire is 83%. For people who speak english, the probability of the forest on fire is 48%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.48
0.95*0.48 - 0.05*0.83 = 0.50
0.50 > 0",fork,forest_fire,1,marginal,P(Y)
14538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how ability to speak english correlates with the forest case by case according to the smoker. Method 2: We look directly at how ability to speak english correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 97%. For people who do not speak english, the probability of the forest on fire is 67%. For people who speak english, the probability of the forest on fire is 54%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.54
0.97*0.54 - 0.03*0.67 = 0.55
0.55 > 0",fork,forest_fire,1,marginal,P(Y)
14546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 97%. The probability of not speaking english and the forest on fire is 2%. The probability of speaking english and the forest on fire is 52%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.52
0.52/0.97 - 0.02/0.03 = -0.12
-0.12 < 0",fork,forest_fire,1,correlation,P(Y | X)
14554,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 48%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.48
0.95*0.48 - 0.05*0.80 = 0.49
0.49 > 0",fork,forest_fire,1,marginal,P(Y)
14555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 48%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.48
0.95*0.48 - 0.05*0.80 = 0.49
0.49 > 0",fork,forest_fire,1,marginal,P(Y)
14556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. The probability of not speaking english and the forest on fire is 4%. The probability of speaking english and the forest on fire is 45%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.45
0.45/0.95 - 0.04/0.05 = -0.33
-0.33 < 0",fork,forest_fire,1,correlation,P(Y | X)
14557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. The probability of not speaking english and the forest on fire is 4%. The probability of speaking english and the forest on fire is 45%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.45
0.45/0.95 - 0.04/0.05 = -0.33
-0.33 < 0",fork,forest_fire,1,correlation,P(Y | X)
14564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 92%. For people who do not speak english, the probability of the forest on fire is 78%. For people who speak english, the probability of the forest on fire is 60%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.60
0.92*0.60 - 0.08*0.78 = 0.61
0.61 > 0",fork,forest_fire,1,marginal,P(Y)
14565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 92%. For people who do not speak english, the probability of the forest on fire is 78%. For people who speak english, the probability of the forest on fire is 60%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.60
0.92*0.60 - 0.08*0.78 = 0.61
0.61 > 0",fork,forest_fire,1,marginal,P(Y)
14570,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 79%. For people who speak english, the probability of the forest on fire is 44%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.44
0.44 - 0.79 = -0.35
-0.35 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 79%. For people who speak english, the probability of the forest on fire is 44%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.44
0.44 - 0.79 = -0.35
-0.35 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. For people who do not speak english, the probability of the forest on fire is 79%. For people who speak english, the probability of the forest on fire is 44%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.44
0.99*0.44 - 0.01*0.79 = 0.44
0.44 > 0",fork,forest_fire,1,marginal,P(Y)
14579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14580,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 71%. For people who speak english, the probability of the forest on fire is 59%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.59
0.59 - 0.71 = -0.13
-0.13 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 71%. For people who speak english, the probability of the forest on fire is 59%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.59
0.59 - 0.71 = -0.13
-0.13 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 71%. For people who speak english, the probability of the forest on fire is 59%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.59
0.59 - 0.71 = -0.13
-0.13 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. For people who do not speak english, the probability of the forest on fire is 71%. For people who speak english, the probability of the forest on fire is 59%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.59
0.99*0.59 - 0.01*0.71 = 0.59
0.59 > 0",fork,forest_fire,1,marginal,P(Y)
14586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. The probability of not speaking english and the forest on fire is 1%. The probability of speaking english and the forest on fire is 58%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.58
0.58/0.99 - 0.01/0.01 = -0.13
-0.13 < 0",fork,forest_fire,1,correlation,P(Y | X)
14589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 47%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.47
0.47 - 0.80 = -0.34
-0.34 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 47%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.47
0.47 - 0.80 = -0.34
-0.34 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 98%. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 47%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.47
0.98*0.47 - 0.02*0.80 = 0.48
0.48 > 0",fork,forest_fire,1,marginal,P(Y)
14595,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 98%. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 47%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.47
0.98*0.47 - 0.02*0.80 = 0.48
0.48 > 0",fork,forest_fire,1,marginal,P(Y)
14596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 98%. The probability of not speaking english and the forest on fire is 2%. The probability of speaking english and the forest on fire is 46%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.46
0.46/0.98 - 0.02/0.02 = -0.34
-0.34 < 0",fork,forest_fire,1,correlation,P(Y | X)
14598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how ability to speak english correlates with the forest case by case according to the smoker. Method 2: We look directly at how ability to speak english correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14603,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 79%. For people who speak english, the probability of the forest on fire is 65%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.65
0.65 - 0.79 = -0.13
-0.13 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14604,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 93%. For people who do not speak english, the probability of the forest on fire is 79%. For people who speak english, the probability of the forest on fire is 65%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.65
0.93*0.65 - 0.07*0.79 = 0.66
0.66 > 0",fork,forest_fire,1,marginal,P(Y)
14605,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 93%. For people who do not speak english, the probability of the forest on fire is 79%. For people who speak english, the probability of the forest on fire is 65%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.65
0.93*0.65 - 0.07*0.79 = 0.66
0.66 > 0",fork,forest_fire,1,marginal,P(Y)
14606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 93%. The probability of not speaking english and the forest on fire is 5%. The probability of speaking english and the forest on fire is 61%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.61
0.61/0.93 - 0.05/0.07 = -0.13
-0.13 < 0",fork,forest_fire,1,correlation,P(Y | X)
14609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 49%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.49
0.49 - 0.80 = -0.32
-0.32 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 49%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.49
0.49 - 0.80 = -0.32
-0.32 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 80%. For people who speak english, the probability of the forest on fire is 49%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.49
0.49 - 0.80 = -0.32
-0.32 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14617,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 92%. The probability of not speaking english and the forest on fire is 7%. The probability of speaking english and the forest on fire is 45%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.45
0.45/0.92 - 0.07/0.08 = -0.32
-0.32 < 0",fork,forest_fire,1,correlation,P(Y | X)
14622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 81%. For people who speak english, the probability of the forest on fire is 64%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.64
0.64 - 0.81 = -0.17
-0.17 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 81%. For people who speak english, the probability of the forest on fire is 64%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.64
0.64 - 0.81 = -0.17
-0.17 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 82%. For people who speak english, the probability of the forest on fire is 50%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.50
0.50 - 0.82 = -0.32
-0.32 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 93%. For people who do not speak english, the probability of the forest on fire is 82%. For people who speak english, the probability of the forest on fire is 50%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.50
0.93*0.50 - 0.07*0.82 = 0.52
0.52 > 0",fork,forest_fire,1,marginal,P(Y)
14636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 93%. The probability of not speaking english and the forest on fire is 6%. The probability of speaking english and the forest on fire is 46%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.46
0.46/0.93 - 0.06/0.07 = -0.32
-0.32 < 0",fork,forest_fire,1,correlation,P(Y | X)
14637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 93%. The probability of not speaking english and the forest on fire is 6%. The probability of speaking english and the forest on fire is 46%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.46
0.46/0.93 - 0.06/0.07 = -0.32
-0.32 < 0",fork,forest_fire,1,correlation,P(Y | X)
14640,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 71%. For people who speak english, the probability of the forest on fire is 57%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.57
0.57 - 0.71 = -0.14
-0.14 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 71%. For people who speak english, the probability of the forest on fire is 57%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.57
0.57 - 0.71 = -0.14
-0.14 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 95%. For people who do not speak english, the probability of the forest on fire is 71%. For people who speak english, the probability of the forest on fire is 57%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.57
0.95*0.57 - 0.05*0.71 = 0.58
0.58 > 0",fork,forest_fire,1,marginal,P(Y)
14650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 97%. For people who speak english, the probability of the forest on fire is 65%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.65
0.65 - 0.97 = -0.32
-0.32 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 97%. For people who speak english, the probability of the forest on fire is 65%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.65
0.65 - 0.97 = -0.32
-0.32 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14661,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 73%. For people who speak english, the probability of the forest on fire is 57%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.57
0.57 - 0.73 = -0.16
-0.16 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. The probability of not speaking english and the forest on fire is 1%. The probability of speaking english and the forest on fire is 56%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.56
0.56/0.99 - 0.01/0.01 = -0.16
-0.16 < 0",fork,forest_fire,1,correlation,P(Y | X)
14667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. The probability of not speaking english and the forest on fire is 1%. The probability of speaking english and the forest on fire is 56%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.56
0.56/0.99 - 0.01/0.01 = -0.16
-0.16 < 0",fork,forest_fire,1,correlation,P(Y | X)
14668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look at how ability to speak english correlates with the forest case by case according to the smoker. Method 2: We look directly at how ability to speak english correlates with the forest in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 87%. For people who speak english, the probability of the forest on fire is 53%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.53
0.53 - 0.87 = -0.33
-0.33 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14672,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 87%. For people who speak english, the probability of the forest on fire is 53%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.53
0.53 - 0.87 = -0.33
-0.33 < 0",fork,forest_fire,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14674,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 100%. For people who do not speak english, the probability of the forest on fire is 87%. For people who speak english, the probability of the forest on fire is 53%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 1.00
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.53
1.00*0.53 - 0.00*0.87 = 0.53
0.53 > 0",fork,forest_fire,1,marginal,P(Y)
14675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 100%. For people who do not speak english, the probability of the forest on fire is 87%. For people who speak english, the probability of the forest on fire is 53%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 1.00
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.53
1.00*0.53 - 0.00*0.87 = 0.53
0.53 > 0",fork,forest_fire,1,marginal,P(Y)
14676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 100%. The probability of not speaking english and the forest on fire is 0%. The probability of speaking english and the forest on fire is 53%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 1.00
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.53
0.53/1.00 - 0.00/0.00 = -0.33
-0.33 < 0",fork,forest_fire,1,correlation,P(Y | X)
14677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 100%. The probability of not speaking english and the forest on fire is 0%. The probability of speaking english and the forest on fire is 53%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 1.00
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.53
0.53/1.00 - 0.00/0.00 = -0.33
-0.33 < 0",fork,forest_fire,1,correlation,P(Y | X)
14679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 78%. For people who speak english, the probability of the forest on fire is 45%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.45
0.45 - 0.78 = -0.33
-0.33 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. For people who do not speak english, the probability of the forest on fire is 78%. For people who speak english, the probability of the forest on fire is 45%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.45
0.99*0.45 - 0.01*0.78 = 0.45
0.45 > 0",fork,forest_fire,1,marginal,P(Y)
14690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 94%. For people who speak english, the probability of the forest on fire is 78%.",no,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.78
0.78 - 0.94 = -0.16
-0.16 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. For people who do not speak english, the probability of the forest on fire is 94%. For people who speak english, the probability of the forest on fire is 78%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.78
0.78 - 0.94 = -0.16
-0.16 < 0",fork,forest_fire,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. The overall probability of speaking english is 99%. The probability of not speaking english and the forest on fire is 1%. The probability of speaking english and the forest on fire is 78%.",yes,"Let V2 = the smoker; X = ability to speak english; Y = the forest.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.78
0.78/0.99 - 0.01/0.01 = -0.16
-0.16 < 0",fork,forest_fire,1,correlation,P(Y | X)
14699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on the forest. The smoker has a direct effect on the forest. Method 1: We look directly at how ability to speak english correlates with the forest in general. Method 2: We look at this correlation case by case according to the smoker.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,forest_fire,2,backadj,[backdoor adjustment set for Y given X]
14700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 37%. For days when Alice wakes up late, the probability of high rainfall is 71%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.71
0.71 - 0.37 = 0.34
0.34 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 37%. For days when Alice wakes up late, the probability of high rainfall is 71%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.71
0.71 - 0.37 = 0.34
0.34 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 9%. For days when Alice wakes up on time, the probability of high rainfall is 37%. For days when Alice wakes up late, the probability of high rainfall is 71%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.71
0.09*0.71 - 0.91*0.37 = 0.40
0.40 > 0",fork,getting_late,1,marginal,P(Y)
14706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 9%. The probability of waking up on time and high rainfall is 33%. The probability of waking up late and high rainfall is 6%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.06
0.06/0.09 - 0.33/0.91 = 0.34
0.34 > 0",fork,getting_late,1,correlation,P(Y | X)
14709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 44%. For days when Alice wakes up late, the probability of high rainfall is 78%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.78
0.78 - 0.44 = 0.34
0.34 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 19%. For days when Alice wakes up on time, the probability of high rainfall is 44%. For days when Alice wakes up late, the probability of high rainfall is 78%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.78
0.19*0.78 - 0.81*0.44 = 0.50
0.50 > 0",fork,getting_late,1,marginal,P(Y)
14718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 47%. For days when Alice wakes up late, the probability of high rainfall is 84%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.84
0.84 - 0.47 = 0.37
0.37 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 2%. The probability of waking up on time and high rainfall is 46%. The probability of waking up late and high rainfall is 1%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.46/0.98 = 0.37
0.37 > 0",fork,getting_late,1,correlation,P(Y | X)
14731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 85%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.85
0.85 - 0.52 = 0.33
0.33 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14733,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 85%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.85
0.85 - 0.52 = 0.33
0.33 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14744,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 8%. For days when Alice wakes up on time, the probability of high rainfall is 54%. For days when Alice wakes up late, the probability of high rainfall is 90%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.90
0.08*0.90 - 0.92*0.54 = 0.57
0.57 > 0",fork,getting_late,1,marginal,P(Y)
14745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 8%. For days when Alice wakes up on time, the probability of high rainfall is 54%. For days when Alice wakes up late, the probability of high rainfall is 90%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.90
0.08*0.90 - 0.92*0.54 = 0.57
0.57 > 0",fork,getting_late,1,marginal,P(Y)
14748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 18%. For days when Alice wakes up on time, the probability of high rainfall is 43%. For days when Alice wakes up late, the probability of high rainfall is 76%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.76
0.18*0.76 - 0.82*0.43 = 0.49
0.49 > 0",fork,getting_late,1,marginal,P(Y)
14755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 18%. For days when Alice wakes up on time, the probability of high rainfall is 43%. For days when Alice wakes up late, the probability of high rainfall is 76%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.76
0.18*0.76 - 0.82*0.43 = 0.49
0.49 > 0",fork,getting_late,1,marginal,P(Y)
14759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 2%. The probability of waking up on time and high rainfall is 43%. The probability of waking up late and high rainfall is 1%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.43/0.98 = 0.34
0.34 > 0",fork,getting_late,1,correlation,P(Y | X)
14769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 45%. For days when Alice wakes up late, the probability of high rainfall is 77%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.77
0.77 - 0.45 = 0.32
0.32 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 13%. The probability of waking up on time and high rainfall is 39%. The probability of waking up late and high rainfall is 10%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.10
0.10/0.13 - 0.39/0.87 = 0.32
0.32 > 0",fork,getting_late,1,correlation,P(Y | X)
14778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14782,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 56%. For days when Alice wakes up late, the probability of high rainfall is 88%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.88
0.88 - 0.56 = 0.33
0.33 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 56%. For days when Alice wakes up late, the probability of high rainfall is 88%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.88
0.88 - 0.56 = 0.33
0.33 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 2%. The probability of waking up on time and high rainfall is 55%. The probability of waking up late and high rainfall is 2%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.55
P(Y=1, X=1=1) = 0.02
0.02/0.02 - 0.55/0.98 = 0.33
0.33 > 0",fork,getting_late,1,correlation,P(Y | X)
14787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 2%. The probability of waking up on time and high rainfall is 55%. The probability of waking up late and high rainfall is 2%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.55
P(Y=1, X=1=1) = 0.02
0.02/0.02 - 0.55/0.98 = 0.33
0.33 > 0",fork,getting_late,1,correlation,P(Y | X)
14788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 42%. For days when Alice wakes up late, the probability of high rainfall is 76%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.76
0.76 - 0.42 = 0.34
0.34 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 42%. For days when Alice wakes up late, the probability of high rainfall is 76%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.76
0.76 - 0.42 = 0.34
0.34 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 46%. For days when Alice wakes up late, the probability of high rainfall is 79%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.79
0.79 - 0.46 = 0.34
0.34 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 53%. For days when Alice wakes up late, the probability of high rainfall is 85%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.85
0.85 - 0.53 = 0.31
0.31 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 53%. For days when Alice wakes up late, the probability of high rainfall is 85%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.85
0.85 - 0.53 = 0.31
0.31 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 53%. For days when Alice wakes up late, the probability of high rainfall is 85%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.85
0.85 - 0.53 = 0.31
0.31 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 11%. For days when Alice wakes up on time, the probability of high rainfall is 53%. For days when Alice wakes up late, the probability of high rainfall is 85%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.85
0.11*0.85 - 0.89*0.53 = 0.57
0.57 > 0",fork,getting_late,1,marginal,P(Y)
14816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 11%. The probability of waking up on time and high rainfall is 47%. The probability of waking up late and high rainfall is 10%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.10
0.10/0.11 - 0.47/0.89 = 0.31
0.31 > 0",fork,getting_late,1,correlation,P(Y | X)
14818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 43%. For days when Alice wakes up late, the probability of high rainfall is 76%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.76
0.76 - 0.43 = 0.34
0.34 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 43%. For days when Alice wakes up late, the probability of high rainfall is 76%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.76
0.76 - 0.43 = 0.34
0.34 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 43%. For days when Alice wakes up late, the probability of high rainfall is 76%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.76
0.76 - 0.43 = 0.34
0.34 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14823,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 43%. For days when Alice wakes up late, the probability of high rainfall is 76%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.76
0.76 - 0.43 = 0.34
0.34 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 12%. The probability of waking up on time and high rainfall is 37%. The probability of waking up late and high rainfall is 9%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.09
0.09/0.12 - 0.37/0.88 = 0.34
0.34 > 0",fork,getting_late,1,correlation,P(Y | X)
14832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 38%. For days when Alice wakes up late, the probability of high rainfall is 71%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.71
0.71 - 0.38 = 0.33
0.33 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 16%. The probability of waking up on time and high rainfall is 32%. The probability of waking up late and high rainfall is 12%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.12
0.12/0.16 - 0.32/0.84 = 0.33
0.33 > 0",fork,getting_late,1,correlation,P(Y | X)
14842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 87%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.87
0.87 - 0.52 = 0.35
0.35 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 87%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.87
0.87 - 0.52 = 0.35
0.35 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14844,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 5%. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 87%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.87
0.05*0.87 - 0.95*0.52 = 0.54
0.54 > 0",fork,getting_late,1,marginal,P(Y)
14845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 5%. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 87%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.87
0.05*0.87 - 0.95*0.52 = 0.54
0.54 > 0",fork,getting_late,1,marginal,P(Y)
14850,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 38%. For days when Alice wakes up late, the probability of high rainfall is 72%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.72
0.72 - 0.38 = 0.34
0.34 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 17%. For days when Alice wakes up on time, the probability of high rainfall is 38%. For days when Alice wakes up late, the probability of high rainfall is 72%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.72
0.17*0.72 - 0.83*0.38 = 0.44
0.44 > 0",fork,getting_late,1,marginal,P(Y)
14856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 17%. The probability of waking up on time and high rainfall is 32%. The probability of waking up late and high rainfall is 12%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.12
0.12/0.17 - 0.32/0.83 = 0.34
0.34 > 0",fork,getting_late,1,correlation,P(Y | X)
14858,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 4%. The probability of waking up on time and high rainfall is 44%. The probability of waking up late and high rainfall is 3%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.03
0.03/0.04 - 0.44/0.96 = 0.34
0.34 > 0",fork,getting_late,1,correlation,P(Y | X)
14870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 84%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.84
0.84 - 0.52 = 0.33
0.33 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 84%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.84
0.84 - 0.52 = 0.33
0.33 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 11%. The probability of waking up on time and high rainfall is 46%. The probability of waking up late and high rainfall is 10%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.10
0.10/0.11 - 0.46/0.89 = 0.33
0.33 > 0",fork,getting_late,1,correlation,P(Y | X)
14879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 83%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.83
0.83 - 0.52 = 0.32
0.32 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14883,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 83%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.83
0.83 - 0.52 = 0.32
0.32 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 8%. For days when Alice wakes up on time, the probability of high rainfall is 52%. For days when Alice wakes up late, the probability of high rainfall is 83%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.83
0.08*0.83 - 0.92*0.52 = 0.54
0.54 > 0",fork,getting_late,1,marginal,P(Y)
14888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 46%. For days when Alice wakes up late, the probability of high rainfall is 78%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.78
0.78 - 0.46 = 0.32
0.32 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14892,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 46%. For days when Alice wakes up late, the probability of high rainfall is 78%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.78
0.78 - 0.46 = 0.32
0.32 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 5%. For days when Alice wakes up on time, the probability of high rainfall is 46%. For days when Alice wakes up late, the probability of high rainfall is 78%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.78
0.05*0.78 - 0.95*0.46 = 0.48
0.48 > 0",fork,getting_late,1,marginal,P(Y)
14895,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 5%. For days when Alice wakes up on time, the probability of high rainfall is 46%. For days when Alice wakes up late, the probability of high rainfall is 78%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.78
0.05*0.78 - 0.95*0.46 = 0.48
0.48 > 0",fork,getting_late,1,marginal,P(Y)
14896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 5%. The probability of waking up on time and high rainfall is 44%. The probability of waking up late and high rainfall is 4%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.04
0.04/0.05 - 0.44/0.95 = 0.32
0.32 > 0",fork,getting_late,1,correlation,P(Y | X)
14899,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 14%. For days when Alice wakes up on time, the probability of high rainfall is 54%. For days when Alice wakes up late, the probability of high rainfall is 85%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.85
0.14*0.85 - 0.86*0.54 = 0.59
0.59 > 0",fork,getting_late,1,marginal,P(Y)
14905,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 14%. For days when Alice wakes up on time, the probability of high rainfall is 54%. For days when Alice wakes up late, the probability of high rainfall is 85%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.85
0.14*0.85 - 0.86*0.54 = 0.59
0.59 > 0",fork,getting_late,1,marginal,P(Y)
14911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 58%. For days when Alice wakes up late, the probability of high rainfall is 89%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.89
0.89 - 0.58 = 0.31
0.31 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 9%. For days when Alice wakes up on time, the probability of high rainfall is 58%. For days when Alice wakes up late, the probability of high rainfall is 89%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.89
0.09*0.89 - 0.91*0.58 = 0.61
0.61 > 0",fork,getting_late,1,marginal,P(Y)
14917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 9%. The probability of waking up on time and high rainfall is 53%. The probability of waking up late and high rainfall is 8%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.08
0.08/0.09 - 0.53/0.91 = 0.31
0.31 > 0",fork,getting_late,1,correlation,P(Y | X)
14918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 49%. For days when Alice wakes up late, the probability of high rainfall is 84%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.84
0.84 - 0.49 = 0.35
0.35 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 49%. For days when Alice wakes up late, the probability of high rainfall is 84%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.84
0.84 - 0.49 = 0.35
0.35 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 13%. For days when Alice wakes up on time, the probability of high rainfall is 49%. For days when Alice wakes up late, the probability of high rainfall is 84%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.84
0.13*0.84 - 0.87*0.49 = 0.53
0.53 > 0",fork,getting_late,1,marginal,P(Y)
14927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 13%. The probability of waking up on time and high rainfall is 43%. The probability of waking up late and high rainfall is 11%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.11
0.11/0.13 - 0.43/0.87 = 0.35
0.35 > 0",fork,getting_late,1,correlation,P(Y | X)
14928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14929,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 53%. For days when Alice wakes up late, the probability of high rainfall is 83%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.83
0.83 - 0.53 = 0.31
0.31 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14932,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 53%. For days when Alice wakes up late, the probability of high rainfall is 83%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.83
0.83 - 0.53 = 0.31
0.31 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 3%. For days when Alice wakes up on time, the probability of high rainfall is 53%. For days when Alice wakes up late, the probability of high rainfall is 83%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.83
0.03*0.83 - 0.97*0.53 = 0.54
0.54 > 0",fork,getting_late,1,marginal,P(Y)
14937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 3%. The probability of waking up on time and high rainfall is 51%. The probability of waking up late and high rainfall is 2%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.51
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.51/0.97 = 0.31
0.31 > 0",fork,getting_late,1,correlation,P(Y | X)
14940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 46%. For days when Alice wakes up late, the probability of high rainfall is 78%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.78
0.78 - 0.46 = 0.32
0.32 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 46%. For days when Alice wakes up late, the probability of high rainfall is 78%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.78
0.78 - 0.46 = 0.32
0.32 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 11%. For days when Alice wakes up on time, the probability of high rainfall is 46%. For days when Alice wakes up late, the probability of high rainfall is 78%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.78
0.11*0.78 - 0.89*0.46 = 0.49
0.49 > 0",fork,getting_late,1,marginal,P(Y)
14946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 11%. The probability of waking up on time and high rainfall is 40%. The probability of waking up late and high rainfall is 9%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.09
0.09/0.11 - 0.40/0.89 = 0.32
0.32 > 0",fork,getting_late,1,correlation,P(Y | X)
14950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 51%. For days when Alice wakes up late, the probability of high rainfall is 82%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.82
0.82 - 0.51 = 0.31
0.31 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look at how Alice waking up correlates with rainfall case by case according to traffic. Method 2: We look directly at how Alice waking up correlates with rainfall in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 48%. For days when Alice wakes up late, the probability of high rainfall is 80%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.80
0.80 - 0.48 = 0.32
0.32 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 14%. For days when Alice wakes up on time, the probability of high rainfall is 48%. For days when Alice wakes up late, the probability of high rainfall is 80%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.80
0.14*0.80 - 0.86*0.48 = 0.52
0.52 > 0",fork,getting_late,1,marginal,P(Y)
14965,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 14%. For days when Alice wakes up on time, the probability of high rainfall is 48%. For days when Alice wakes up late, the probability of high rainfall is 80%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.80
0.14*0.80 - 0.86*0.48 = 0.52
0.52 > 0",fork,getting_late,1,marginal,P(Y)
14967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 14%. The probability of waking up on time and high rainfall is 41%. The probability of waking up late and high rainfall is 11%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.11
0.11/0.14 - 0.41/0.86 = 0.32
0.32 > 0",fork,getting_late,1,correlation,P(Y | X)
14969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. Method 1: We look directly at how Alice waking up correlates with rainfall in general. Method 2: We look at this correlation case by case according to traffic.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_late,2,backadj,[backdoor adjustment set for Y given X]
14971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 47%. For days when Alice wakes up late, the probability of high rainfall is 86%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.86
0.86 - 0.47 = 0.39
0.39 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 47%. For days when Alice wakes up late, the probability of high rainfall is 86%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.86
0.86 - 0.47 = 0.39
0.39 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 47%. For days when Alice wakes up late, the probability of high rainfall is 86%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.86
0.86 - 0.47 = 0.39
0.39 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 6%. For days when Alice wakes up on time, the probability of high rainfall is 47%. For days when Alice wakes up late, the probability of high rainfall is 86%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.86
0.06*0.86 - 0.94*0.47 = 0.49
0.49 > 0",fork,getting_late,1,marginal,P(Y)
14976,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 6%. The probability of waking up on time and high rainfall is 44%. The probability of waking up late and high rainfall is 5%.",yes,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.05
0.05/0.06 - 0.44/0.94 = 0.39
0.39 > 0",fork,getting_late,1,correlation,P(Y | X)
14977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 6%. The probability of waking up on time and high rainfall is 44%. The probability of waking up late and high rainfall is 5%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.05
0.05/0.06 - 0.44/0.94 = 0.39
0.39 > 0",fork,getting_late,1,correlation,P(Y | X)
14981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 39%. For days when Alice wakes up late, the probability of high rainfall is 70%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.70
0.70 - 0.39 = 0.32
0.32 > 0",fork,getting_late,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
14982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 39%. For days when Alice wakes up late, the probability of high rainfall is 70%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.70
0.70 - 0.39 = 0.32
0.32 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 11%. For days when Alice wakes up on time, the probability of high rainfall is 39%. For days when Alice wakes up late, the probability of high rainfall is 70%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.70
0.11*0.70 - 0.89*0.39 = 0.43
0.43 > 0",fork,getting_late,1,marginal,P(Y)
14987,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 11%. The probability of waking up on time and high rainfall is 35%. The probability of waking up late and high rainfall is 8%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.08
0.08/0.11 - 0.35/0.89 = 0.32
0.32 > 0",fork,getting_late,1,correlation,P(Y | X)
14992,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. For days when Alice wakes up on time, the probability of high rainfall is 48%. For days when Alice wakes up late, the probability of high rainfall is 80%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.80
0.80 - 0.48 = 0.32
0.32 > 0",fork,getting_late,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
14995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Alice waking up has a direct effect on rainfall. Traffic has a direct effect on rainfall. The overall probability of waking up late is 14%. For days when Alice wakes up on time, the probability of high rainfall is 48%. For days when Alice wakes up late, the probability of high rainfall is 80%.",no,"Let V2 = traffic; X = Alice waking up; Y = rainfall.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.80
0.14*0.80 - 0.86*0.48 = 0.53
0.53 > 0",fork,getting_late,1,marginal,P(Y)
15001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 54%. For people who went to tanning salons, the probability of black hair is 16%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.16
0.16 - 0.54 = -0.38
-0.38 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15002,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 54%. For people who went to tanning salons, the probability of black hair is 16%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.16
0.16 - 0.54 = -0.38
-0.38 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 89%. For people not using tanning salon treatments, the probability of black hair is 54%. For people who went to tanning salons, the probability of black hair is 16%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.16
0.89*0.16 - 0.11*0.54 = 0.20
0.20 > 0",fork,getting_tanned,1,marginal,P(Y)
15007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 89%. The probability of no tanning salon treatment and black hair is 6%. The probability of tanning salon treatment and black hair is 14%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.14
0.14/0.89 - 0.06/0.11 = -0.38
-0.38 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15013,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 62%. For people who went to tanning salons, the probability of black hair is 18%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.18
0.18 - 0.62 = -0.44
-0.44 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 95%. The probability of no tanning salon treatment and black hair is 3%. The probability of tanning salon treatment and black hair is 17%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.17
0.17/0.95 - 0.03/0.05 = -0.44
-0.44 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 17%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.17
0.17 - 0.74 = -0.57
-0.57 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 17%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.17
0.17 - 0.74 = -0.57
-0.57 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 84%. The probability of no tanning salon treatment and black hair is 12%. The probability of tanning salon treatment and black hair is 14%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.14
0.14/0.84 - 0.12/0.16 = -0.57
-0.57 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 84%. The probability of no tanning salon treatment and black hair is 12%. The probability of tanning salon treatment and black hair is 14%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.14
0.14/0.84 - 0.12/0.16 = -0.57
-0.57 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 59%. For people who went to tanning salons, the probability of black hair is 21%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.21
0.21 - 0.59 = -0.38
-0.38 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 59%. For people who went to tanning salons, the probability of black hair is 21%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.21
0.21 - 0.59 = -0.38
-0.38 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 42%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.42
0.42 - 0.74 = -0.32
-0.32 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 42%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.42
0.42 - 0.74 = -0.32
-0.32 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 42%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.42
0.42 - 0.74 = -0.32
-0.32 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 85%. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 42%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.42
0.85*0.42 - 0.15*0.74 = 0.47
0.47 > 0",fork,getting_tanned,1,marginal,P(Y)
15046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 85%. The probability of no tanning salon treatment and black hair is 11%. The probability of tanning salon treatment and black hair is 36%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.36
0.36/0.85 - 0.11/0.15 = -0.32
-0.32 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 30%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.30
0.30 - 0.74 = -0.44
-0.44 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 30%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.30
0.30 - 0.74 = -0.44
-0.44 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15052,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 74%. For people who went to tanning salons, the probability of black hair is 30%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.30
0.30 - 0.74 = -0.44
-0.44 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 91%. The probability of no tanning salon treatment and black hair is 6%. The probability of tanning salon treatment and black hair is 27%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.27
0.27/0.91 - 0.06/0.09 = -0.44
-0.44 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 61%. For people who went to tanning salons, the probability of black hair is 15%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.15
0.15 - 0.61 = -0.46
-0.46 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 97%. For people not using tanning salon treatments, the probability of black hair is 61%. For people who went to tanning salons, the probability of black hair is 15%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.15
0.97*0.15 - 0.03*0.61 = 0.17
0.17 > 0",fork,getting_tanned,1,marginal,P(Y)
15075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 93%. For people not using tanning salon treatments, the probability of black hair is 76%. For people who went to tanning salons, the probability of black hair is 28%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.28
0.93*0.28 - 0.07*0.76 = 0.32
0.32 > 0",fork,getting_tanned,1,marginal,P(Y)
15076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 93%. The probability of no tanning salon treatment and black hair is 5%. The probability of tanning salon treatment and black hair is 26%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.26
0.26/0.93 - 0.05/0.07 = -0.47
-0.47 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 93%. The probability of no tanning salon treatment and black hair is 5%. The probability of tanning salon treatment and black hair is 26%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.26
0.26/0.93 - 0.05/0.07 = -0.47
-0.47 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 70%. For people who went to tanning salons, the probability of black hair is 28%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.28
0.28 - 0.70 = -0.42
-0.42 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 70%. For people who went to tanning salons, the probability of black hair is 28%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.28
0.28 - 0.70 = -0.42
-0.42 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 93%. For people not using tanning salon treatments, the probability of black hair is 70%. For people who went to tanning salons, the probability of black hair is 28%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.28
0.93*0.28 - 0.07*0.70 = 0.31
0.31 > 0",fork,getting_tanned,1,marginal,P(Y)
15086,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 93%. The probability of no tanning salon treatment and black hair is 5%. The probability of tanning salon treatment and black hair is 27%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.27
0.27/0.93 - 0.05/0.07 = -0.42
-0.42 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 93%. The probability of no tanning salon treatment and black hair is 5%. The probability of tanning salon treatment and black hair is 27%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.27
0.27/0.93 - 0.05/0.07 = -0.42
-0.42 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 72%. For people who went to tanning salons, the probability of black hair is 30%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.30
0.30 - 0.72 = -0.43
-0.43 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 72%. For people who went to tanning salons, the probability of black hair is 30%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.30
0.30 - 0.72 = -0.43
-0.43 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15094,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 88%. For people not using tanning salon treatments, the probability of black hair is 72%. For people who went to tanning salons, the probability of black hair is 30%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.30
0.88*0.30 - 0.12*0.72 = 0.35
0.35 > 0",fork,getting_tanned,1,marginal,P(Y)
15097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 88%. The probability of no tanning salon treatment and black hair is 8%. The probability of tanning salon treatment and black hair is 26%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.26
0.26/0.88 - 0.08/0.12 = -0.43
-0.43 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15100,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 53%. For people who went to tanning salons, the probability of black hair is 15%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.15
0.15 - 0.53 = -0.38
-0.38 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15103,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 53%. For people who went to tanning salons, the probability of black hair is 15%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.15
0.15 - 0.53 = -0.38
-0.38 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15104,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 93%. For people not using tanning salon treatments, the probability of black hair is 53%. For people who went to tanning salons, the probability of black hair is 15%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.15
0.93*0.15 - 0.07*0.53 = 0.18
0.18 > 0",fork,getting_tanned,1,marginal,P(Y)
15112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 69%. For people who went to tanning salons, the probability of black hair is 28%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.28
0.28 - 0.69 = -0.41
-0.41 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 95%. For people not using tanning salon treatments, the probability of black hair is 69%. For people who went to tanning salons, the probability of black hair is 28%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.28
0.95*0.28 - 0.05*0.69 = 0.30
0.30 > 0",fork,getting_tanned,1,marginal,P(Y)
15116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 95%. The probability of no tanning salon treatment and black hair is 3%. The probability of tanning salon treatment and black hair is 27%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.27
0.27/0.95 - 0.03/0.05 = -0.41
-0.41 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 67%. For people who went to tanning salons, the probability of black hair is 23%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.23
0.23 - 0.67 = -0.44
-0.44 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 67%. For people who went to tanning salons, the probability of black hair is 23%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.23
0.23 - 0.67 = -0.44
-0.44 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 82%. The probability of no tanning salon treatment and black hair is 12%. The probability of tanning salon treatment and black hair is 19%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.19
0.19/0.82 - 0.12/0.18 = -0.44
-0.44 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 65%. For people who went to tanning salons, the probability of black hair is 29%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.29
0.29 - 0.65 = -0.36
-0.36 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 75%. For people who went to tanning salons, the probability of black hair is 34%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.34
0.34 - 0.75 = -0.42
-0.42 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 92%. The probability of no tanning salon treatment and black hair is 6%. The probability of tanning salon treatment and black hair is 31%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.31
0.31/0.92 - 0.06/0.08 = -0.42
-0.42 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 83%. For people who went to tanning salons, the probability of black hair is 33%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.33
0.33 - 0.83 = -0.50
-0.50 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 100%. For people not using tanning salon treatments, the probability of black hair is 83%. For people who went to tanning salons, the probability of black hair is 33%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 1.00
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.33
1.00*0.33 - 0.00*0.83 = 0.33
0.33 > 0",fork,getting_tanned,1,marginal,P(Y)
15157,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 100%. The probability of no tanning salon treatment and black hair is 0%. The probability of tanning salon treatment and black hair is 33%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 1.00
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.33
0.33/1.00 - 0.00/0.00 = -0.50
-0.50 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 56%. For people who went to tanning salons, the probability of black hair is 20%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.20
0.20 - 0.56 = -0.36
-0.36 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15162,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 56%. For people who went to tanning salons, the probability of black hair is 20%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.20
0.20 - 0.56 = -0.36
-0.36 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15166,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 91%. The probability of no tanning salon treatment and black hair is 5%. The probability of tanning salon treatment and black hair is 18%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.18
0.18/0.91 - 0.05/0.09 = -0.36
-0.36 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 66%. For people who went to tanning salons, the probability of black hair is 24%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.24
0.24 - 0.66 = -0.42
-0.42 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 99%. For people not using tanning salon treatments, the probability of black hair is 66%. For people who went to tanning salons, the probability of black hair is 24%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.24
0.99*0.24 - 0.01*0.66 = 0.25
0.25 > 0",fork,getting_tanned,1,marginal,P(Y)
15179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 56%. For people who went to tanning salons, the probability of black hair is 22%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.22
0.22 - 0.56 = -0.35
-0.35 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 96%. The probability of no tanning salon treatment and black hair is 2%. The probability of tanning salon treatment and black hair is 21%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.21
0.21/0.96 - 0.02/0.04 = -0.35
-0.35 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 63%. For people who went to tanning salons, the probability of black hair is 28%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.28
0.28 - 0.63 = -0.35
-0.35 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 63%. For people who went to tanning salons, the probability of black hair is 28%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.28
0.28 - 0.63 = -0.35
-0.35 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15198,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15202,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 75%. For people who went to tanning salons, the probability of black hair is 35%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.35
0.35 - 0.75 = -0.40
-0.40 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 85%. For people not using tanning salon treatments, the probability of black hair is 75%. For people who went to tanning salons, the probability of black hair is 35%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.35
0.85*0.35 - 0.15*0.75 = 0.41
0.41 > 0",fork,getting_tanned,1,marginal,P(Y)
15209,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 58%. For people who went to tanning salons, the probability of black hair is 18%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.18
0.18 - 0.58 = -0.39
-0.39 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 58%. For people who went to tanning salons, the probability of black hair is 18%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.18
0.18 - 0.58 = -0.39
-0.39 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 85%. For people not using tanning salon treatments, the probability of black hair is 58%. For people who went to tanning salons, the probability of black hair is 18%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.18
0.85*0.18 - 0.15*0.58 = 0.24
0.24 > 0",fork,getting_tanned,1,marginal,P(Y)
15215,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 85%. For people not using tanning salon treatments, the probability of black hair is 58%. For people who went to tanning salons, the probability of black hair is 18%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.18
0.85*0.18 - 0.15*0.58 = 0.24
0.24 > 0",fork,getting_tanned,1,marginal,P(Y)
15217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 85%. The probability of no tanning salon treatment and black hair is 8%. The probability of tanning salon treatment and black hair is 16%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.16
0.16/0.85 - 0.08/0.15 = -0.39
-0.39 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15219,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 69%. For people who went to tanning salons, the probability of black hair is 23%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.23
0.23 - 0.69 = -0.46
-0.46 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 69%. For people who went to tanning salons, the probability of black hair is 23%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.23
0.23 - 0.69 = -0.46
-0.46 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 82%. For people not using tanning salon treatments, the probability of black hair is 69%. For people who went to tanning salons, the probability of black hair is 23%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.23
0.82*0.23 - 0.18*0.69 = 0.31
0.31 > 0",fork,getting_tanned,1,marginal,P(Y)
15226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 82%. The probability of no tanning salon treatment and black hair is 13%. The probability of tanning salon treatment and black hair is 19%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.19
0.19/0.82 - 0.13/0.18 = -0.46
-0.46 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 65%. For people who went to tanning salons, the probability of black hair is 27%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.27
0.27 - 0.65 = -0.39
-0.39 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 96%. For people not using tanning salon treatments, the probability of black hair is 65%. For people who went to tanning salons, the probability of black hair is 27%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.27
0.96*0.27 - 0.04*0.65 = 0.28
0.28 > 0",fork,getting_tanned,1,marginal,P(Y)
15238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 71%. For people who went to tanning salons, the probability of black hair is 31%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.31
0.31 - 0.71 = -0.40
-0.40 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 71%. For people who went to tanning salons, the probability of black hair is 31%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.31
0.31 - 0.71 = -0.40
-0.40 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 93%. For people not using tanning salon treatments, the probability of black hair is 71%. For people who went to tanning salons, the probability of black hair is 31%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.31
0.93*0.31 - 0.07*0.71 = 0.34
0.34 > 0",fork,getting_tanned,1,marginal,P(Y)
15248,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 50%. For people who went to tanning salons, the probability of black hair is 12%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.12
0.12 - 0.50 = -0.38
-0.38 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 50%. For people who went to tanning salons, the probability of black hair is 12%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.12
0.12 - 0.50 = -0.38
-0.38 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 50%. For people who went to tanning salons, the probability of black hair is 12%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.12
0.12 - 0.50 = -0.38
-0.38 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 91%. For people not using tanning salon treatments, the probability of black hair is 50%. For people who went to tanning salons, the probability of black hair is 12%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.12
0.91*0.12 - 0.09*0.50 = 0.16
0.16 > 0",fork,getting_tanned,1,marginal,P(Y)
15255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 91%. For people not using tanning salon treatments, the probability of black hair is 50%. For people who went to tanning salons, the probability of black hair is 12%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.12
0.91*0.12 - 0.09*0.50 = 0.16
0.16 > 0",fork,getting_tanned,1,marginal,P(Y)
15256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 91%. The probability of no tanning salon treatment and black hair is 5%. The probability of tanning salon treatment and black hair is 11%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.11
0.11/0.91 - 0.05/0.09 = -0.38
-0.38 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 91%. The probability of no tanning salon treatment and black hair is 5%. The probability of tanning salon treatment and black hair is 11%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.11
0.11/0.91 - 0.05/0.09 = -0.38
-0.38 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 71%. For people who went to tanning salons, the probability of black hair is 19%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.19
0.19 - 0.71 = -0.51
-0.51 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15262,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 71%. For people who went to tanning salons, the probability of black hair is 19%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.19
0.19 - 0.71 = -0.51
-0.51 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 71%. For people who went to tanning salons, the probability of black hair is 19%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.19
0.19 - 0.71 = -0.51
-0.51 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 100%. For people not using tanning salon treatments, the probability of black hair is 71%. For people who went to tanning salons, the probability of black hair is 19%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 1.00
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.19
1.00*0.19 - 0.00*0.71 = 0.20
0.20 > 0",fork,getting_tanned,1,marginal,P(Y)
15267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 100%. The probability of no tanning salon treatment and black hair is 0%. The probability of tanning salon treatment and black hair is 19%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 1.00
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.19
0.19/1.00 - 0.00/0.00 = -0.51
-0.51 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 89%. The probability of no tanning salon treatment and black hair is 8%. The probability of tanning salon treatment and black hair is 35%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.35
0.35/0.89 - 0.08/0.11 = -0.38
-0.38 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15278,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 65%. For people who went to tanning salons, the probability of black hair is 20%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.20
0.20 - 0.65 = -0.45
-0.45 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 82%. For people not using tanning salon treatments, the probability of black hair is 65%. For people who went to tanning salons, the probability of black hair is 20%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.20
0.82*0.20 - 0.18*0.65 = 0.28
0.28 > 0",fork,getting_tanned,1,marginal,P(Y)
15286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 82%. The probability of no tanning salon treatment and black hair is 11%. The probability of tanning salon treatment and black hair is 16%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.16
0.16/0.82 - 0.11/0.18 = -0.45
-0.45 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look at how tanning salon treatment correlates with black hair case by case according to going to the beach. Method 2: We look directly at how tanning salon treatment correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 72%. For people who went to tanning salons, the probability of black hair is 33%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y|X)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.33
0.33 - 0.72 = -0.38
-0.38 < 0",fork,getting_tanned,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. For people not using tanning salon treatments, the probability of black hair is 72%. For people who went to tanning salons, the probability of black hair is 33%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.33
0.33 - 0.72 = -0.38
-0.38 < 0",fork,getting_tanned,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 100%. For people not using tanning salon treatments, the probability of black hair is 72%. For people who went to tanning salons, the probability of black hair is 33%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 1.00
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.33
1.00*0.33 - 0.00*0.72 = 0.34
0.34 > 0",fork,getting_tanned,1,marginal,P(Y)
15296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 100%. The probability of no tanning salon treatment and black hair is 0%. The probability of tanning salon treatment and black hair is 33%.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 1.00
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.33
0.33/1.00 - 0.00/0.00 = -0.38
-0.38 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. The overall probability of tanning salon treatment is 100%. The probability of no tanning salon treatment and black hair is 0%. The probability of tanning salon treatment and black hair is 33%.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = black hair.
X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 1.00
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.33
0.33/1.00 - 0.00/0.00 = -0.38
-0.38 < 0",fork,getting_tanned,1,correlation,P(Y | X)
15299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on black hair. Going to the beach has a direct effect on black hair. Method 1: We look directly at how tanning salon treatment correlates with black hair in general. Method 2: We look at this correlation case by case according to going to the beach.",yes,"nan
nan
nan
nan
nan
nan
nan",fork,getting_tanned,2,backadj,[backdoor adjustment set for Y given X]
15300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 79%. For those who choose to take the elevator, the probability of curly hair is 30%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.30
0.30 - 0.79 = -0.49
-0.49 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15302,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 79%. For those who choose to take the elevator, the probability of curly hair is 30%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.30
0.30 - 0.79 = -0.49
-0.49 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15303,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 79%. For those who choose to take the elevator, the probability of curly hair is 30%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.30
0.30 - 0.79 = -0.49
-0.49 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 96%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 71%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 49%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 26%. For those who choose to take the stairs, the probability of penguin happiness is 66%. For those who choose to take the elevator, the probability of penguin happiness is 82%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.96
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.26
P(V2=1 | X=0) = 0.66
P(V2=1 | X=1) = 0.82
0.82 * (0.71 - 0.96)+ 0.66 * (0.26 - 0.49)= -0.04
-0.04 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 96%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 71%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 49%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 26%. For those who choose to take the stairs, the probability of penguin happiness is 66%. For those who choose to take the elevator, the probability of penguin happiness is 82%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.96
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.26
P(V2=1 | X=0) = 0.66
P(V2=1 | X=1) = 0.82
0.66 * (0.26 - 0.49) + 0.82 * (0.71 - 0.96) = -0.46
-0.46 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 5%. For those who choose to take the stairs, the probability of curly hair is 79%. For those who choose to take the elevator, the probability of curly hair is 30%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.30
0.05*0.30 - 0.95*0.79 = 0.77
0.77 > 0",mediation,penguin,1,marginal,P(Y)
15313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 63%. For those who choose to take the elevator, the probability of curly hair is 7%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.07
0.07 - 0.63 = -0.55
-0.55 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15317,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 63%. For those who choose to take the elevator, the probability of curly hair is 7%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.07
0.07 - 0.63 = -0.55
-0.55 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 63%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 53%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 19%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 6%. For those who choose to take the stairs, the probability of penguin happiness is 6%. For those who choose to take the elevator, the probability of penguin happiness is 92%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.53
P(Y=1 | X=1, V2=0) = 0.19
P(Y=1 | X=1, V2=1) = 0.06
P(V2=1 | X=0) = 0.06
P(V2=1 | X=1) = 0.92
0.06 * (0.06 - 0.19) + 0.92 * (0.53 - 0.63) = -0.44
-0.44 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15324,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 16%. The probability of taking the stairs and curly hair is 53%. The probability of taking the elevator and curly hair is 1%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.01
0.01/0.16 - 0.53/0.84 = -0.55
-0.55 < 0",mediation,penguin,1,correlation,P(Y | X)
15325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 16%. The probability of taking the stairs and curly hair is 53%. The probability of taking the elevator and curly hair is 1%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.01
0.01/0.16 - 0.53/0.84 = -0.55
-0.55 < 0",mediation,penguin,1,correlation,P(Y | X)
15326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 70%. For those who choose to take the elevator, the probability of curly hair is 17%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.17
0.17 - 0.70 = -0.53
-0.53 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 80%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 60%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 42%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 16%. For those who choose to take the stairs, the probability of penguin happiness is 48%. For those who choose to take the elevator, the probability of penguin happiness is 94%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.80
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.16
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.94
0.48 * (0.16 - 0.42) + 0.94 * (0.60 - 0.80) = -0.41
-0.41 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 20%. For those who choose to take the stairs, the probability of curly hair is 70%. For those who choose to take the elevator, the probability of curly hair is 17%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.17
0.20*0.17 - 0.80*0.70 = 0.60
0.60 > 0",mediation,penguin,1,marginal,P(Y)
15341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 72%. For those who choose to take the elevator, the probability of curly hair is 24%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.24
0.24 - 0.72 = -0.49
-0.49 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 76%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 64%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 18%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 25%. For those who choose to take the stairs, the probability of penguin happiness is 32%. For those who choose to take the elevator, the probability of penguin happiness is 80%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.25
P(V2=1 | X=0) = 0.32
P(V2=1 | X=1) = 0.80
0.80 * (0.64 - 0.76)+ 0.32 * (0.25 - 0.18)= -0.06
-0.06 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 11%. The probability of taking the stairs and curly hair is 65%. The probability of taking the elevator and curly hair is 3%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.03
0.03/0.11 - 0.65/0.89 = -0.49
-0.49 < 0",mediation,penguin,1,correlation,P(Y | X)
15353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 11%. The probability of taking the stairs and curly hair is 65%. The probability of taking the elevator and curly hair is 3%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.03
0.03/0.11 - 0.65/0.89 = -0.49
-0.49 < 0",mediation,penguin,1,correlation,P(Y | X)
15354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 63%. For those who choose to take the elevator, the probability of curly hair is 21%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.21
0.21 - 0.63 = -0.43
-0.43 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 63%. For those who choose to take the elevator, the probability of curly hair is 21%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.21
0.21 - 0.63 = -0.43
-0.43 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 76%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 51%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 36%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 12%. For those who choose to take the stairs, the probability of penguin happiness is 50%. For those who choose to take the elevator, the probability of penguin happiness is 65%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.36
P(Y=1 | X=1, V2=1) = 0.12
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.65
0.50 * (0.12 - 0.36) + 0.65 * (0.51 - 0.76) = -0.39
-0.39 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 1%. The probability of taking the stairs and curly hair is 63%. The probability of taking the elevator and curly hair is 0%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.00
0.00/0.01 - 0.63/0.99 = -0.43
-0.43 < 0",mediation,penguin,1,correlation,P(Y | X)
15369,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 48%. For those who choose to take the elevator, the probability of curly hair is 4%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.04
0.04 - 0.48 = -0.43
-0.43 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15373,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 48%. For those who choose to take the elevator, the probability of curly hair is 4%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.04
0.04 - 0.48 = -0.43
-0.43 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 48%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 48%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 14%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 3%. For those who choose to take the stairs, the probability of penguin happiness is 51%. For those who choose to take the elevator, the probability of penguin happiness is 90%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.14
P(Y=1 | X=1, V2=1) = 0.03
P(V2=1 | X=0) = 0.51
P(V2=1 | X=1) = 0.90
0.51 * (0.03 - 0.14) + 0.90 * (0.48 - 0.48) = -0.39
-0.39 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 48%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 48%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 14%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 3%. For those who choose to take the stairs, the probability of penguin happiness is 51%. For those who choose to take the elevator, the probability of penguin happiness is 90%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.14
P(Y=1 | X=1, V2=1) = 0.03
P(V2=1 | X=0) = 0.51
P(V2=1 | X=1) = 0.90
0.51 * (0.03 - 0.14) + 0.90 * (0.48 - 0.48) = -0.39
-0.39 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 8%. The probability of taking the stairs and curly hair is 44%. The probability of taking the elevator and curly hair is 0%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.00
0.00/0.08 - 0.44/0.92 = -0.43
-0.43 < 0",mediation,penguin,1,correlation,P(Y | X)
15381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 8%. The probability of taking the stairs and curly hair is 44%. The probability of taking the elevator and curly hair is 0%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.00
0.00/0.08 - 0.44/0.92 = -0.43
-0.43 < 0",mediation,penguin,1,correlation,P(Y | X)
15388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 71%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 47%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 35%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 15%. For those who choose to take the stairs, the probability of penguin happiness is 4%. For those who choose to take the elevator, the probability of penguin happiness is 54%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.47
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.15
P(V2=1 | X=0) = 0.04
P(V2=1 | X=1) = 0.54
0.54 * (0.47 - 0.71)+ 0.04 * (0.15 - 0.35)= -0.12
-0.12 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15389,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 71%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 47%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 35%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 15%. For those who choose to take the stairs, the probability of penguin happiness is 4%. For those who choose to take the elevator, the probability of penguin happiness is 54%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.47
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.15
P(V2=1 | X=0) = 0.04
P(V2=1 | X=1) = 0.54
0.54 * (0.47 - 0.71)+ 0.04 * (0.15 - 0.35)= -0.12
-0.12 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 56%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 64%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 26%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 17%. For those who choose to take the stairs, the probability of penguin happiness is 12%. For those who choose to take the elevator, the probability of penguin happiness is 99%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.56
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.26
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.12
P(V2=1 | X=1) = 0.99
0.99 * (0.64 - 0.56)+ 0.12 * (0.17 - 0.26)= 0.07
0.07 > 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 56%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 64%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 26%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 17%. For those who choose to take the stairs, the probability of penguin happiness is 12%. For those who choose to take the elevator, the probability of penguin happiness is 99%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.56
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.26
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.12
P(V2=1 | X=1) = 0.99
0.99 * (0.64 - 0.56)+ 0.12 * (0.17 - 0.26)= 0.07
0.07 > 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 56%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 64%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 26%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 17%. For those who choose to take the stairs, the probability of penguin happiness is 12%. For those who choose to take the elevator, the probability of penguin happiness is 99%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.56
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.26
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.12
P(V2=1 | X=1) = 0.99
0.12 * (0.17 - 0.26) + 0.99 * (0.64 - 0.56) = -0.33
-0.33 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 56%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 64%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 26%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 17%. For those who choose to take the stairs, the probability of penguin happiness is 12%. For those who choose to take the elevator, the probability of penguin happiness is 99%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.56
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.26
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.12
P(V2=1 | X=1) = 0.99
0.12 * (0.17 - 0.26) + 0.99 * (0.64 - 0.56) = -0.33
-0.33 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 7%. For those who choose to take the stairs, the probability of curly hair is 57%. For those who choose to take the elevator, the probability of curly hair is 17%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.17
0.07*0.17 - 0.93*0.57 = 0.55
0.55 > 0",mediation,penguin,1,marginal,P(Y)
15414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 57%. For those who choose to take the elevator, the probability of curly hair is 2%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.02
0.02 - 0.57 = -0.55
-0.55 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 57%. For those who choose to take the elevator, the probability of curly hair is 2%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.02
0.02 - 0.57 = -0.55
-0.55 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 72%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 38%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 20%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 0%. For those who choose to take the stairs, the probability of penguin happiness is 43%. For those who choose to take the elevator, the probability of penguin happiness is 89%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.72
P(Y=1 | X=0, V2=1) = 0.38
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.00
P(V2=1 | X=0) = 0.43
P(V2=1 | X=1) = 0.89
0.43 * (0.00 - 0.20) + 0.89 * (0.38 - 0.72) = -0.46
-0.46 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15419,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 72%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 38%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 20%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 0%. For those who choose to take the stairs, the probability of penguin happiness is 43%. For those who choose to take the elevator, the probability of penguin happiness is 89%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.72
P(Y=1 | X=0, V2=1) = 0.38
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.00
P(V2=1 | X=0) = 0.43
P(V2=1 | X=1) = 0.89
0.43 * (0.00 - 0.20) + 0.89 * (0.38 - 0.72) = -0.46
-0.46 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 7%. For those who choose to take the stairs, the probability of curly hair is 57%. For those who choose to take the elevator, the probability of curly hair is 2%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.02
0.07*0.02 - 0.93*0.57 = 0.53
0.53 > 0",mediation,penguin,1,marginal,P(Y)
15423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 7%. The probability of taking the stairs and curly hair is 53%. The probability of taking the elevator and curly hair is 0%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.00
0.00/0.07 - 0.53/0.93 = -0.55
-0.55 < 0",mediation,penguin,1,correlation,P(Y | X)
15424,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 78%. For those who choose to take the elevator, the probability of curly hair is 11%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.11
0.11 - 0.78 = -0.67
-0.67 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 78%. For those who choose to take the elevator, the probability of curly hair is 11%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.11
0.11 - 0.78 = -0.67
-0.67 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 84%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 66%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 22%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 7%. For those who choose to take the stairs, the probability of penguin happiness is 32%. For those who choose to take the elevator, the probability of penguin happiness is 74%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.84
P(Y=1 | X=0, V2=1) = 0.66
P(Y=1 | X=1, V2=0) = 0.22
P(Y=1 | X=1, V2=1) = 0.07
P(V2=1 | X=0) = 0.32
P(V2=1 | X=1) = 0.74
0.32 * (0.07 - 0.22) + 0.74 * (0.66 - 0.84) = -0.61
-0.61 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15435,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 10%. For those who choose to take the stairs, the probability of curly hair is 78%. For those who choose to take the elevator, the probability of curly hair is 11%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.11
0.10*0.11 - 0.90*0.78 = 0.71
0.71 > 0",mediation,penguin,1,marginal,P(Y)
15439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 87%. For those who choose to take the elevator, the probability of curly hair is 24%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.24
0.24 - 0.87 = -0.63
-0.63 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 87%. For those who choose to take the elevator, the probability of curly hair is 24%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.24
0.24 - 0.87 = -0.63
-0.63 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 87%. For those who choose to take the elevator, the probability of curly hair is 24%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.24
0.24 - 0.87 = -0.63
-0.63 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15445,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 88%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 65%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 45%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 12%. For those who choose to take the stairs, the probability of penguin happiness is 6%. For those who choose to take the elevator, the probability of penguin happiness is 62%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.65
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.12
P(V2=1 | X=0) = 0.06
P(V2=1 | X=1) = 0.62
0.62 * (0.65 - 0.88)+ 0.06 * (0.12 - 0.45)= -0.13
-0.13 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 1%. For those who choose to take the stairs, the probability of curly hair is 87%. For those who choose to take the elevator, the probability of curly hair is 24%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.24
0.01*0.24 - 0.99*0.87 = 0.86
0.86 > 0",mediation,penguin,1,marginal,P(Y)
15454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 53%. For those who choose to take the elevator, the probability of curly hair is 11%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.11
0.11 - 0.53 = -0.42
-0.42 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 53%. For those who choose to take the elevator, the probability of curly hair is 11%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.11
0.11 - 0.53 = -0.42
-0.42 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15457,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 53%. For those who choose to take the elevator, the probability of curly hair is 11%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.11
0.11 - 0.53 = -0.42
-0.42 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 53%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 53%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 19%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 6%. For those who choose to take the stairs, the probability of penguin happiness is 35%. For those who choose to take the elevator, the probability of penguin happiness is 66%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.53
P(Y=1 | X=1, V2=0) = 0.19
P(Y=1 | X=1, V2=1) = 0.06
P(V2=1 | X=0) = 0.35
P(V2=1 | X=1) = 0.66
0.35 * (0.06 - 0.19) + 0.66 * (0.53 - 0.53) = -0.38
-0.38 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15464,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 14%. The probability of taking the stairs and curly hair is 46%. The probability of taking the elevator and curly hair is 1%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.01
0.01/0.14 - 0.46/0.86 = -0.42
-0.42 < 0",mediation,penguin,1,correlation,P(Y | X)
15469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 73%. For those who choose to take the elevator, the probability of curly hair is 23%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.23
0.23 - 0.73 = -0.50
-0.50 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 10%. For those who choose to take the stairs, the probability of curly hair is 73%. For those who choose to take the elevator, the probability of curly hair is 23%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.23
0.10*0.23 - 0.90*0.73 = 0.69
0.69 > 0",mediation,penguin,1,marginal,P(Y)
15478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 10%. The probability of taking the stairs and curly hair is 66%. The probability of taking the elevator and curly hair is 2%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.02
0.02/0.10 - 0.66/0.90 = -0.50
-0.50 < 0",mediation,penguin,1,correlation,P(Y | X)
15482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 94%. For those who choose to take the elevator, the probability of curly hair is 45%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.45
0.45 - 0.94 = -0.49
-0.49 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 2%. For those who choose to take the stairs, the probability of curly hair is 94%. For those who choose to take the elevator, the probability of curly hair is 45%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.45
0.02*0.45 - 0.98*0.94 = 0.93
0.93 > 0",mediation,penguin,1,marginal,P(Y)
15491,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 2%. For those who choose to take the stairs, the probability of curly hair is 94%. For those who choose to take the elevator, the probability of curly hair is 45%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.45
0.02*0.45 - 0.98*0.94 = 0.93
0.93 > 0",mediation,penguin,1,marginal,P(Y)
15494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15497,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 80%. For those who choose to take the elevator, the probability of curly hair is 24%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.24
0.24 - 0.80 = -0.56
-0.56 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 80%. For those who choose to take the elevator, the probability of curly hair is 24%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.24
0.24 - 0.80 = -0.56
-0.56 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 85%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 57%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 42%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 15%. For those who choose to take the stairs, the probability of penguin happiness is 19%. For those who choose to take the elevator, the probability of penguin happiness is 66%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.85
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.15
P(V2=1 | X=0) = 0.19
P(V2=1 | X=1) = 0.66
0.19 * (0.15 - 0.42) + 0.66 * (0.57 - 0.85) = -0.43
-0.43 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 1%. For those who choose to take the stairs, the probability of curly hair is 80%. For those who choose to take the elevator, the probability of curly hair is 24%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.24
0.01*0.24 - 0.99*0.80 = 0.79
0.79 > 0",mediation,penguin,1,marginal,P(Y)
15506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 1%. The probability of taking the stairs and curly hair is 79%. The probability of taking the elevator and curly hair is 0%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.79
P(Y=1, X=1=1) = 0.00
0.00/0.01 - 0.79/0.99 = -0.56
-0.56 < 0",mediation,penguin,1,correlation,P(Y | X)
15509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 70%. For those who choose to take the elevator, the probability of curly hair is 29%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.29
0.29 - 0.70 = -0.41
-0.41 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15514,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 71%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 68%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 21%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 34%. For those who choose to take the stairs, the probability of penguin happiness is 30%. For those who choose to take the elevator, the probability of penguin happiness is 65%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.68
P(Y=1 | X=1, V2=0) = 0.21
P(Y=1 | X=1, V2=1) = 0.34
P(V2=1 | X=0) = 0.30
P(V2=1 | X=1) = 0.65
0.65 * (0.68 - 0.71)+ 0.30 * (0.34 - 0.21)= -0.01
-0.01 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 6%. The probability of taking the stairs and curly hair is 66%. The probability of taking the elevator and curly hair is 2%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.02
0.02/0.06 - 0.66/0.94 = -0.41
-0.41 < 0",mediation,penguin,1,correlation,P(Y | X)
15522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 58%. For those who choose to take the elevator, the probability of curly hair is 3%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.03
0.03 - 0.58 = -0.55
-0.55 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 76%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 44%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 26%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 1%. For those who choose to take the stairs, the probability of penguin happiness is 55%. For those who choose to take the elevator, the probability of penguin happiness is 92%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.44
P(Y=1 | X=1, V2=0) = 0.26
P(Y=1 | X=1, V2=1) = 0.01
P(V2=1 | X=0) = 0.55
P(V2=1 | X=1) = 0.92
0.92 * (0.44 - 0.76)+ 0.55 * (0.01 - 0.26)= -0.12
-0.12 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 76%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 44%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 26%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 1%. For those who choose to take the stairs, the probability of penguin happiness is 55%. For those who choose to take the elevator, the probability of penguin happiness is 92%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.44
P(Y=1 | X=1, V2=0) = 0.26
P(Y=1 | X=1, V2=1) = 0.01
P(V2=1 | X=0) = 0.55
P(V2=1 | X=1) = 0.92
0.92 * (0.44 - 0.76)+ 0.55 * (0.01 - 0.26)= -0.12
-0.12 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 78%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 84%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 20%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 31%. For those who choose to take the stairs, the probability of penguin happiness is 65%. For those who choose to take the elevator, the probability of penguin happiness is 87%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.31
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.87
0.87 * (0.84 - 0.78)+ 0.65 * (0.31 - 0.20)= 0.02
0.02 > 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 78%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 84%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 20%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 31%. For those who choose to take the stairs, the probability of penguin happiness is 65%. For those who choose to take the elevator, the probability of penguin happiness is 87%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.31
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.87
0.65 * (0.31 - 0.20) + 0.87 * (0.84 - 0.78) = -0.55
-0.55 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 78%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 84%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 20%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 31%. For those who choose to take the stairs, the probability of penguin happiness is 65%. For those who choose to take the elevator, the probability of penguin happiness is 87%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.31
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.87
0.65 * (0.31 - 0.20) + 0.87 * (0.84 - 0.78) = -0.55
-0.55 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 19%. For those who choose to take the stairs, the probability of curly hair is 82%. For those who choose to take the elevator, the probability of curly hair is 30%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.30
0.19*0.30 - 0.81*0.82 = 0.72
0.72 > 0",mediation,penguin,1,marginal,P(Y)
15551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 70%. For those who choose to take the elevator, the probability of curly hair is 29%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.29
0.29 - 0.70 = -0.41
-0.41 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 70%. For those who choose to take the elevator, the probability of curly hair is 29%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.29
0.29 - 0.70 = -0.41
-0.41 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15559,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 81%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 55%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 43%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 23%. For those who choose to take the stairs, the probability of penguin happiness is 42%. For those who choose to take the elevator, the probability of penguin happiness is 71%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.81
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.71
0.42 * (0.23 - 0.43) + 0.71 * (0.55 - 0.81) = -0.35
-0.35 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 16%. For those who choose to take the stairs, the probability of curly hair is 70%. For those who choose to take the elevator, the probability of curly hair is 29%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.29
0.16*0.29 - 0.84*0.70 = 0.63
0.63 > 0",mediation,penguin,1,marginal,P(Y)
15563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 16%. The probability of taking the stairs and curly hair is 59%. The probability of taking the elevator and curly hair is 5%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.05
0.05/0.16 - 0.59/0.84 = -0.41
-0.41 < 0",mediation,penguin,1,correlation,P(Y | X)
15565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 64%. For those who choose to take the elevator, the probability of curly hair is 25%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.25
0.25 - 0.64 = -0.39
-0.39 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 64%. For those who choose to take the elevator, the probability of curly hair is 25%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.25
0.25 - 0.64 = -0.39
-0.39 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 66%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 59%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 19%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 28%. For those who choose to take the stairs, the probability of penguin happiness is 27%. For those who choose to take the elevator, the probability of penguin happiness is 66%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.66
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.19
P(Y=1 | X=1, V2=1) = 0.28
P(V2=1 | X=0) = 0.27
P(V2=1 | X=1) = 0.66
0.66 * (0.59 - 0.66)+ 0.27 * (0.28 - 0.19)= -0.03
-0.03 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 10%. For those who choose to take the stairs, the probability of curly hair is 64%. For those who choose to take the elevator, the probability of curly hair is 25%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.25
0.10*0.25 - 0.90*0.64 = 0.59
0.59 > 0",mediation,penguin,1,marginal,P(Y)
15575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 10%. For those who choose to take the stairs, the probability of curly hair is 64%. For those who choose to take the elevator, the probability of curly hair is 25%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.25
0.10*0.25 - 0.90*0.64 = 0.59
0.59 > 0",mediation,penguin,1,marginal,P(Y)
15577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 10%. The probability of taking the stairs and curly hair is 58%. The probability of taking the elevator and curly hair is 3%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.03
0.03/0.10 - 0.58/0.90 = -0.39
-0.39 < 0",mediation,penguin,1,correlation,P(Y | X)
15580,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 68%. For those who choose to take the elevator, the probability of curly hair is 21%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.21
0.21 - 0.68 = -0.47
-0.47 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 77%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 57%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 39%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 19%. For those who choose to take the stairs, the probability of penguin happiness is 44%. For those who choose to take the elevator, the probability of penguin happiness is 87%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.77
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.19
P(V2=1 | X=0) = 0.44
P(V2=1 | X=1) = 0.87
0.87 * (0.57 - 0.77)+ 0.44 * (0.19 - 0.39)= -0.09
-0.09 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 77%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 57%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 39%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 19%. For those who choose to take the stairs, the probability of penguin happiness is 44%. For those who choose to take the elevator, the probability of penguin happiness is 87%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.77
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.19
P(V2=1 | X=0) = 0.44
P(V2=1 | X=1) = 0.87
0.44 * (0.19 - 0.39) + 0.87 * (0.57 - 0.77) = -0.38
-0.38 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 15%. For those who choose to take the stairs, the probability of curly hair is 68%. For those who choose to take the elevator, the probability of curly hair is 21%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.21
0.15*0.21 - 0.85*0.68 = 0.61
0.61 > 0",mediation,penguin,1,marginal,P(Y)
15590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 15%. The probability of taking the stairs and curly hair is 58%. The probability of taking the elevator and curly hair is 3%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.03
0.03/0.15 - 0.58/0.85 = -0.47
-0.47 < 0",mediation,penguin,1,correlation,P(Y | X)
15593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15595,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 75%. For those who choose to take the elevator, the probability of curly hair is 32%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.32
0.32 - 0.75 = -0.43
-0.43 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 75%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 73%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 16%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 32%. For those who choose to take the stairs, the probability of penguin happiness is 20%. For those who choose to take the elevator, the probability of penguin happiness is 100%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.75
P(Y=1 | X=0, V2=1) = 0.73
P(Y=1 | X=1, V2=0) = 0.16
P(Y=1 | X=1, V2=1) = 0.32
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 1.00
1.00 * (0.73 - 0.75)+ 0.20 * (0.32 - 0.16)= -0.02
-0.02 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 75%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 73%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 16%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 32%. For those who choose to take the stairs, the probability of penguin happiness is 20%. For those who choose to take the elevator, the probability of penguin happiness is 100%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.75
P(Y=1 | X=0, V2=1) = 0.73
P(Y=1 | X=1, V2=0) = 0.16
P(Y=1 | X=1, V2=1) = 0.32
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 1.00
1.00 * (0.73 - 0.75)+ 0.20 * (0.32 - 0.16)= -0.02
-0.02 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15600,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 75%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 73%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 16%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 32%. For those who choose to take the stairs, the probability of penguin happiness is 20%. For those who choose to take the elevator, the probability of penguin happiness is 100%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.75
P(Y=1 | X=0, V2=1) = 0.73
P(Y=1 | X=1, V2=0) = 0.16
P(Y=1 | X=1, V2=1) = 0.32
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 1.00
0.20 * (0.32 - 0.16) + 1.00 * (0.73 - 0.75) = -0.56
-0.56 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15603,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 11%. For those who choose to take the stairs, the probability of curly hair is 75%. For those who choose to take the elevator, the probability of curly hair is 32%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.32
0.11*0.32 - 0.89*0.75 = 0.69
0.69 > 0",mediation,penguin,1,marginal,P(Y)
15605,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 11%. The probability of taking the stairs and curly hair is 67%. The probability of taking the elevator and curly hair is 3%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.67
P(Y=1, X=1=1) = 0.03
0.03/0.11 - 0.67/0.89 = -0.43
-0.43 < 0",mediation,penguin,1,correlation,P(Y | X)
15606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15607,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 72%. For those who choose to take the elevator, the probability of curly hair is 24%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.24
0.24 - 0.72 = -0.48
-0.48 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 78%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 50%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 39%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 15%. For those who choose to take the stairs, the probability of penguin happiness is 25%. For those who choose to take the elevator, the probability of penguin happiness is 64%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.15
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.64
0.64 * (0.50 - 0.78)+ 0.25 * (0.15 - 0.39)= -0.11
-0.11 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 78%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 50%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 39%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 15%. For those who choose to take the stairs, the probability of penguin happiness is 25%. For those who choose to take the elevator, the probability of penguin happiness is 64%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.39
P(Y=1 | X=1, V2=1) = 0.15
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.64
0.64 * (0.50 - 0.78)+ 0.25 * (0.15 - 0.39)= -0.11
-0.11 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 8%. For those who choose to take the stairs, the probability of curly hair is 72%. For those who choose to take the elevator, the probability of curly hair is 24%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.24
0.08*0.24 - 0.92*0.72 = 0.68
0.68 > 0",mediation,penguin,1,marginal,P(Y)
15621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 65%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 50%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 13%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 12%. For those who choose to take the stairs, the probability of penguin happiness is 21%. For those who choose to take the elevator, the probability of penguin happiness is 67%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.65
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.13
P(Y=1 | X=1, V2=1) = 0.12
P(V2=1 | X=0) = 0.21
P(V2=1 | X=1) = 0.67
0.67 * (0.50 - 0.65)+ 0.21 * (0.12 - 0.13)= -0.07
-0.07 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 65%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 50%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 13%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 12%. For those who choose to take the stairs, the probability of penguin happiness is 21%. For those who choose to take the elevator, the probability of penguin happiness is 67%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.65
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.13
P(Y=1 | X=1, V2=1) = 0.12
P(V2=1 | X=0) = 0.21
P(V2=1 | X=1) = 0.67
0.21 * (0.12 - 0.13) + 0.67 * (0.50 - 0.65) = -0.49
-0.49 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15630,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 4%. For those who choose to take the stairs, the probability of curly hair is 62%. For those who choose to take the elevator, the probability of curly hair is 12%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.12
0.04*0.12 - 0.96*0.62 = 0.60
0.60 > 0",mediation,penguin,1,marginal,P(Y)
15631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 4%. For those who choose to take the stairs, the probability of curly hair is 62%. For those who choose to take the elevator, the probability of curly hair is 12%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.12
0.04*0.12 - 0.96*0.62 = 0.60
0.60 > 0",mediation,penguin,1,marginal,P(Y)
15632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 4%. The probability of taking the stairs and curly hair is 59%. The probability of taking the elevator and curly hair is 0%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.00
0.00/0.04 - 0.59/0.96 = -0.50
-0.50 < 0",mediation,penguin,1,correlation,P(Y | X)
15633,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 4%. The probability of taking the stairs and curly hair is 59%. The probability of taking the elevator and curly hair is 0%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.59
P(Y=1, X=1=1) = 0.00
0.00/0.04 - 0.59/0.96 = -0.50
-0.50 < 0",mediation,penguin,1,correlation,P(Y | X)
15634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 68%. For those who choose to take the elevator, the probability of curly hair is 19%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.19
0.19 - 0.68 = -0.49
-0.49 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 18%. For those who choose to take the stairs, the probability of curly hair is 68%. For those who choose to take the elevator, the probability of curly hair is 19%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.19
0.18*0.19 - 0.82*0.68 = 0.59
0.59 > 0",mediation,penguin,1,marginal,P(Y)
15651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 80%. For those who choose to take the elevator, the probability of curly hair is 27%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.27
0.27 - 0.80 = -0.53
-0.53 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 4%. For those who choose to take the stairs, the probability of curly hair is 80%. For those who choose to take the elevator, the probability of curly hair is 27%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.27
0.04*0.27 - 0.96*0.80 = 0.77
0.77 > 0",mediation,penguin,1,marginal,P(Y)
15660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 4%. The probability of taking the stairs and curly hair is 76%. The probability of taking the elevator and curly hair is 1%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.01
0.01/0.04 - 0.76/0.96 = -0.53
-0.53 < 0",mediation,penguin,1,correlation,P(Y | X)
15661,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 4%. The probability of taking the stairs and curly hair is 76%. The probability of taking the elevator and curly hair is 1%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.04
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.01
0.01/0.04 - 0.76/0.96 = -0.53
-0.53 < 0",mediation,penguin,1,correlation,P(Y | X)
15663,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look directly at how my decision correlates with curly hair in general. Method 2: We look at this correlation case by case according to penguin mood.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 75%. For those who choose to take the elevator, the probability of curly hair is 30%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.30
0.30 - 0.75 = -0.44
-0.44 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 85%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 59%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 45%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 23%. For those who choose to take the stairs, the probability of penguin happiness is 40%. For those who choose to take the elevator, the probability of penguin happiness is 68%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.85
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.68
0.68 * (0.59 - 0.85)+ 0.40 * (0.23 - 0.45)= -0.07
-0.07 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 85%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 59%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 45%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 23%. For those who choose to take the stairs, the probability of penguin happiness is 40%. For those who choose to take the elevator, the probability of penguin happiness is 68%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.85
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.68
0.68 * (0.59 - 0.85)+ 0.40 * (0.23 - 0.45)= -0.07
-0.07 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 85%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 59%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 45%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 23%. For those who choose to take the stairs, the probability of penguin happiness is 40%. For those who choose to take the elevator, the probability of penguin happiness is 68%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.85
P(Y=1 | X=0, V2=1) = 0.59
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.68
0.40 * (0.23 - 0.45) + 0.68 * (0.59 - 0.85) = -0.38
-0.38 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 1%. For those who choose to take the stairs, the probability of curly hair is 75%. For those who choose to take the elevator, the probability of curly hair is 30%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.30
0.01*0.30 - 0.99*0.75 = 0.74
0.74 > 0",mediation,penguin,1,marginal,P(Y)
15675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 1%. The probability of taking the stairs and curly hair is 74%. The probability of taking the elevator and curly hair is 0%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.74
P(Y=1, X=1=1) = 0.00
0.00/0.01 - 0.74/0.99 = -0.44
-0.44 < 0",mediation,penguin,1,correlation,P(Y | X)
15682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 90%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 91%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 48%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 54%. For those who choose to take the stairs, the probability of penguin happiness is 33%. For those who choose to take the elevator, the probability of penguin happiness is 75%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.91
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.54
P(V2=1 | X=0) = 0.33
P(V2=1 | X=1) = 0.75
0.75 * (0.91 - 0.90)+ 0.33 * (0.54 - 0.48)= 0.00
0.00 = 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 90%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 91%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 48%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 54%. For those who choose to take the stairs, the probability of penguin happiness is 33%. For those who choose to take the elevator, the probability of penguin happiness is 75%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.91
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.54
P(V2=1 | X=0) = 0.33
P(V2=1 | X=1) = 0.75
0.75 * (0.91 - 0.90)+ 0.33 * (0.54 - 0.48)= 0.00
0.00 = 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 90%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 91%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 48%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 54%. For those who choose to take the stairs, the probability of penguin happiness is 33%. For those who choose to take the elevator, the probability of penguin happiness is 75%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.91
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.54
P(V2=1 | X=0) = 0.33
P(V2=1 | X=1) = 0.75
0.33 * (0.54 - 0.48) + 0.75 * (0.91 - 0.90) = -0.41
-0.41 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 90%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 91%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 48%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 54%. For those who choose to take the stairs, the probability of penguin happiness is 33%. For those who choose to take the elevator, the probability of penguin happiness is 75%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.91
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.54
P(V2=1 | X=0) = 0.33
P(V2=1 | X=1) = 0.75
0.33 * (0.54 - 0.48) + 0.75 * (0.91 - 0.90) = -0.41
-0.41 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 16%. The probability of taking the stairs and curly hair is 76%. The probability of taking the elevator and curly hair is 9%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.09
0.09/0.16 - 0.76/0.84 = -0.38
-0.38 < 0",mediation,penguin,1,correlation,P(Y | X)
15690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. Method 1: We look at how my decision correlates with curly hair case by case according to penguin mood. Method 2: We look directly at how my decision correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,penguin,2,backadj,[backdoor adjustment set for Y given X]
15699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 73%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 69%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 36%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 25%. For those who choose to take the stairs, the probability of penguin happiness is 10%. For those who choose to take the elevator, the probability of penguin happiness is 71%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.73
P(Y=1 | X=0, V2=1) = 0.69
P(Y=1 | X=1, V2=0) = 0.36
P(Y=1 | X=1, V2=1) = 0.25
P(V2=1 | X=0) = 0.10
P(V2=1 | X=1) = 0.71
0.10 * (0.25 - 0.36) + 0.71 * (0.69 - 0.73) = -0.38
-0.38 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 87%. For those who choose to take the elevator, the probability of curly hair is 29%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.29
0.29 - 0.87 = -0.58
-0.58 < 0",mediation,penguin,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs, the probability of curly hair is 87%. For those who choose to take the elevator, the probability of curly hair is 29%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.29
0.29 - 0.87 = -0.58
-0.58 < 0",mediation,penguin,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 87%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 60%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 38%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 14%. For those who choose to take the stairs, the probability of penguin happiness is 2%. For those who choose to take the elevator, the probability of penguin happiness is 40%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.87
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.38
P(Y=1 | X=1, V2=1) = 0.14
P(V2=1 | X=0) = 0.02
P(V2=1 | X=1) = 0.40
0.40 * (0.60 - 0.87)+ 0.02 * (0.14 - 0.38)= -0.11
-0.11 < 0",mediation,penguin,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
15712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. For those who choose to take the stairs and penguins who are sad, the probability of curly hair is 87%. For those who choose to take the stairs and penguins who are happy, the probability of curly hair is 60%. For those who choose to take the elevator and penguins who are sad, the probability of curly hair is 38%. For those who choose to take the elevator and penguins who are happy, the probability of curly hair is 14%. For those who choose to take the stairs, the probability of penguin happiness is 2%. For those who choose to take the elevator, the probability of penguin happiness is 40%.",no,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.87
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.38
P(Y=1 | X=1, V2=1) = 0.14
P(V2=1 | X=0) = 0.02
P(V2=1 | X=1) = 0.40
0.02 * (0.14 - 0.38) + 0.40 * (0.60 - 0.87) = -0.49
-0.49 < 0",mediation,penguin,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
15714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 2%. For those who choose to take the stairs, the probability of curly hair is 87%. For those who choose to take the elevator, the probability of curly hair is 29%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.29
0.02*0.29 - 0.98*0.87 = 0.86
0.86 > 0",mediation,penguin,1,marginal,P(Y)
15717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and curly hair. Penguin mood has a direct effect on curly hair. The overall probability of taking the elevator is 2%. The probability of taking the stairs and curly hair is 85%. The probability of taking the elevator and curly hair is 0%.",yes,"Let X = my decision; V2 = penguin mood; Y = curly hair.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.85
P(Y=1, X=1=1) = 0.00
0.00/0.02 - 0.85/0.98 = -0.58
-0.58 < 0",mediation,penguin,1,correlation,P(Y | X)
15723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 54%. For vaccinated individuals, the probability of black hair is 48%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.48
0.48 - 0.54 = -0.06
-0.06 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 54%. For vaccinated individuals, the probability of black hair is 48%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.48
0.48 - 0.54 = -0.06
-0.06 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 16%. The probability of lack of vaccination and black hair is 45%. The probability of vaccination and black hair is 8%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.08
0.08/0.16 - 0.45/0.84 = -0.06
-0.06 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 47%. For vaccinated individuals, the probability of black hair is 44%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.44
0.44 - 0.47 = -0.03
-0.03 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 6%. For unvaccinated individuals, the probability of black hair is 47%. For vaccinated individuals, the probability of black hair is 44%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.44
0.06*0.44 - 0.94*0.47 = 0.47
0.47 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 6%. For unvaccinated individuals, the probability of black hair is 47%. For vaccinated individuals, the probability of black hair is 44%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.44
0.06*0.44 - 0.94*0.47 = 0.47
0.47 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 57%. For vaccinated individuals, the probability of black hair is 66%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.66
0.66 - 0.57 = 0.09
0.09 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 57%. For vaccinated individuals, the probability of black hair is 66%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.66
0.66 - 0.57 = 0.09
0.09 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 57%. For vaccinated individuals, the probability of black hair is 66%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.66
0.66 - 0.57 = 0.09
0.09 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 6%. For unvaccinated individuals, the probability of black hair is 57%. For vaccinated individuals, the probability of black hair is 66%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.66
0.06*0.66 - 0.94*0.57 = 0.57
0.57 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 6%. For unvaccinated individuals, the probability of black hair is 57%. For vaccinated individuals, the probability of black hair is 66%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.66
0.06*0.66 - 0.94*0.57 = 0.57
0.57 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15752,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 6%. The probability of lack of vaccination and black hair is 53%. The probability of vaccination and black hair is 4%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.04
0.04/0.06 - 0.53/0.94 = 0.09
0.09 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 43%. For vaccinated individuals, the probability of black hair is 54%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.54
0.54 - 0.43 = 0.11
0.11 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 2%. For unvaccinated individuals, the probability of black hair is 43%. For vaccinated individuals, the probability of black hair is 54%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.54
0.02*0.54 - 0.98*0.43 = 0.43
0.43 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 2%. For unvaccinated individuals, the probability of black hair is 43%. For vaccinated individuals, the probability of black hair is 54%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.54
0.02*0.54 - 0.98*0.43 = 0.43
0.43 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 48%. For vaccinated individuals, the probability of black hair is 58%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.58
0.58 - 0.48 = 0.09
0.09 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 48%. For vaccinated individuals, the probability of black hair is 58%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.58
0.58 - 0.48 = 0.09
0.09 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 1%. The probability of lack of vaccination and black hair is 48%. The probability of vaccination and black hair is 1%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.01
0.01/0.01 - 0.48/0.99 = 0.09
0.09 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 35%. For vaccinated individuals, the probability of black hair is 40%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.40
0.40 - 0.35 = 0.05
0.05 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 6%. For unvaccinated individuals, the probability of black hair is 35%. For vaccinated individuals, the probability of black hair is 40%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.40
0.06*0.40 - 0.94*0.35 = 0.35
0.35 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 6%. The probability of lack of vaccination and black hair is 33%. The probability of vaccination and black hair is 2%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.02
0.02/0.06 - 0.33/0.94 = 0.05
0.05 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15790,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 28%. For vaccinated individuals, the probability of black hair is 42%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.42
0.42 - 0.28 = 0.13
0.13 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 28%. For vaccinated individuals, the probability of black hair is 42%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.42
0.42 - 0.28 = 0.13
0.13 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 2%. The probability of lack of vaccination and black hair is 28%. The probability of vaccination and black hair is 1%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.28/0.98 = 0.13
0.13 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 2%. The probability of lack of vaccination and black hair is 28%. The probability of vaccination and black hair is 1%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.28
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.28/0.98 = 0.13
0.13 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 49%. For vaccinated individuals, the probability of black hair is 49%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.49 - 0.49 = -0.00
0.00 = 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 49%. For vaccinated individuals, the probability of black hair is 49%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.49
0.49 - 0.49 = -0.00
0.00 = 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 9%. The probability of lack of vaccination and black hair is 45%. The probability of vaccination and black hair is 4%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.04
0.04/0.09 - 0.45/0.91 = -0.00
0.00 = 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 40%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.40
0.40 - 0.51 = -0.12
-0.12 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 8%. The probability of lack of vaccination and black hair is 47%. The probability of vaccination and black hair is 3%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.47/0.92 = -0.12
-0.12 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 8%. The probability of lack of vaccination and black hair is 47%. The probability of vaccination and black hair is 3%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.47/0.92 = -0.12
-0.12 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 56%. For vaccinated individuals, the probability of black hair is 55%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.55
0.55 - 0.56 = -0.01
-0.01 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15833,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 56%. For vaccinated individuals, the probability of black hair is 55%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.55
0.55 - 0.56 = -0.01
-0.01 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15840,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 41%. For vaccinated individuals, the probability of black hair is 42%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.42
0.42 - 0.41 = 0.02
0.02 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 41%. For vaccinated individuals, the probability of black hair is 42%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.42
0.42 - 0.41 = 0.02
0.02 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 41%. For vaccinated individuals, the probability of black hair is 42%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.42
0.42 - 0.41 = 0.02
0.02 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. For unvaccinated individuals, the probability of black hair is 41%. For vaccinated individuals, the probability of black hair is 42%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.42
0.10*0.42 - 0.90*0.41 = 0.41
0.41 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 43%. For vaccinated individuals, the probability of black hair is 41%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.41
0.41 - 0.43 = -0.02
-0.02 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 43%. For vaccinated individuals, the probability of black hair is 41%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.41
0.41 - 0.43 = -0.02
-0.02 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15862,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 41%. For vaccinated individuals, the probability of black hair is 51%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.51
0.51 - 0.41 = 0.11
0.11 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 41%. For vaccinated individuals, the probability of black hair is 51%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.51
0.51 - 0.41 = 0.11
0.11 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15873,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 2%. The probability of lack of vaccination and black hair is 40%. The probability of vaccination and black hair is 1%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.40/0.98 = 0.11
0.11 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15877,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 47%. For vaccinated individuals, the probability of black hair is 52%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.52
0.52 - 0.47 = 0.06
0.06 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15878,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 47%. For vaccinated individuals, the probability of black hair is 52%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.52
0.52 - 0.47 = 0.06
0.06 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15884,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 16%. The probability of lack of vaccination and black hair is 39%. The probability of vaccination and black hair is 9%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.09
0.09/0.16 - 0.39/0.84 = 0.06
0.06 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 32%. For vaccinated individuals, the probability of black hair is 38%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.38
0.38 - 0.32 = 0.06
0.06 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 32%. For vaccinated individuals, the probability of black hair is 38%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.38
0.38 - 0.32 = 0.06
0.06 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 32%. For vaccinated individuals, the probability of black hair is 38%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.38
0.38 - 0.32 = 0.06
0.06 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 4%. For unvaccinated individuals, the probability of black hair is 32%. For vaccinated individuals, the probability of black hair is 38%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.38
0.04*0.38 - 0.96*0.32 = 0.32
0.32 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15899,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 55%. For vaccinated individuals, the probability of black hair is 55%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.55
0.55 - 0.55 = -0.00
0.00 = 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 55%. For vaccinated individuals, the probability of black hair is 55%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.55
0.55 - 0.55 = -0.00
0.00 = 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15905,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 55%. For vaccinated individuals, the probability of black hair is 55%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.55
0.55 - 0.55 = -0.00
0.00 = 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 7%. The probability of lack of vaccination and black hair is 52%. The probability of vaccination and black hair is 4%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.52/0.93 = -0.00
0.00 = 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 7%. The probability of lack of vaccination and black hair is 52%. The probability of vaccination and black hair is 4%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.52/0.93 = -0.00
0.00 = 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 52%. For vaccinated individuals, the probability of black hair is 59%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.59
0.59 - 0.52 = 0.07
0.07 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15916,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 52%. For vaccinated individuals, the probability of black hair is 59%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.59
0.59 - 0.52 = 0.07
0.07 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 52%. For vaccinated individuals, the probability of black hair is 59%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.59
0.59 - 0.52 = 0.07
0.07 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 14%. For unvaccinated individuals, the probability of black hair is 52%. For vaccinated individuals, the probability of black hair is 59%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.59
0.14*0.59 - 0.86*0.52 = 0.53
0.53 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 45%. For vaccinated individuals, the probability of black hair is 49%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.49
0.49 - 0.45 = 0.05
0.05 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 45%. For vaccinated individuals, the probability of black hair is 49%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.49
0.49 - 0.45 = 0.05
0.05 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15936,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 40%. For vaccinated individuals, the probability of black hair is 38%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.38
0.38 - 0.40 = -0.03
-0.03 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 40%. For vaccinated individuals, the probability of black hair is 38%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.38
0.38 - 0.40 = -0.03
-0.03 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 40%. For vaccinated individuals, the probability of black hair is 38%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.38
0.38 - 0.40 = -0.03
-0.03 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 3%. For unvaccinated individuals, the probability of black hair is 40%. For vaccinated individuals, the probability of black hair is 38%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.38
0.03*0.38 - 0.97*0.40 = 0.40
0.40 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 3%. The probability of lack of vaccination and black hair is 39%. The probability of vaccination and black hair is 1%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.39/0.97 = -0.03
-0.03 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15947,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 56%. For vaccinated individuals, the probability of black hair is 52%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.52
0.52 - 0.56 = -0.04
-0.04 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
15952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 56%. For vaccinated individuals, the probability of black hair is 52%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.52
0.52 - 0.56 = -0.04
-0.04 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 18%. For unvaccinated individuals, the probability of black hair is 56%. For vaccinated individuals, the probability of black hair is 52%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.52
0.18*0.52 - 0.82*0.56 = 0.56
0.56 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 18%. The probability of lack of vaccination and black hair is 46%. The probability of vaccination and black hair is 10%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.10
0.10/0.18 - 0.46/0.82 = -0.04
-0.04 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 59%. For vaccinated individuals, the probability of black hair is 53%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.53
0.53 - 0.59 = -0.06
-0.06 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 59%. For vaccinated individuals, the probability of black hair is 53%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.53
0.53 - 0.59 = -0.06
-0.06 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
15965,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 59%. For vaccinated individuals, the probability of black hair is 53%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.53
0.53 - 0.59 = -0.06
-0.06 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 4%. For unvaccinated individuals, the probability of black hair is 59%. For vaccinated individuals, the probability of black hair is 53%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.53
0.04*0.53 - 0.96*0.59 = 0.59
0.59 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 4%. For unvaccinated individuals, the probability of black hair is 59%. For vaccinated individuals, the probability of black hair is 53%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.53
0.04*0.53 - 0.96*0.59 = 0.59
0.59 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15976,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 42%. For vaccinated individuals, the probability of black hair is 33%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.33
0.33 - 0.42 = -0.10
-0.10 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 42%. For vaccinated individuals, the probability of black hair is 33%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.33
0.33 - 0.42 = -0.10
-0.10 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 12%. For unvaccinated individuals, the probability of black hair is 42%. For vaccinated individuals, the probability of black hair is 33%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.33
0.12*0.33 - 0.88*0.42 = 0.41
0.41 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 12%. The probability of lack of vaccination and black hair is 38%. The probability of vaccination and black hair is 4%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.04
0.04/0.12 - 0.38/0.88 = -0.10
-0.10 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15983,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
15988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 42%. For vaccinated individuals, the probability of black hair is 60%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.60
0.60 - 0.42 = 0.18
0.18 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15989,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 42%. For vaccinated individuals, the probability of black hair is 60%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.60
0.60 - 0.42 = 0.18
0.18 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
15990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. For unvaccinated individuals, the probability of black hair is 42%. For vaccinated individuals, the probability of black hair is 60%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.60
0.10*0.60 - 0.90*0.42 = 0.44
0.44 > 0",diamond,vaccine_kills,1,marginal,P(Y)
15992,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. The probability of lack of vaccination and black hair is 38%. The probability of vaccination and black hair is 6%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.38/0.90 = 0.18
0.18 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. The probability of lack of vaccination and black hair is 38%. The probability of vaccination and black hair is 6%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.38
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.38/0.90 = 0.18
0.18 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
15997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 27%. For vaccinated individuals, the probability of black hair is 37%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.37
0.37 - 0.27 = 0.10
0.10 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 27%. For vaccinated individuals, the probability of black hair is 37%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.37
0.37 - 0.27 = 0.10
0.10 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
16003,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 5%. For unvaccinated individuals, the probability of black hair is 27%. For vaccinated individuals, the probability of black hair is 37%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.37
0.05*0.37 - 0.95*0.27 = 0.27
0.27 > 0",diamond,vaccine_kills,1,marginal,P(Y)
16007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 54%. For vaccinated individuals, the probability of black hair is 46%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.46
0.46 - 0.54 = -0.09
-0.09 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 54%. For vaccinated individuals, the probability of black hair is 46%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.46
0.46 - 0.54 = -0.09
-0.09 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 9%. The probability of lack of vaccination and black hair is 49%. The probability of vaccination and black hair is 4%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.04
0.04/0.09 - 0.49/0.91 = -0.09
-0.09 < 0",diamond,vaccine_kills,1,correlation,P(Y | X)
16019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 44%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.44
0.44 - 0.51 = -0.08
-0.08 < 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16022,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 44%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.44
0.44 - 0.51 = -0.08
-0.08 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 44%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.44
0.44 - 0.51 = -0.08
-0.08 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 44%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.44
0.44 - 0.51 = -0.08
-0.08 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
16026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 1%. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 44%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.44
0.01*0.44 - 0.99*0.51 = 0.51
0.51 > 0",diamond,vaccine_kills,1,marginal,P(Y)
16027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 1%. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 44%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.44
0.01*0.44 - 0.99*0.51 = 0.51
0.51 > 0",diamond,vaccine_kills,1,marginal,P(Y)
16031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 62%. For vaccinated individuals, the probability of black hair is 62%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.62
0.62 - 0.62 = -0.00
0.00 = 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16036,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 62%. For vaccinated individuals, the probability of black hair is 62%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.62
0.62 - 0.62 = -0.00
0.00 = 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
16037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 62%. For vaccinated individuals, the probability of black hair is 62%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.62
0.62 - 0.62 = -0.00
0.00 = 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
16038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. For unvaccinated individuals, the probability of black hair is 62%. For vaccinated individuals, the probability of black hair is 62%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.62
0.10*0.62 - 0.90*0.62 = 0.62
0.62 > 0",diamond,vaccine_kills,1,marginal,P(Y)
16042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 11%. For unvaccinated individuals, the probability of black hair is 53%. For vaccinated individuals, the probability of black hair is 58%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.58
0.11*0.58 - 0.89*0.53 = 0.53
0.53 > 0",diamond,vaccine_kills,1,marginal,P(Y)
16053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 11%. The probability of lack of vaccination and black hair is 47%. The probability of vaccination and black hair is 6%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.06
0.06/0.11 - 0.47/0.89 = 0.05
0.05 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
16054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 64%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.64
0.64 - 0.51 = 0.12
0.12 > 0",diamond,vaccine_kills,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16058,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 64%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.64
0.64 - 0.51 = 0.12
0.12 > 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 64%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.64
0.64 - 0.51 = 0.12
0.12 > 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
16062,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 64%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.64
0.10*0.64 - 0.90*0.51 = 0.53
0.53 > 0",diamond,vaccine_kills,1,marginal,P(Y)
16063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. For unvaccinated individuals, the probability of black hair is 51%. For vaccinated individuals, the probability of black hair is 64%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.64
0.10*0.64 - 0.90*0.51 = 0.53
0.53 > 0",diamond,vaccine_kills,1,marginal,P(Y)
16064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. The probability of lack of vaccination and black hair is 46%. The probability of vaccination and black hair is 7%.",yes,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.07
0.07/0.10 - 0.46/0.90 = 0.12
0.12 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
16065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. The overall probability of vaccination is 10%. The probability of lack of vaccination and black hair is 46%. The probability of vaccination and black hair is 7%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.07
0.07/0.10 - 0.46/0.90 = 0.12
0.12 > 0",diamond,vaccine_kills,1,correlation,P(Y | X)
16067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 61%. For vaccinated individuals, the probability of black hair is 50%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.50
0.50 - 0.61 = -0.11
-0.11 < 0",diamond,vaccine_kills,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. For unvaccinated individuals, the probability of black hair is 61%. For vaccinated individuals, the probability of black hair is 50%.",no,"Let X = vaccination status; V3 = vaccination reaction; V2 = getting smallpox; Y = black hair.
X->V3,X->V2,V2->Y,V3->Y
E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.50
0.50 - 0.61 = -0.11
-0.11 < 0",diamond,vaccine_kills,3,nie,"E[Y_{X=0, V2=1, V3=1} - Y_{X=0, V2=0, V3=0}]"
16078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look at how vaccination status correlates with black hair case by case according to vaccination reaction. Method 2: We look directly at how vaccination status correlates with black hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16079,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Vaccination status has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on black hair. Vaccination reaction has a direct effect on black hair. Method 1: We look directly at how vaccination status correlates with black hair in general. Method 2: We look at this correlation case by case according to vaccination reaction.",yes,"nan
nan
nan
nan
nan
nan
nan",diamond,vaccine_kills,2,backadj,[backdoor adjustment set for Y given X]
16080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 45%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.45
0.45 - 0.62 = -0.17
-0.17 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 45%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.45
0.45 - 0.62 = -0.17
-0.17 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16083,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 45%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.45
0.45 - 0.62 = -0.17
-0.17 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 76%. For people who have a sister and with low blood pressure, the probability of healthy heart is 19%. For people who have a sister and with high blood pressure, the probability of healthy heart is 47%. For people who do not have a sister, the probability of high blood pressure is 50%. For people who have a sister, the probability of high blood pressure is 92%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.76
P(Y=1 | X=1, V2=0) = 0.19
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.92
0.92 * (0.76 - 0.48)+ 0.50 * (0.47 - 0.19)= 0.12
0.12 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 7%. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 45%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.45
0.07*0.45 - 0.93*0.62 = 0.61
0.61 > 0",mediation,blood_pressure,1,marginal,P(Y)
16098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 69%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 98%. For people who have a sister and with low blood pressure, the probability of healthy heart is 36%. For people who have a sister and with high blood pressure, the probability of healthy heart is 61%. For people who do not have a sister, the probability of high blood pressure is 70%. For people who have a sister, the probability of high blood pressure is 55%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.69
P(Y=1 | X=0, V2=1) = 0.98
P(Y=1 | X=1, V2=0) = 0.36
P(Y=1 | X=1, V2=1) = 0.61
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.55
0.55 * (0.98 - 0.69)+ 0.70 * (0.61 - 0.36)= -0.04
-0.04 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16100,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 69%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 98%. For people who have a sister and with low blood pressure, the probability of healthy heart is 36%. For people who have a sister and with high blood pressure, the probability of healthy heart is 61%. For people who do not have a sister, the probability of high blood pressure is 70%. For people who have a sister, the probability of high blood pressure is 55%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.69
P(Y=1 | X=0, V2=1) = 0.98
P(Y=1 | X=1, V2=0) = 0.36
P(Y=1 | X=1, V2=1) = 0.61
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.55
0.70 * (0.61 - 0.36) + 0.55 * (0.98 - 0.69) = -0.36
-0.36 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 69%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 98%. For people who have a sister and with low blood pressure, the probability of healthy heart is 36%. For people who have a sister and with high blood pressure, the probability of healthy heart is 61%. For people who do not have a sister, the probability of high blood pressure is 70%. For people who have a sister, the probability of high blood pressure is 55%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.69
P(Y=1 | X=0, V2=1) = 0.98
P(Y=1 | X=1, V2=0) = 0.36
P(Y=1 | X=1, V2=1) = 0.61
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.55
0.70 * (0.61 - 0.36) + 0.55 * (0.98 - 0.69) = -0.36
-0.36 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16103,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 3%. For people who do not have a sister, the probability of healthy heart is 89%. For people who have a sister, the probability of healthy heart is 50%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.50
0.03*0.50 - 0.97*0.89 = 0.88
0.88 > 0",mediation,blood_pressure,1,marginal,P(Y)
16105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 3%. The probability of not having a sister and healthy heart is 87%. The probability of having a sister and healthy heart is 2%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.87
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.87/0.97 = -0.40
-0.40 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16110,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 57%. For people who have a sister, the probability of healthy heart is 39%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.39
0.39 - 0.57 = -0.18
-0.18 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 9%. The probability of not having a sister and healthy heart is 52%. The probability of having a sister and healthy heart is 3%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.03
0.03/0.09 - 0.52/0.91 = -0.18
-0.18 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 9%. The probability of not having a sister and healthy heart is 52%. The probability of having a sister and healthy heart is 3%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.03
0.03/0.09 - 0.52/0.91 = -0.18
-0.18 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 80%. For people who have a sister, the probability of healthy heart is 22%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.22
0.22 - 0.80 = -0.58
-0.58 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16125,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 80%. For people who have a sister, the probability of healthy heart is 22%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.22
0.22 - 0.80 = -0.58
-0.58 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 61%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 92%. For people who have a sister and with low blood pressure, the probability of healthy heart is 18%. For people who have a sister and with high blood pressure, the probability of healthy heart is 45%. For people who do not have a sister, the probability of high blood pressure is 61%. For people who have a sister, the probability of high blood pressure is 14%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.61
P(Y=1 | X=0, V2=1) = 0.92
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.61
P(V2=1 | X=1) = 0.14
0.14 * (0.92 - 0.61)+ 0.61 * (0.45 - 0.18)= -0.14
-0.14 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 6%. The probability of not having a sister and healthy heart is 75%. The probability of having a sister and healthy heart is 1%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.75
P(Y=1, X=1=1) = 0.01
0.01/0.06 - 0.75/0.94 = -0.58
-0.58 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 6%. The probability of not having a sister and healthy heart is 75%. The probability of having a sister and healthy heart is 1%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.75
P(Y=1, X=1=1) = 0.01
0.01/0.06 - 0.75/0.94 = -0.58
-0.58 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 59%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 86%. For people who have a sister and with low blood pressure, the probability of healthy heart is 25%. For people who have a sister and with high blood pressure, the probability of healthy heart is 54%. For people who do not have a sister, the probability of high blood pressure is 36%. For people who have a sister, the probability of high blood pressure is 89%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.86
P(Y=1 | X=1, V2=0) = 0.25
P(Y=1 | X=1, V2=1) = 0.54
P(V2=1 | X=0) = 0.36
P(V2=1 | X=1) = 0.89
0.36 * (0.54 - 0.25) + 0.89 * (0.86 - 0.59) = -0.33
-0.33 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 5%. For people who do not have a sister, the probability of healthy heart is 69%. For people who have a sister, the probability of healthy heart is 51%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.51
0.05*0.51 - 0.95*0.69 = 0.68
0.68 > 0",mediation,blood_pressure,1,marginal,P(Y)
16145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 5%. For people who do not have a sister, the probability of healthy heart is 69%. For people who have a sister, the probability of healthy heart is 51%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.51
0.05*0.51 - 0.95*0.69 = 0.68
0.68 > 0",mediation,blood_pressure,1,marginal,P(Y)
16158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. For people who do not have a sister, the probability of healthy heart is 64%. For people who have a sister, the probability of healthy heart is 31%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.31
0.19*0.31 - 0.81*0.64 = 0.58
0.58 > 0",mediation,blood_pressure,1,marginal,P(Y)
16163,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 68%. For people who have a sister, the probability of healthy heart is 40%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.40
0.40 - 0.68 = -0.28
-0.28 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 68%. For people who have a sister, the probability of healthy heart is 40%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.40
0.40 - 0.68 = -0.28
-0.28 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 68%. For people who have a sister, the probability of healthy heart is 40%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.40
0.40 - 0.68 = -0.28
-0.28 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. For people who do not have a sister, the probability of healthy heart is 68%. For people who have a sister, the probability of healthy heart is 40%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.40
0.19*0.40 - 0.81*0.68 = 0.63
0.63 > 0",mediation,blood_pressure,1,marginal,P(Y)
16173,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. For people who do not have a sister, the probability of healthy heart is 68%. For people who have a sister, the probability of healthy heart is 40%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.40
0.19*0.40 - 0.81*0.68 = 0.63
0.63 > 0",mediation,blood_pressure,1,marginal,P(Y)
16178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 59%. For people who have a sister, the probability of healthy heart is 36%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.36
0.36 - 0.59 = -0.23
-0.23 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 59%. For people who have a sister, the probability of healthy heart is 36%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.36
0.36 - 0.59 = -0.23
-0.23 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 77%. For people who have a sister and with low blood pressure, the probability of healthy heart is 20%. For people who have a sister and with high blood pressure, the probability of healthy heart is 46%. For people who do not have a sister, the probability of high blood pressure is 37%. For people who have a sister, the probability of high blood pressure is 60%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.77
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.60
0.60 * (0.77 - 0.48)+ 0.37 * (0.46 - 0.20)= 0.06
0.06 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 77%. For people who have a sister and with low blood pressure, the probability of healthy heart is 20%. For people who have a sister and with high blood pressure, the probability of healthy heart is 46%. For people who do not have a sister, the probability of high blood pressure is 37%. For people who have a sister, the probability of high blood pressure is 60%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.77
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.60
0.60 * (0.77 - 0.48)+ 0.37 * (0.46 - 0.20)= 0.06
0.06 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 77%. For people who have a sister and with low blood pressure, the probability of healthy heart is 20%. For people who have a sister and with high blood pressure, the probability of healthy heart is 46%. For people who do not have a sister, the probability of high blood pressure is 37%. For people who have a sister, the probability of high blood pressure is 60%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.77
P(Y=1 | X=1, V2=0) = 0.20
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.37
P(V2=1 | X=1) = 0.60
0.37 * (0.46 - 0.20) + 0.60 * (0.77 - 0.48) = -0.29
-0.29 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 2%. The probability of not having a sister and healthy heart is 58%. The probability of having a sister and healthy heart is 1%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.58/0.98 = -0.23
-0.23 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 45%. For people who have a sister, the probability of healthy heart is 28%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.28
0.28 - 0.45 = -0.18
-0.18 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16197,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 38%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 69%. For people who have a sister and with low blood pressure, the probability of healthy heart is 4%. For people who have a sister and with high blood pressure, the probability of healthy heart is 34%. For people who do not have a sister, the probability of high blood pressure is 25%. For people who have a sister, the probability of high blood pressure is 80%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.69
P(Y=1 | X=1, V2=0) = 0.04
P(Y=1 | X=1, V2=1) = 0.34
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.80
0.80 * (0.69 - 0.38)+ 0.25 * (0.34 - 0.04)= 0.17
0.17 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16198,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 38%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 69%. For people who have a sister and with low blood pressure, the probability of healthy heart is 4%. For people who have a sister and with high blood pressure, the probability of healthy heart is 34%. For people who do not have a sister, the probability of high blood pressure is 25%. For people who have a sister, the probability of high blood pressure is 80%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.69
P(Y=1 | X=1, V2=0) = 0.04
P(Y=1 | X=1, V2=1) = 0.34
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.80
0.25 * (0.34 - 0.04) + 0.80 * (0.69 - 0.38) = -0.34
-0.34 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 38%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 69%. For people who have a sister and with low blood pressure, the probability of healthy heart is 4%. For people who have a sister and with high blood pressure, the probability of healthy heart is 34%. For people who do not have a sister, the probability of high blood pressure is 25%. For people who have a sister, the probability of high blood pressure is 80%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.69
P(Y=1 | X=1, V2=0) = 0.04
P(Y=1 | X=1, V2=1) = 0.34
P(V2=1 | X=0) = 0.25
P(V2=1 | X=1) = 0.80
0.25 * (0.34 - 0.04) + 0.80 * (0.69 - 0.38) = -0.34
-0.34 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 5%. For people who do not have a sister, the probability of healthy heart is 45%. For people who have a sister, the probability of healthy heart is 28%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.28
0.05*0.28 - 0.95*0.45 = 0.45
0.45 > 0",mediation,blood_pressure,1,marginal,P(Y)
16206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 55%. For people who have a sister, the probability of healthy heart is 30%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.30
0.30 - 0.55 = -0.25
-0.25 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 55%. For people who have a sister, the probability of healthy heart is 30%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.30
0.30 - 0.55 = -0.25
-0.25 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 43%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 71%. For people who have a sister and with low blood pressure, the probability of healthy heart is 18%. For people who have a sister and with high blood pressure, the probability of healthy heart is 43%. For people who do not have a sister, the probability of high blood pressure is 42%. For people who have a sister, the probability of high blood pressure is 49%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.43
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.49
0.49 * (0.71 - 0.43)+ 0.42 * (0.43 - 0.18)= 0.02
0.02 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 43%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 71%. For people who have a sister and with low blood pressure, the probability of healthy heart is 18%. For people who have a sister and with high blood pressure, the probability of healthy heart is 43%. For people who do not have a sister, the probability of high blood pressure is 42%. For people who have a sister, the probability of high blood pressure is 49%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.43
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.49
0.42 * (0.43 - 0.18) + 0.49 * (0.71 - 0.43) = -0.26
-0.26 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 43%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 71%. For people who have a sister and with low blood pressure, the probability of healthy heart is 18%. For people who have a sister and with high blood pressure, the probability of healthy heart is 43%. For people who do not have a sister, the probability of high blood pressure is 42%. For people who have a sister, the probability of high blood pressure is 49%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.43
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.49
0.42 * (0.43 - 0.18) + 0.49 * (0.71 - 0.43) = -0.26
-0.26 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. The probability of not having a sister and healthy heart is 44%. The probability of having a sister and healthy heart is 6%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.06
0.06/0.19 - 0.44/0.81 = -0.25
-0.25 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. The probability of not having a sister and healthy heart is 44%. The probability of having a sister and healthy heart is 6%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.06
0.06/0.19 - 0.44/0.81 = -0.25
-0.25 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16219,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 75%. For people who have a sister, the probability of healthy heart is 56%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.56
0.56 - 0.75 = -0.19
-0.19 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 63%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 91%. For people who have a sister and with low blood pressure, the probability of healthy heart is 37%. For people who have a sister and with high blood pressure, the probability of healthy heart is 67%. For people who do not have a sister, the probability of high blood pressure is 42%. For people who have a sister, the probability of high blood pressure is 62%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.91
P(Y=1 | X=1, V2=0) = 0.37
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.62
0.62 * (0.91 - 0.63)+ 0.42 * (0.67 - 0.37)= 0.06
0.06 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 63%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 91%. For people who have a sister and with low blood pressure, the probability of healthy heart is 37%. For people who have a sister and with high blood pressure, the probability of healthy heart is 67%. For people who do not have a sister, the probability of high blood pressure is 42%. For people who have a sister, the probability of high blood pressure is 62%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.91
P(Y=1 | X=1, V2=0) = 0.37
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.62
0.42 * (0.67 - 0.37) + 0.62 * (0.91 - 0.63) = -0.25
-0.25 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 63%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 91%. For people who have a sister and with low blood pressure, the probability of healthy heart is 37%. For people who have a sister and with high blood pressure, the probability of healthy heart is 67%. For people who do not have a sister, the probability of high blood pressure is 42%. For people who have a sister, the probability of high blood pressure is 62%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.91
P(Y=1 | X=1, V2=0) = 0.37
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.62
0.42 * (0.67 - 0.37) + 0.62 * (0.91 - 0.63) = -0.25
-0.25 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 1%. For people who do not have a sister, the probability of healthy heart is 75%. For people who have a sister, the probability of healthy heart is 56%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.56
0.01*0.56 - 0.99*0.75 = 0.75
0.75 > 0",mediation,blood_pressure,1,marginal,P(Y)
16229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 1%. For people who do not have a sister, the probability of healthy heart is 75%. For people who have a sister, the probability of healthy heart is 56%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.56
0.01*0.56 - 0.99*0.75 = 0.75
0.75 > 0",mediation,blood_pressure,1,marginal,P(Y)
16230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 1%. The probability of not having a sister and healthy heart is 74%. The probability of having a sister and healthy heart is 1%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.74
P(Y=1, X=1=1) = 0.01
0.01/0.01 - 0.74/0.99 = -0.19
-0.19 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 75%. For people who have a sister, the probability of healthy heart is 28%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.28
0.28 - 0.75 = -0.47
-0.47 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 75%. For people who have a sister, the probability of healthy heart is 28%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.28
0.28 - 0.75 = -0.47
-0.47 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 45%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 78%. For people who have a sister and with low blood pressure, the probability of healthy heart is 8%. For people who have a sister and with high blood pressure, the probability of healthy heart is 51%. For people who do not have a sister, the probability of high blood pressure is 93%. For people who have a sister, the probability of high blood pressure is 47%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.45
P(Y=1 | X=0, V2=1) = 0.78
P(Y=1 | X=1, V2=0) = 0.08
P(Y=1 | X=1, V2=1) = 0.51
P(V2=1 | X=0) = 0.93
P(V2=1 | X=1) = 0.47
0.93 * (0.51 - 0.08) + 0.47 * (0.78 - 0.45) = -0.27
-0.27 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 55%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.55
0.55 - 0.62 = -0.07
-0.07 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 55%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.55
0.55 - 0.62 = -0.07
-0.07 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 57%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 89%. For people who have a sister and with low blood pressure, the probability of healthy heart is 31%. For people who have a sister and with high blood pressure, the probability of healthy heart is 65%. For people who do not have a sister, the probability of high blood pressure is 17%. For people who have a sister, the probability of high blood pressure is 71%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.57
P(Y=1 | X=0, V2=1) = 0.89
P(Y=1 | X=1, V2=0) = 0.31
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.17
P(V2=1 | X=1) = 0.71
0.71 * (0.89 - 0.57)+ 0.17 * (0.65 - 0.31)= 0.17
0.17 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 55%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.55
0.19*0.55 - 0.81*0.62 = 0.61
0.61 > 0",mediation,blood_pressure,1,marginal,P(Y)
16258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. The probability of not having a sister and healthy heart is 50%. The probability of having a sister and healthy heart is 11%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.11
0.11/0.19 - 0.50/0.81 = -0.07
-0.07 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. The probability of not having a sister and healthy heart is 50%. The probability of having a sister and healthy heart is 11%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.11
0.11/0.19 - 0.50/0.81 = -0.07
-0.07 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 64%. For people who have a sister, the probability of healthy heart is 21%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.21
0.21 - 0.64 = -0.43
-0.43 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 80%. For people who have a sister and with low blood pressure, the probability of healthy heart is 7%. For people who have a sister and with high blood pressure, the probability of healthy heart is 49%. For people who do not have a sister, the probability of high blood pressure is 51%. For people who have a sister, the probability of high blood pressure is 33%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.80
P(Y=1 | X=1, V2=0) = 0.07
P(Y=1 | X=1, V2=1) = 0.49
P(V2=1 | X=0) = 0.51
P(V2=1 | X=1) = 0.33
0.51 * (0.49 - 0.07) + 0.33 * (0.80 - 0.48) = -0.36
-0.36 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 17%. The probability of not having a sister and healthy heart is 53%. The probability of having a sister and healthy heart is 4%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.04
0.04/0.17 - 0.53/0.83 = -0.43
-0.43 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 37%. For people who have a sister, the probability of healthy heart is 37%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.37
0.37 - 0.37 = -0.00
0.00 = 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 37%. For people who have a sister, the probability of healthy heart is 37%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.37
0.37 - 0.37 = -0.00
0.00 = 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 35%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 70%. For people who have a sister and with low blood pressure, the probability of healthy heart is 7%. For people who have a sister and with high blood pressure, the probability of healthy heart is 44%. For people who do not have a sister, the probability of high blood pressure is 7%. For people who have a sister, the probability of high blood pressure is 82%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.35
P(Y=1 | X=0, V2=1) = 0.70
P(Y=1 | X=1, V2=0) = 0.07
P(Y=1 | X=1, V2=1) = 0.44
P(V2=1 | X=0) = 0.07
P(V2=1 | X=1) = 0.82
0.07 * (0.44 - 0.07) + 0.82 * (0.70 - 0.35) = -0.27
-0.27 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 6%. For people who do not have a sister, the probability of healthy heart is 37%. For people who have a sister, the probability of healthy heart is 37%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.37
0.06*0.37 - 0.94*0.37 = 0.37
0.37 > 0",mediation,blood_pressure,1,marginal,P(Y)
16287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 6%. The probability of not having a sister and healthy heart is 35%. The probability of having a sister and healthy heart is 2%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.02
0.02/0.06 - 0.35/0.94 = -0.00
0.00 = 0",mediation,blood_pressure,1,correlation,P(Y | X)
16288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 67%. For people who have a sister, the probability of healthy heart is 39%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.39
0.39 - 0.67 = -0.28
-0.28 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 67%. For people who have a sister, the probability of healthy heart is 39%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.39
0.39 - 0.67 = -0.28
-0.28 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 12%. For people who do not have a sister, the probability of healthy heart is 67%. For people who have a sister, the probability of healthy heart is 39%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.39
0.12*0.39 - 0.88*0.67 = 0.63
0.63 > 0",mediation,blood_pressure,1,marginal,P(Y)
16302,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 57%. For people who have a sister, the probability of healthy heart is 39%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.39
0.39 - 0.57 = -0.18
-0.18 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 57%. For people who have a sister, the probability of healthy heart is 39%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.39
0.39 - 0.57 = -0.18
-0.18 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 48%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 73%. For people who have a sister and with low blood pressure, the probability of healthy heart is 24%. For people who have a sister and with high blood pressure, the probability of healthy heart is 48%. For people who do not have a sister, the probability of high blood pressure is 36%. For people who have a sister, the probability of high blood pressure is 64%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.48
P(Y=1 | X=0, V2=1) = 0.73
P(Y=1 | X=1, V2=0) = 0.24
P(Y=1 | X=1, V2=1) = 0.48
P(V2=1 | X=0) = 0.36
P(V2=1 | X=1) = 0.64
0.36 * (0.48 - 0.24) + 0.64 * (0.73 - 0.48) = -0.25
-0.25 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16317,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 95%. For people who have a sister, the probability of healthy heart is 28%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.28
0.28 - 0.95 = -0.67
-0.67 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16321,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 95%. For people who have a sister, the probability of healthy heart is 28%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.28
0.28 - 0.95 = -0.67
-0.67 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 64%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 97%. For people who have a sister and with low blood pressure, the probability of healthy heart is 23%. For people who have a sister and with high blood pressure, the probability of healthy heart is 53%. For people who do not have a sister, the probability of high blood pressure is 93%. For people who have a sister, the probability of high blood pressure is 15%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.64
P(Y=1 | X=0, V2=1) = 0.97
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.53
P(V2=1 | X=0) = 0.93
P(V2=1 | X=1) = 0.15
0.15 * (0.97 - 0.64)+ 0.93 * (0.53 - 0.23)= -0.26
-0.26 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 9%. For people who do not have a sister, the probability of healthy heart is 95%. For people who have a sister, the probability of healthy heart is 28%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.28
0.09*0.28 - 0.91*0.95 = 0.88
0.88 > 0",mediation,blood_pressure,1,marginal,P(Y)
16327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 9%. For people who do not have a sister, the probability of healthy heart is 95%. For people who have a sister, the probability of healthy heart is 28%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.28
0.09*0.28 - 0.91*0.95 = 0.88
0.88 > 0",mediation,blood_pressure,1,marginal,P(Y)
16331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 51%. For people who have a sister, the probability of healthy heart is 42%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.42
0.42 - 0.51 = -0.10
-0.10 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16335,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 51%. For people who have a sister, the probability of healthy heart is 42%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.42
0.42 - 0.51 = -0.10
-0.10 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 46%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 79%. For people who have a sister and with low blood pressure, the probability of healthy heart is 18%. For people who have a sister and with high blood pressure, the probability of healthy heart is 47%. For people who do not have a sister, the probability of high blood pressure is 16%. For people who have a sister, the probability of high blood pressure is 81%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.46
P(Y=1 | X=0, V2=1) = 0.79
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.81
0.81 * (0.79 - 0.46)+ 0.16 * (0.47 - 0.18)= 0.21
0.21 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 46%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 79%. For people who have a sister and with low blood pressure, the probability of healthy heart is 18%. For people who have a sister and with high blood pressure, the probability of healthy heart is 47%. For people who do not have a sister, the probability of high blood pressure is 16%. For people who have a sister, the probability of high blood pressure is 81%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.46
P(Y=1 | X=0, V2=1) = 0.79
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.81
0.81 * (0.79 - 0.46)+ 0.16 * (0.47 - 0.18)= 0.21
0.21 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 46%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 79%. For people who have a sister and with low blood pressure, the probability of healthy heart is 18%. For people who have a sister and with high blood pressure, the probability of healthy heart is 47%. For people who do not have a sister, the probability of high blood pressure is 16%. For people who have a sister, the probability of high blood pressure is 81%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.46
P(Y=1 | X=0, V2=1) = 0.79
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.81
0.16 * (0.47 - 0.18) + 0.81 * (0.79 - 0.46) = -0.28
-0.28 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 46%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 68%. For people who have a sister and with low blood pressure, the probability of healthy heart is 7%. For people who have a sister and with high blood pressure, the probability of healthy heart is 43%. For people who do not have a sister, the probability of high blood pressure is 82%. For people who have a sister, the probability of high blood pressure is 45%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.46
P(Y=1 | X=0, V2=1) = 0.68
P(Y=1 | X=1, V2=0) = 0.07
P(Y=1 | X=1, V2=1) = 0.43
P(V2=1 | X=0) = 0.82
P(V2=1 | X=1) = 0.45
0.45 * (0.68 - 0.46)+ 0.82 * (0.43 - 0.07)= -0.08
-0.08 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 9%. For people who do not have a sister, the probability of healthy heart is 64%. For people who have a sister, the probability of healthy heart is 23%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.23
0.09*0.23 - 0.91*0.64 = 0.61
0.61 > 0",mediation,blood_pressure,1,marginal,P(Y)
16355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 9%. For people who do not have a sister, the probability of healthy heart is 64%. For people who have a sister, the probability of healthy heart is 23%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.23
0.09*0.23 - 0.91*0.64 = 0.61
0.61 > 0",mediation,blood_pressure,1,marginal,P(Y)
16356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 9%. The probability of not having a sister and healthy heart is 58%. The probability of having a sister and healthy heart is 2%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.02
0.02/0.09 - 0.58/0.91 = -0.41
-0.41 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 64%. For people who have a sister, the probability of healthy heart is 53%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.53
0.53 - 0.64 = -0.11
-0.11 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 64%. For people who have a sister, the probability of healthy heart is 53%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.53
0.53 - 0.64 = -0.11
-0.11 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 19%. The probability of not having a sister and healthy heart is 52%. The probability of having a sister and healthy heart is 10%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.10
0.10/0.19 - 0.52/0.81 = -0.11
-0.11 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 48%. For people who have a sister, the probability of healthy heart is 38%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.38
0.38 - 0.48 = -0.10
-0.10 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 48%. For people who have a sister, the probability of healthy heart is 38%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.38
0.38 - 0.48 = -0.10
-0.10 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16378,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 43%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 72%. For people who have a sister and with low blood pressure, the probability of healthy heart is 14%. For people who have a sister and with high blood pressure, the probability of healthy heart is 49%. For people who do not have a sister, the probability of high blood pressure is 20%. For people who have a sister, the probability of high blood pressure is 70%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.72
P(Y=1 | X=1, V2=0) = 0.14
P(Y=1 | X=1, V2=1) = 0.49
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.70
0.70 * (0.72 - 0.43)+ 0.20 * (0.49 - 0.14)= 0.15
0.15 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 2%. For people who do not have a sister, the probability of healthy heart is 48%. For people who have a sister, the probability of healthy heart is 38%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.38
0.02*0.38 - 0.98*0.48 = 0.48
0.48 > 0",mediation,blood_pressure,1,marginal,P(Y)
16388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 45%. For people who have a sister, the probability of healthy heart is 31%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.31
0.31 - 0.45 = -0.15
-0.15 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 45%. For people who have a sister, the probability of healthy heart is 31%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.31
0.31 - 0.45 = -0.15
-0.15 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16392,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 36%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 63%. For people who have a sister and with low blood pressure, the probability of healthy heart is 6%. For people who have a sister and with high blood pressure, the probability of healthy heart is 36%. For people who do not have a sister, the probability of high blood pressure is 34%. For people who have a sister, the probability of high blood pressure is 83%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.36
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.06
P(Y=1 | X=1, V2=1) = 0.36
P(V2=1 | X=0) = 0.34
P(V2=1 | X=1) = 0.83
0.83 * (0.63 - 0.36)+ 0.34 * (0.36 - 0.06)= 0.13
0.13 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 3%. For people who do not have a sister, the probability of healthy heart is 45%. For people who have a sister, the probability of healthy heart is 31%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.31
0.03*0.31 - 0.97*0.45 = 0.45
0.45 > 0",mediation,blood_pressure,1,marginal,P(Y)
16402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 71%. For people who have a sister, the probability of healthy heart is 43%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.43
0.43 - 0.71 = -0.28
-0.28 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 71%. For people who have a sister, the probability of healthy heart is 43%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.43
0.43 - 0.71 = -0.28
-0.28 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 58%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 84%. For people who have a sister and with low blood pressure, the probability of healthy heart is 24%. For people who have a sister and with high blood pressure, the probability of healthy heart is 51%. For people who do not have a sister, the probability of high blood pressure is 50%. For people who have a sister, the probability of high blood pressure is 70%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.58
P(Y=1 | X=0, V2=1) = 0.84
P(Y=1 | X=1, V2=0) = 0.24
P(Y=1 | X=1, V2=1) = 0.51
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.70
0.50 * (0.51 - 0.24) + 0.70 * (0.84 - 0.58) = -0.33
-0.33 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16416,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 67%. For people who have a sister, the probability of healthy heart is 44%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.44
0.44 - 0.67 = -0.23
-0.23 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 67%. For people who have a sister, the probability of healthy heart is 44%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.44
0.44 - 0.67 = -0.23
-0.23 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 56%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 83%. For people who have a sister and with low blood pressure, the probability of healthy heart is 27%. For people who have a sister and with high blood pressure, the probability of healthy heart is 51%. For people who do not have a sister, the probability of high blood pressure is 41%. For people who have a sister, the probability of high blood pressure is 71%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.56
P(Y=1 | X=0, V2=1) = 0.83
P(Y=1 | X=1, V2=0) = 0.27
P(Y=1 | X=1, V2=1) = 0.51
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.71
0.71 * (0.83 - 0.56)+ 0.41 * (0.51 - 0.27)= 0.08
0.08 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 56%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 83%. For people who have a sister and with low blood pressure, the probability of healthy heart is 27%. For people who have a sister and with high blood pressure, the probability of healthy heart is 51%. For people who do not have a sister, the probability of high blood pressure is 41%. For people who have a sister, the probability of high blood pressure is 71%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.56
P(Y=1 | X=0, V2=1) = 0.83
P(Y=1 | X=1, V2=0) = 0.27
P(Y=1 | X=1, V2=1) = 0.51
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.71
0.41 * (0.51 - 0.27) + 0.71 * (0.83 - 0.56) = -0.31
-0.31 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 18%. The probability of not having a sister and healthy heart is 55%. The probability of having a sister and healthy heart is 8%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.55
P(Y=1, X=1=1) = 0.08
0.08/0.18 - 0.55/0.82 = -0.23
-0.23 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 18%. The probability of not having a sister and healthy heart is 55%. The probability of having a sister and healthy heart is 8%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.55
P(Y=1, X=1=1) = 0.08
0.08/0.18 - 0.55/0.82 = -0.23
-0.23 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 35%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.35
0.35 - 0.62 = -0.27
-0.27 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16435,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 53%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 75%. For people who have a sister and with low blood pressure, the probability of healthy heart is 23%. For people who have a sister and with high blood pressure, the probability of healthy heart is 52%. For people who do not have a sister, the probability of high blood pressure is 41%. For people who have a sister, the probability of high blood pressure is 43%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.75
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.41
P(V2=1 | X=1) = 0.43
0.43 * (0.75 - 0.53)+ 0.41 * (0.52 - 0.23)= 0.00
0.00 = 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 14%. For people who do not have a sister, the probability of healthy heart is 62%. For people who have a sister, the probability of healthy heart is 35%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.35
0.14*0.35 - 0.86*0.62 = 0.58
0.58 > 0",mediation,blood_pressure,1,marginal,P(Y)
16440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 14%. The probability of not having a sister and healthy heart is 53%. The probability of having a sister and healthy heart is 5%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.05
0.05/0.14 - 0.53/0.86 = -0.27
-0.27 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 14%. The probability of not having a sister and healthy heart is 53%. The probability of having a sister and healthy heart is 5%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.05
0.05/0.14 - 0.53/0.86 = -0.27
-0.27 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 56%. For people who have a sister, the probability of healthy heart is 28%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.28
0.28 - 0.56 = -0.29
-0.29 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 44%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 71%. For people who have a sister and with low blood pressure, the probability of healthy heart is 9%. For people who have a sister and with high blood pressure, the probability of healthy heart is 35%. For people who do not have a sister, the probability of high blood pressure is 47%. For people who have a sister, the probability of high blood pressure is 73%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.09
P(Y=1 | X=1, V2=1) = 0.35
P(V2=1 | X=0) = 0.47
P(V2=1 | X=1) = 0.73
0.73 * (0.71 - 0.44)+ 0.47 * (0.35 - 0.09)= 0.07
0.07 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 44%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 71%. For people who have a sister and with low blood pressure, the probability of healthy heart is 9%. For people who have a sister and with high blood pressure, the probability of healthy heart is 35%. For people who do not have a sister, the probability of high blood pressure is 47%. For people who have a sister, the probability of high blood pressure is 73%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.09
P(Y=1 | X=1, V2=1) = 0.35
P(V2=1 | X=0) = 0.47
P(V2=1 | X=1) = 0.73
0.73 * (0.71 - 0.44)+ 0.47 * (0.35 - 0.09)= 0.07
0.07 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 44%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 71%. For people who have a sister and with low blood pressure, the probability of healthy heart is 9%. For people who have a sister and with high blood pressure, the probability of healthy heart is 35%. For people who do not have a sister, the probability of high blood pressure is 47%. For people who have a sister, the probability of high blood pressure is 73%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.09
P(Y=1 | X=1, V2=1) = 0.35
P(V2=1 | X=0) = 0.47
P(V2=1 | X=1) = 0.73
0.47 * (0.35 - 0.09) + 0.73 * (0.71 - 0.44) = -0.35
-0.35 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 44%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 71%. For people who have a sister and with low blood pressure, the probability of healthy heart is 9%. For people who have a sister and with high blood pressure, the probability of healthy heart is 35%. For people who do not have a sister, the probability of high blood pressure is 47%. For people who have a sister, the probability of high blood pressure is 73%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.44
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.09
P(Y=1 | X=1, V2=1) = 0.35
P(V2=1 | X=0) = 0.47
P(V2=1 | X=1) = 0.73
0.47 * (0.35 - 0.09) + 0.73 * (0.71 - 0.44) = -0.35
-0.35 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 12%. The probability of not having a sister and healthy heart is 50%. The probability of having a sister and healthy heart is 3%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.03
0.03/0.12 - 0.50/0.88 = -0.29
-0.29 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 12%. The probability of not having a sister and healthy heart is 50%. The probability of having a sister and healthy heart is 3%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.03
0.03/0.12 - 0.50/0.88 = -0.29
-0.29 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16458,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 73%. For people who have a sister, the probability of healthy heart is 37%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.37
0.37 - 0.73 = -0.36
-0.36 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 73%. For people who have a sister, the probability of healthy heart is 37%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.37
0.37 - 0.73 = -0.36
-0.36 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 10%. For people who do not have a sister, the probability of healthy heart is 73%. For people who have a sister, the probability of healthy heart is 37%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.37
0.10*0.37 - 0.90*0.73 = 0.69
0.69 > 0",mediation,blood_pressure,1,marginal,P(Y)
16468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. The overall probability of having a sister is 10%. The probability of not having a sister and healthy heart is 66%. The probability of having a sister and healthy heart is 4%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.04
0.04/0.10 - 0.66/0.90 = -0.36
-0.36 < 0",mediation,blood_pressure,1,correlation,P(Y | X)
16470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 56%. For people who have a sister, the probability of healthy heart is 17%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.17
0.17 - 0.56 = -0.38
-0.38 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16475,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 56%. For people who have a sister, the probability of healthy heart is 17%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.17
0.17 - 0.56 = -0.38
-0.38 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 40%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 69%. For people who have a sister and with low blood pressure, the probability of healthy heart is 7%. For people who have a sister and with high blood pressure, the probability of healthy heart is 44%. For people who do not have a sister, the probability of high blood pressure is 54%. For people who have a sister, the probability of high blood pressure is 28%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.40
P(Y=1 | X=0, V2=1) = 0.69
P(Y=1 | X=1, V2=0) = 0.07
P(Y=1 | X=1, V2=1) = 0.44
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.28
0.28 * (0.69 - 0.40)+ 0.54 * (0.44 - 0.07)= -0.07
-0.07 < 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 40%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 69%. For people who have a sister and with low blood pressure, the probability of healthy heart is 7%. For people who have a sister and with high blood pressure, the probability of healthy heart is 44%. For people who do not have a sister, the probability of high blood pressure is 54%. For people who have a sister, the probability of high blood pressure is 28%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.40
P(Y=1 | X=0, V2=1) = 0.69
P(Y=1 | X=1, V2=0) = 0.07
P(Y=1 | X=1, V2=1) = 0.44
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.28
0.54 * (0.44 - 0.07) + 0.28 * (0.69 - 0.40) = -0.29
-0.29 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 40%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 69%. For people who have a sister and with low blood pressure, the probability of healthy heart is 7%. For people who have a sister and with high blood pressure, the probability of healthy heart is 44%. For people who do not have a sister, the probability of high blood pressure is 54%. For people who have a sister, the probability of high blood pressure is 28%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.40
P(Y=1 | X=0, V2=1) = 0.69
P(Y=1 | X=1, V2=0) = 0.07
P(Y=1 | X=1, V2=1) = 0.44
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.28
0.54 * (0.44 - 0.07) + 0.28 * (0.69 - 0.40) = -0.29
-0.29 < 0",mediation,blood_pressure,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
16484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16486,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 69%. For people who have a sister, the probability of healthy heart is 47%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.47
0.47 - 0.69 = -0.22
-0.22 < 0",mediation,blood_pressure,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 69%. For people who have a sister, the probability of healthy heart is 47%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.47
0.47 - 0.69 = -0.22
-0.22 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister, the probability of healthy heart is 69%. For people who have a sister, the probability of healthy heart is 47%.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.47
0.47 - 0.69 = -0.22
-0.22 < 0",mediation,blood_pressure,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
16490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. For people who do not have a sister and with low blood pressure, the probability of healthy heart is 61%. For people who do not have a sister and with high blood pressure, the probability of healthy heart is 87%. For people who have a sister and with low blood pressure, the probability of healthy heart is 29%. For people who have a sister and with high blood pressure, the probability of healthy heart is 50%. For people who do not have a sister, the probability of high blood pressure is 30%. For people who have a sister, the probability of high blood pressure is 88%.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.61
P(Y=1 | X=0, V2=1) = 0.87
P(Y=1 | X=1, V2=0) = 0.29
P(Y=1 | X=1, V2=1) = 0.50
P(V2=1 | X=0) = 0.30
P(V2=1 | X=1) = 0.88
0.88 * (0.87 - 0.61)+ 0.30 * (0.50 - 0.29)= 0.15
0.15 > 0",mediation,blood_pressure,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
16498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look at how having a sister correlates with heart condition case by case according to blood pressure. Method 2: We look directly at how having a sister correlates with heart condition in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. Method 1: We look directly at how having a sister correlates with heart condition in general. Method 2: We look at this correlation case by case according to blood pressure.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,blood_pressure,2,backadj,[backdoor adjustment set for Y given X]
16500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 95%. For people who do not speak english, the probability of talent is 83%. For people who speak english, the probability of talent is 83%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.83
0.95*0.83 - 0.05*0.83 = 0.83
0.83 > 0",collision,celebrity,1,marginal,P(Y)
16504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.20.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 85%. For people who do not speak english, the probability of talent is 94%. For people who speak english, the probability of talent is 94%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.94
0.85*0.94 - 0.15*0.94 = 0.94
0.94 > 0",collision,celebrity,1,marginal,P(Y)
16511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 85%. For people who do not speak english, the probability of talent is 94%. For people who speak english, the probability of talent is 94%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.94
0.85*0.94 - 0.15*0.94 = 0.94
0.94 > 0",collision,celebrity,1,marginal,P(Y)
16515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.01.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.01.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 85%. For people who do not speak english and are not famous, the probability of talent is 98%. For people who do not speak english and are famous, the probability of talent is 91%. For people who speak english and are not famous, the probability of talent is 96%. For people who speak english and are famous, the probability of talent is 90%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.85
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.96
P(Y=1 | X=1, V3=1) = 0.90
0.90 - (0.85*0.90 + 0.15*0.91) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 85%. For people who do not speak english and are not famous, the probability of talent is 98%. For people who do not speak english and are famous, the probability of talent is 91%. For people who speak english and are not famous, the probability of talent is 96%. For people who speak english and are famous, the probability of talent is 90%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.85
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.96
P(Y=1 | X=1, V3=1) = 0.90
0.90 - (0.85*0.90 + 0.15*0.91) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 97%. For people who do not speak english, the probability of talent is 89%. For people who speak english, the probability of talent is 89%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.89
0.97*0.89 - 0.03*0.89 = 0.89
0.89 > 0",collision,celebrity,1,marginal,P(Y)
16524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.03.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 97%. For people who do not speak english and are not famous, the probability of talent is 95%. For people who do not speak english and are famous, the probability of talent is 82%. For people who speak english and are not famous, the probability of talent is 93%. For people who speak english and are famous, the probability of talent is 76%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.97
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.76
0.76 - (0.97*0.76 + 0.03*0.82) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 93%. For people who do not speak english, the probability of talent is 80%. For people who speak english, the probability of talent is 80%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.80
0.93*0.80 - 0.07*0.80 = 0.80
0.80 > 0",collision,celebrity,1,marginal,P(Y)
16544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.18.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 96%. For people who do not speak english and are not famous, the probability of talent is 88%. For people who do not speak english and are famous, the probability of talent is 63%. For people who speak english and are not famous, the probability of talent is 86%. For people who speak english and are famous, the probability of talent is 35%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.96
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.35
0.35 - (0.96*0.35 + 0.04*0.63) = -0.03
-0.03 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 81%. For people who do not speak english, the probability of talent is 92%. For people who speak english, the probability of talent is 92%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.92
0.81*0.92 - 0.19*0.92 = 0.92
0.92 > 0",collision,celebrity,1,marginal,P(Y)
16557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.06.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16558,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 81%. For people who do not speak english and are not famous, the probability of talent is 97%. For people who do not speak english and are famous, the probability of talent is 89%. For people who speak english and are not famous, the probability of talent is 95%. For people who speak english and are famous, the probability of talent is 85%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.81
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.95
P(Y=1 | X=1, V3=1) = 0.85
0.85 - (0.81*0.85 + 0.19*0.89) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 84%. For people who do not speak english, the probability of talent is 80%. For people who speak english, the probability of talent is 80%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.80
0.84*0.80 - 0.16*0.80 = 0.80
0.80 > 0",collision,celebrity,1,marginal,P(Y)
16565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 84%. For people who do not speak english and are not famous, the probability of talent is 91%. For people who do not speak english and are famous, the probability of talent is 76%. For people who speak english and are not famous, the probability of talent is 87%. For people who speak english and are famous, the probability of talent is 73%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.84
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.73
0.73 - (0.84*0.73 + 0.16*0.76) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16570,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 95%. For people who do not speak english, the probability of talent is 93%. For people who speak english, the probability of talent is 93%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.93
0.95*0.93 - 0.05*0.93 = 0.93
0.93 > 0",collision,celebrity,1,marginal,P(Y)
16571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 95%. For people who do not speak english, the probability of talent is 93%. For people who speak english, the probability of talent is 93%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.93
0.95*0.93 - 0.05*0.93 = 0.93
0.93 > 0",collision,celebrity,1,marginal,P(Y)
16574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16580,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 91%. For people who do not speak english, the probability of talent is 84%. For people who speak english, the probability of talent is 84%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.84
0.91*0.84 - 0.09*0.84 = 0.84
0.84 > 0",collision,celebrity,1,marginal,P(Y)
16581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 91%. For people who do not speak english, the probability of talent is 84%. For people who speak english, the probability of talent is 84%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.84
0.91*0.84 - 0.09*0.84 = 0.84
0.84 > 0",collision,celebrity,1,marginal,P(Y)
16584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 91%. For people who do not speak english and are not famous, the probability of talent is 96%. For people who do not speak english and are famous, the probability of talent is 74%. For people who speak english and are not famous, the probability of talent is 92%. For people who speak english and are famous, the probability of talent is 63%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.91
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.63
0.63 - (0.91*0.63 + 0.09*0.74) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 98%. For people who do not speak english, the probability of talent is 87%. For people who speak english, the probability of talent is 87%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.87
0.98*0.87 - 0.02*0.87 = 0.87
0.87 > 0",collision,celebrity,1,marginal,P(Y)
16596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.04.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 98%. For people who do not speak english and are not famous, the probability of talent is 94%. For people who do not speak english and are famous, the probability of talent is 81%. For people who speak english and are not famous, the probability of talent is 91%. For people who speak english and are famous, the probability of talent is 74%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.98
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.81
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.98*0.74 + 0.02*0.81) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 98%. For people who do not speak english and are not famous, the probability of talent is 94%. For people who do not speak english and are famous, the probability of talent is 81%. For people who speak english and are not famous, the probability of talent is 91%. For people who speak english and are famous, the probability of talent is 74%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.98
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.81
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.98*0.74 + 0.02*0.81) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 84%. For people who do not speak english, the probability of talent is 88%. For people who speak english, the probability of talent is 88%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.88
0.84*0.88 - 0.16*0.88 = 0.88
0.88 > 0",collision,celebrity,1,marginal,P(Y)
16606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.09.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 94%. For people who do not speak english, the probability of talent is 83%. For people who speak english, the probability of talent is 83%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.83
0.94*0.83 - 0.06*0.83 = 0.83
0.83 > 0",collision,celebrity,1,marginal,P(Y)
16627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.08.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 94%. For people who do not speak english and are not famous, the probability of talent is 90%. For people who do not speak english and are famous, the probability of talent is 78%. For people who speak english and are not famous, the probability of talent is 88%. For people who speak english and are famous, the probability of talent is 68%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.94
P(Y=1 | X=0, V3=0) = 0.90
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.88
P(Y=1 | X=1, V3=1) = 0.68
0.68 - (0.94*0.68 + 0.06*0.78) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16630,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 92%. For people who do not speak english, the probability of talent is 84%. For people who speak english, the probability of talent is 84%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.84
0.92*0.84 - 0.08*0.84 = 0.84
0.84 > 0",collision,celebrity,1,marginal,P(Y)
16635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16638,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 92%. For people who do not speak english and are not famous, the probability of talent is 95%. For people who do not speak english and are famous, the probability of talent is 76%. For people who speak english and are not famous, the probability of talent is 88%. For people who speak english and are famous, the probability of talent is 67%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.92
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.88
P(Y=1 | X=1, V3=1) = 0.67
0.67 - (0.92*0.67 + 0.08*0.76) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16641,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 94%. For people who do not speak english, the probability of talent is 97%. For people who speak english, the probability of talent is 97%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.97
0.94*0.97 - 0.06*0.97 = 0.97
0.97 > 0",collision,celebrity,1,marginal,P(Y)
16647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.12.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16654,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 98%. For people who do not speak english and are not famous, the probability of talent is 93%. For people who do not speak english and are famous, the probability of talent is 79%. For people who speak english and are not famous, the probability of talent is 90%. For people who speak english and are famous, the probability of talent is 74%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.98
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.79
P(Y=1 | X=1, V3=0) = 0.90
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.98*0.74 + 0.02*0.79) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 96%. For people who do not speak english, the probability of talent is 97%. For people who speak english, the probability of talent is 97%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.97
0.96*0.97 - 0.04*0.97 = 0.97
0.97 > 0",collision,celebrity,1,marginal,P(Y)
16664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.02.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 96%. For people who do not speak english and are not famous, the probability of talent is 98%. For people who do not speak english and are famous, the probability of talent is 95%. For people who speak english and are not famous, the probability of talent is 98%. For people who speak english and are famous, the probability of talent is 93%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.96
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.95
P(Y=1 | X=1, V3=0) = 0.98
P(Y=1 | X=1, V3=1) = 0.93
0.93 - (0.96*0.93 + 0.04*0.95) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 89%. For people who do not speak english, the probability of talent is 98%. For people who speak english, the probability of talent is 98%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.98
P(Y=1 | X=1) = 0.98
0.89*0.98 - 0.11*0.98 = 0.98
0.98 > 0",collision,celebrity,1,marginal,P(Y)
16676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.51.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 89%. For people who do not speak english and are not famous, the probability of talent is 99%. For people who do not speak english and are famous, the probability of talent is 97%. For people who speak english and are not famous, the probability of talent is 99%. For people who speak english and are famous, the probability of talent is 57%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.89
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.99
P(Y=1 | X=1, V3=1) = 0.57
0.57 - (0.89*0.57 + 0.11*0.97) = -0.29
-0.29 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.02.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 83%. For people who do not speak english, the probability of talent is 91%. For people who speak english, the probability of talent is 91%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.91
0.83*0.91 - 0.17*0.91 = 0.91
0.91 > 0",collision,celebrity,1,marginal,P(Y)
16694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.10.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.10.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 81%. For people who do not speak english and are not famous, the probability of talent is 94%. For people who do not speak english and are famous, the probability of talent is 83%. For people who speak english and are not famous, the probability of talent is 92%. For people who speak english and are famous, the probability of talent is 75%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.81
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.75
0.75 - (0.81*0.75 + 0.19*0.83) = -0.03
-0.03 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 86%. For people who do not speak english, the probability of talent is 95%. For people who speak english, the probability of talent is 95%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.95
0.86*0.95 - 0.14*0.95 = 0.95
0.95 > 0",collision,celebrity,1,marginal,P(Y)
16718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 86%. For people who do not speak english and are not famous, the probability of talent is 97%. For people who do not speak english and are famous, the probability of talent is 92%. For people who speak english and are not famous, the probability of talent is 97%. For people who speak english and are famous, the probability of talent is 74%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.86
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.92
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.86*0.74 + 0.14*0.92) = -0.09
-0.09 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.66.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 90%. For people who do not speak english and are not famous, the probability of talent is 98%. For people who do not speak english and are famous, the probability of talent is 85%. For people who speak english and are not famous, the probability of talent is 96%. For people who speak english and are famous, the probability of talent is 19%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.90
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.85
P(Y=1 | X=1, V3=0) = 0.96
P(Y=1 | X=1, V3=1) = 0.19
0.19 - (0.90*0.19 + 0.10*0.85) = -0.34
-0.34 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.10.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 81%. For people who do not speak english and are not famous, the probability of talent is 98%. For people who do not speak english and are famous, the probability of talent is 92%. For people who speak english and are not famous, the probability of talent is 97%. For people who speak english and are famous, the probability of talent is 86%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.81
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.92
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.86
0.86 - (0.81*0.86 + 0.19*0.92) = -0.03
-0.03 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 94%. For people who do not speak english, the probability of talent is 93%. For people who speak english, the probability of talent is 93%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.93
0.94*0.93 - 0.06*0.93 = 0.93
0.93 > 0",collision,celebrity,1,marginal,P(Y)
16744,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.25.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.25.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 94%. For people who do not speak english and are not famous, the probability of talent is 97%. For people who do not speak english and are famous, the probability of talent is 87%. For people who speak english and are not famous, the probability of talent is 95%. For people who speak english and are famous, the probability of talent is 62%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.94
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.87
P(Y=1 | X=1, V3=0) = 0.95
P(Y=1 | X=1, V3=1) = 0.62
0.62 - (0.94*0.62 + 0.06*0.87) = -0.07
-0.07 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.01.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 92%. For people who do not speak english and are not famous, the probability of talent is 93%. For people who do not speak english and are famous, the probability of talent is 76%. For people who speak english and are not famous, the probability of talent is 87%. For people who speak english and are famous, the probability of talent is 75%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.92
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.75
0.75 - (0.92*0.75 + 0.08*0.76) = -0.00
0.00 = 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 86%. For people who do not speak english, the probability of talent is 86%. For people who speak english, the probability of talent is 86%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.86
0.86*0.86 - 0.14*0.86 = 0.86
0.86 > 0",collision,celebrity,1,marginal,P(Y)
16765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.04.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 86%. For people who do not speak english and are not famous, the probability of talent is 92%. For people who do not speak english and are famous, the probability of talent is 81%. For people who speak english and are not famous, the probability of talent is 90%. For people who speak english and are famous, the probability of talent is 77%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.86
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.81
P(Y=1 | X=1, V3=0) = 0.90
P(Y=1 | X=1, V3=1) = 0.77
0.77 - (0.86*0.77 + 0.14*0.81) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 81%. For people who do not speak english, the probability of talent is 94%. For people who speak english, the probability of talent is 94%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.94
0.81*0.94 - 0.19*0.94 = 0.94
0.94 > 0",collision,celebrity,1,marginal,P(Y)
16775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look directly at how ability to speak english correlates with talent in general. Method 2: We look at this correlation case by case according to fame.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.06.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 81%. For people who do not speak english and are not famous, the probability of talent is 98%. For people who do not speak english and are famous, the probability of talent is 91%. For people who speak english and are not famous, the probability of talent is 97%. For people who speak english and are famous, the probability of talent is 87%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.81
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.87
0.87 - (0.81*0.87 + 0.19*0.91) = -0.01
-0.01 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.44.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.44.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16794,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. Method 1: We look at how ability to speak english correlates with talent case by case according to fame. Method 2: We look directly at how ability to speak english correlates with talent in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,celebrity,2,backadj,[backdoor adjustment set for Y given X]
16797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. For people who are famous, the correlation between speaking english and talent is -0.10.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,celebrity,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
16798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 91%. For people who do not speak english and are not famous, the probability of talent is 97%. For people who do not speak english and are famous, the probability of talent is 91%. For people who speak english and are not famous, the probability of talent is 97%. For people who speak english and are famous, the probability of talent is 82%.",no,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.91
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.82
0.82 - (0.91*0.82 + 0.09*0.91) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on fame. Talent has a direct effect on fame. The overall probability of speaking english is 91%. For people who do not speak english and are not famous, the probability of talent is 97%. For people who do not speak english and are famous, the probability of talent is 91%. For people who speak english and are not famous, the probability of talent is 97%. For people who speak english and are famous, the probability of talent is 82%.",yes,"Let Y = talent; X = ability to speak english; V3 = fame.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.91
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.82
0.82 - (0.91*0.82 + 0.09*0.91) = -0.02
-0.02 < 0",collision,celebrity,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
16801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 22%. For patients assigned the drug treatment, the probability of low cholesterol is 19%. For patients not assigned the drug treatment, the probability of having a sister is 66%. For patients assigned the drug treatment, the probability of having a sister is 31%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.22
P(Y=1 | V2=1) = 0.19
P(X=1 | V2=0) = 0.66
P(X=1 | V2=1) = 0.31
(0.19 - 0.22) / (0.31 - 0.66) = 0.09
0.09 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 37%. For patients who do not have a sister, the probability of low cholesterol is 17%. For patients who have a sister, the probability of low cholesterol is 23%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.23
0.37*0.23 - 0.63*0.17 = 0.20
0.20 > 0",IV,cholesterol,1,marginal,P(Y)
16805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 37%. The probability of not having a sister and low cholesterol is 11%. The probability of having a sister and low cholesterol is 9%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.09
0.09/0.37 - 0.11/0.63 = 0.06
0.06 > 0",IV,cholesterol,1,correlation,P(Y | X)
16807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 20%. For patients who do not have a sister, the probability of low cholesterol is 81%. For patients who have a sister, the probability of low cholesterol is 70%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.70
0.20*0.70 - 0.80*0.81 = 0.79
0.79 > 0",IV,cholesterol,1,marginal,P(Y)
16812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 20%. The probability of not having a sister and low cholesterol is 65%. The probability of having a sister and low cholesterol is 14%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.14
0.14/0.20 - 0.65/0.80 = -0.10
-0.10 < 0",IV,cholesterol,1,correlation,P(Y | X)
16813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 20%. The probability of not having a sister and low cholesterol is 65%. The probability of having a sister and low cholesterol is 14%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.14
0.14/0.20 - 0.65/0.80 = -0.10
-0.10 < 0",IV,cholesterol,1,correlation,P(Y | X)
16817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 46%. For patients assigned the drug treatment, the probability of low cholesterol is 46%. For patients not assigned the drug treatment, the probability of having a sister is 73%. For patients assigned the drug treatment, the probability of having a sister is 39%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.46
P(Y=1 | V2=1) = 0.46
P(X=1 | V2=0) = 0.73
P(X=1 | V2=1) = 0.39
(0.46 - 0.46) / (0.39 - 0.73) = 0.02
0.02 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 44%. For patients who do not have a sister, the probability of low cholesterol is 45%. For patients who have a sister, the probability of low cholesterol is 46%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.46
0.44*0.46 - 0.56*0.45 = 0.46
0.46 > 0",IV,cholesterol,1,marginal,P(Y)
16827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 21%. For patients who do not have a sister, the probability of low cholesterol is 25%. For patients who have a sister, the probability of low cholesterol is 34%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.21
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.34
0.21*0.34 - 0.79*0.25 = 0.27
0.27 > 0",IV,cholesterol,1,marginal,P(Y)
16828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 21%. The probability of not having a sister and low cholesterol is 20%. The probability of having a sister and low cholesterol is 7%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.21
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.07
0.07/0.21 - 0.20/0.79 = 0.09
0.09 > 0",IV,cholesterol,1,correlation,P(Y | X)
16837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 39%. The probability of not having a sister and low cholesterol is 34%. The probability of having a sister and low cholesterol is 23%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.23
0.23/0.39 - 0.34/0.61 = 0.02
0.02 > 0",IV,cholesterol,1,correlation,P(Y | X)
16842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 15%. For patients who do not have a sister, the probability of low cholesterol is 77%. For patients who have a sister, the probability of low cholesterol is 64%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.64
0.15*0.64 - 0.85*0.77 = 0.75
0.75 > 0",IV,cholesterol,1,marginal,P(Y)
16846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 32%. For patients assigned the drug treatment, the probability of low cholesterol is 39%. For patients not assigned the drug treatment, the probability of having a sister is 76%. For patients assigned the drug treatment, the probability of having a sister is 32%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.32
P(Y=1 | V2=1) = 0.39
P(X=1 | V2=0) = 0.76
P(X=1 | V2=1) = 0.32
(0.39 - 0.32) / (0.32 - 0.76) = -0.17
-0.17 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16850,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 35%. For patients who do not have a sister, the probability of low cholesterol is 45%. For patients who have a sister, the probability of low cholesterol is 26%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.26
0.35*0.26 - 0.65*0.45 = 0.39
0.39 > 0",IV,cholesterol,1,marginal,P(Y)
16851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 35%. For patients who do not have a sister, the probability of low cholesterol is 45%. For patients who have a sister, the probability of low cholesterol is 26%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.26
0.35*0.26 - 0.65*0.45 = 0.39
0.39 > 0",IV,cholesterol,1,marginal,P(Y)
16852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 35%. The probability of not having a sister and low cholesterol is 29%. The probability of having a sister and low cholesterol is 9%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.09
0.09/0.35 - 0.29/0.65 = -0.19
-0.19 < 0",IV,cholesterol,1,correlation,P(Y | X)
16855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 49%. For patients assigned the drug treatment, the probability of low cholesterol is 59%. For patients not assigned the drug treatment, the probability of having a sister is 70%. For patients assigned the drug treatment, the probability of having a sister is 29%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.70
P(X=1 | V2=1) = 0.29
(0.59 - 0.49) / (0.29 - 0.70) = -0.24
-0.24 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16857,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 49%. For patients assigned the drug treatment, the probability of low cholesterol is 59%. For patients not assigned the drug treatment, the probability of having a sister is 70%. For patients assigned the drug treatment, the probability of having a sister is 29%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.70
P(X=1 | V2=1) = 0.29
(0.59 - 0.49) / (0.29 - 0.70) = -0.24
-0.24 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 37%. For patients who do not have a sister, the probability of low cholesterol is 66%. For patients who have a sister, the probability of low cholesterol is 43%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.43
0.37*0.43 - 0.63*0.66 = 0.57
0.57 > 0",IV,cholesterol,1,marginal,P(Y)
16860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 37%. The probability of not having a sister and low cholesterol is 42%. The probability of having a sister and low cholesterol is 16%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.16
0.16/0.37 - 0.42/0.63 = -0.23
-0.23 < 0",IV,cholesterol,1,correlation,P(Y | X)
16863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 45%. The probability of not having a sister and low cholesterol is 17%. The probability of having a sister and low cholesterol is 15%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.15
0.15/0.45 - 0.17/0.55 = 0.02
0.02 > 0",IV,cholesterol,1,correlation,P(Y | X)
16872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 57%. For patients assigned the drug treatment, the probability of low cholesterol is 62%. For patients not assigned the drug treatment, the probability of having a sister is 61%. For patients assigned the drug treatment, the probability of having a sister is 28%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.57
P(Y=1 | V2=1) = 0.62
P(X=1 | V2=0) = 0.61
P(X=1 | V2=1) = 0.28
(0.62 - 0.57) / (0.28 - 0.61) = -0.14
-0.14 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16874,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 29%. For patients who do not have a sister, the probability of low cholesterol is 67%. For patients who have a sister, the probability of low cholesterol is 49%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.29
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.49
0.29*0.49 - 0.71*0.67 = 0.62
0.62 > 0",IV,cholesterol,1,marginal,P(Y)
16877,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 29%. The probability of not having a sister and low cholesterol is 48%. The probability of having a sister and low cholesterol is 14%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.29
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.14
0.14/0.29 - 0.48/0.71 = -0.18
-0.18 < 0",IV,cholesterol,1,correlation,P(Y | X)
16879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 40%. For patients assigned the drug treatment, the probability of low cholesterol is 41%. For patients not assigned the drug treatment, the probability of having a sister is 68%. For patients assigned the drug treatment, the probability of having a sister is 41%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.40
P(Y=1 | V2=1) = 0.41
P(X=1 | V2=0) = 0.68
P(X=1 | V2=1) = 0.41
(0.41 - 0.40) / (0.41 - 0.68) = -0.02
-0.02 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16884,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 43%. The probability of not having a sister and low cholesterol is 24%. The probability of having a sister and low cholesterol is 17%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.17
0.17/0.43 - 0.24/0.57 = -0.02
-0.02 < 0",IV,cholesterol,1,correlation,P(Y | X)
16885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 43%. The probability of not having a sister and low cholesterol is 24%. The probability of having a sister and low cholesterol is 17%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.17
0.17/0.43 - 0.24/0.57 = -0.02
-0.02 < 0",IV,cholesterol,1,correlation,P(Y | X)
16886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 54%. For patients assigned the drug treatment, the probability of low cholesterol is 51%. For patients not assigned the drug treatment, the probability of having a sister is 65%. For patients assigned the drug treatment, the probability of having a sister is 31%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.51
P(X=1 | V2=0) = 0.65
P(X=1 | V2=1) = 0.31
(0.51 - 0.54) / (0.31 - 0.65) = 0.09
0.09 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 54%. For patients assigned the drug treatment, the probability of low cholesterol is 51%. For patients not assigned the drug treatment, the probability of having a sister is 65%. For patients assigned the drug treatment, the probability of having a sister is 31%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.51
P(X=1 | V2=0) = 0.65
P(X=1 | V2=1) = 0.31
(0.51 - 0.54) / (0.31 - 0.65) = 0.09
0.09 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 34%. The probability of not having a sister and low cholesterol is 32%. The probability of having a sister and low cholesterol is 21%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.34
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.21
0.21/0.34 - 0.32/0.66 = 0.11
0.11 > 0",IV,cholesterol,1,correlation,P(Y | X)
16894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 35%. For patients who do not have a sister, the probability of low cholesterol is 73%. For patients who have a sister, the probability of low cholesterol is 29%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.29
0.35*0.29 - 0.65*0.73 = 0.57
0.57 > 0",IV,cholesterol,1,marginal,P(Y)
16899,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 35%. For patients who do not have a sister, the probability of low cholesterol is 73%. For patients who have a sister, the probability of low cholesterol is 29%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.35
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.29
0.35*0.29 - 0.65*0.73 = 0.57
0.57 > 0",IV,cholesterol,1,marginal,P(Y)
16912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 54%. For patients assigned the drug treatment, the probability of low cholesterol is 52%. For patients not assigned the drug treatment, the probability of having a sister is 79%. For patients assigned the drug treatment, the probability of having a sister is 43%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.52
P(X=1 | V2=0) = 0.79
P(X=1 | V2=1) = 0.43
(0.52 - 0.54) / (0.43 - 0.79) = 0.05
0.05 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16913,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 54%. For patients assigned the drug treatment, the probability of low cholesterol is 52%. For patients not assigned the drug treatment, the probability of having a sister is 79%. For patients assigned the drug treatment, the probability of having a sister is 43%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.52
P(X=1 | V2=0) = 0.79
P(X=1 | V2=1) = 0.43
(0.52 - 0.54) / (0.43 - 0.79) = 0.05
0.05 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 44%. For patients who do not have a sister, the probability of low cholesterol is 49%. For patients who have a sister, the probability of low cholesterol is 56%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.56
0.44*0.56 - 0.56*0.49 = 0.52
0.52 > 0",IV,cholesterol,1,marginal,P(Y)
16918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 41%. For patients who do not have a sister, the probability of low cholesterol is 52%. For patients who have a sister, the probability of low cholesterol is 44%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.44
0.41*0.44 - 0.59*0.52 = 0.48
0.48 > 0",IV,cholesterol,1,marginal,P(Y)
16926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16930,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 32%. For patients who do not have a sister, the probability of low cholesterol is 31%. For patients who have a sister, the probability of low cholesterol is 50%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.50
0.32*0.50 - 0.68*0.31 = 0.37
0.37 > 0",IV,cholesterol,1,marginal,P(Y)
16940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 39%. The probability of not having a sister and low cholesterol is 30%. The probability of having a sister and low cholesterol is 17%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.17
0.17/0.39 - 0.30/0.61 = -0.05
-0.05 < 0",IV,cholesterol,1,correlation,P(Y | X)
16941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 39%. The probability of not having a sister and low cholesterol is 30%. The probability of having a sister and low cholesterol is 17%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.17
0.17/0.39 - 0.30/0.61 = -0.05
-0.05 < 0",IV,cholesterol,1,correlation,P(Y | X)
16942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 70%. For patients assigned the drug treatment, the probability of low cholesterol is 83%. For patients not assigned the drug treatment, the probability of having a sister is 43%. For patients assigned the drug treatment, the probability of having a sister is 11%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.70
P(Y=1 | V2=1) = 0.83
P(X=1 | V2=0) = 0.43
P(X=1 | V2=1) = 0.11
(0.83 - 0.70) / (0.11 - 0.43) = -0.39
-0.39 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 13%. For patients who do not have a sister, the probability of low cholesterol is 87%. For patients who have a sister, the probability of low cholesterol is 47%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.47
0.13*0.47 - 0.87*0.87 = 0.82
0.82 > 0",IV,cholesterol,1,marginal,P(Y)
16949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 13%. The probability of not having a sister and low cholesterol is 76%. The probability of having a sister and low cholesterol is 6%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.06
0.06/0.13 - 0.76/0.87 = -0.39
-0.39 < 0",IV,cholesterol,1,correlation,P(Y | X)
16950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 11%. For patients assigned the drug treatment, the probability of low cholesterol is 11%. For patients not assigned the drug treatment, the probability of having a sister is 85%. For patients assigned the drug treatment, the probability of having a sister is 51%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.11
P(Y=1 | V2=1) = 0.11
P(X=1 | V2=0) = 0.85
P(X=1 | V2=1) = 0.51
(0.11 - 0.11) / (0.51 - 0.85) = -0.01
-0.01 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 11%. For patients assigned the drug treatment, the probability of low cholesterol is 11%. For patients not assigned the drug treatment, the probability of having a sister is 85%. For patients assigned the drug treatment, the probability of having a sister is 51%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.11
P(Y=1 | V2=1) = 0.11
P(X=1 | V2=0) = 0.85
P(X=1 | V2=1) = 0.51
(0.11 - 0.11) / (0.51 - 0.85) = -0.01
-0.01 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 57%. For patients who do not have a sister, the probability of low cholesterol is 12%. For patients who have a sister, the probability of low cholesterol is 10%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.10
0.57*0.10 - 0.43*0.12 = 0.11
0.11 > 0",IV,cholesterol,1,marginal,P(Y)
16955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 57%. For patients who do not have a sister, the probability of low cholesterol is 12%. For patients who have a sister, the probability of low cholesterol is 10%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.10
0.57*0.10 - 0.43*0.12 = 0.11
0.11 > 0",IV,cholesterol,1,marginal,P(Y)
16957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 57%. The probability of not having a sister and low cholesterol is 5%. The probability of having a sister and low cholesterol is 6%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.06
0.06/0.57 - 0.05/0.43 = -0.01
-0.01 < 0",IV,cholesterol,1,correlation,P(Y | X)
16959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 73%. For patients assigned the drug treatment, the probability of low cholesterol is 70%. For patients not assigned the drug treatment, the probability of having a sister is 52%. For patients assigned the drug treatment, the probability of having a sister is 18%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.73
P(Y=1 | V2=1) = 0.70
P(X=1 | V2=0) = 0.52
P(X=1 | V2=1) = 0.18
(0.70 - 0.73) / (0.18 - 0.52) = 0.10
0.10 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 21%. The probability of not having a sister and low cholesterol is 54%. The probability of having a sister and low cholesterol is 16%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.21
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.16
0.16/0.21 - 0.54/0.79 = 0.10
0.10 > 0",IV,cholesterol,1,correlation,P(Y | X)
16966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 29%. For patients assigned the drug treatment, the probability of low cholesterol is 35%. For patients not assigned the drug treatment, the probability of having a sister is 82%. For patients assigned the drug treatment, the probability of having a sister is 44%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.29
P(Y=1 | V2=1) = 0.35
P(X=1 | V2=0) = 0.82
P(X=1 | V2=1) = 0.44
(0.35 - 0.29) / (0.44 - 0.82) = -0.17
-0.17 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 51%. For patients who do not have a sister, the probability of low cholesterol is 43%. For patients who have a sister, the probability of low cholesterol is 25%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.25
0.51*0.25 - 0.49*0.43 = 0.34
0.34 > 0",IV,cholesterol,1,marginal,P(Y)
16972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 51%. The probability of not having a sister and low cholesterol is 21%. The probability of having a sister and low cholesterol is 13%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.13
0.13/0.51 - 0.21/0.49 = -0.18
-0.18 < 0",IV,cholesterol,1,correlation,P(Y | X)
16974,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
16978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 13%. For patients who do not have a sister, the probability of low cholesterol is 37%. For patients who have a sister, the probability of low cholesterol is 44%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.44
0.13*0.44 - 0.87*0.37 = 0.38
0.38 > 0",IV,cholesterol,1,marginal,P(Y)
16985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 51%. For patients assigned the drug treatment, the probability of low cholesterol is 64%. For patients not assigned the drug treatment, the probability of having a sister is 67%. For patients assigned the drug treatment, the probability of having a sister is 30%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.51
P(Y=1 | V2=1) = 0.64
P(X=1 | V2=0) = 0.67
P(X=1 | V2=1) = 0.30
(0.64 - 0.51) / (0.30 - 0.67) = -0.38
-0.38 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 36%. For patients who do not have a sister, the probability of low cholesterol is 76%. For patients who have a sister, the probability of low cholesterol is 38%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.38
0.36*0.38 - 0.64*0.76 = 0.62
0.62 > 0",IV,cholesterol,1,marginal,P(Y)
16987,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 36%. For patients who do not have a sister, the probability of low cholesterol is 76%. For patients who have a sister, the probability of low cholesterol is 38%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.38
0.36*0.38 - 0.64*0.76 = 0.62
0.62 > 0",IV,cholesterol,1,marginal,P(Y)
16992,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 50%. For patients assigned the drug treatment, the probability of low cholesterol is 57%. For patients not assigned the drug treatment, the probability of having a sister is 66%. For patients assigned the drug treatment, the probability of having a sister is 6%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.50
P(Y=1 | V2=1) = 0.57
P(X=1 | V2=0) = 0.66
P(X=1 | V2=1) = 0.06
(0.57 - 0.50) / (0.06 - 0.66) = -0.13
-0.13 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
16995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 16%. For patients who do not have a sister, the probability of low cholesterol is 58%. For patients who have a sister, the probability of low cholesterol is 45%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.45
0.16*0.45 - 0.84*0.58 = 0.56
0.56 > 0",IV,cholesterol,1,marginal,P(Y)
16997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 16%. The probability of not having a sister and low cholesterol is 49%. The probability of having a sister and low cholesterol is 7%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.07
0.07/0.16 - 0.49/0.84 = -0.13
-0.13 < 0",IV,cholesterol,1,correlation,P(Y | X)
17002,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 24%. For patients who do not have a sister, the probability of low cholesterol is 63%. For patients who have a sister, the probability of low cholesterol is 66%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.66
0.24*0.66 - 0.76*0.63 = 0.64
0.64 > 0",IV,cholesterol,1,marginal,P(Y)
17004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 24%. The probability of not having a sister and low cholesterol is 48%. The probability of having a sister and low cholesterol is 16%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.16
0.16/0.24 - 0.48/0.76 = 0.03
0.03 > 0",IV,cholesterol,1,correlation,P(Y | X)
17010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 45%. For patients who do not have a sister, the probability of low cholesterol is 82%. For patients who have a sister, the probability of low cholesterol is 89%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.89
0.45*0.89 - 0.55*0.82 = 0.82
0.82 > 0",IV,cholesterol,1,marginal,P(Y)
17012,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 45%. The probability of not having a sister and low cholesterol is 45%. The probability of having a sister and low cholesterol is 40%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.40
0.40/0.45 - 0.45/0.55 = 0.07
0.07 > 0",IV,cholesterol,1,correlation,P(Y | X)
17013,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 45%. The probability of not having a sister and low cholesterol is 45%. The probability of having a sister and low cholesterol is 40%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.40
0.40/0.45 - 0.45/0.55 = 0.07
0.07 > 0",IV,cholesterol,1,correlation,P(Y | X)
17014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look directly at how having a sister correlates with cholesterol level in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
17015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. Method 1: We look at how having a sister correlates with cholesterol level case by case according to unobserved confounders. Method 2: We look directly at how having a sister correlates with cholesterol level in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,cholesterol,2,backadj,[backdoor adjustment set for Y given X]
17016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 52%. For patients assigned the drug treatment, the probability of low cholesterol is 49%. For patients not assigned the drug treatment, the probability of having a sister is 87%. For patients assigned the drug treatment, the probability of having a sister is 44%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.87
P(X=1 | V2=1) = 0.44
(0.49 - 0.52) / (0.44 - 0.87) = 0.07
0.07 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 52%. For patients assigned the drug treatment, the probability of low cholesterol is 49%. For patients not assigned the drug treatment, the probability of having a sister is 87%. For patients assigned the drug treatment, the probability of having a sister is 44%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.87
P(X=1 | V2=1) = 0.44
(0.49 - 0.52) / (0.44 - 0.87) = 0.07
0.07 > 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. The overall probability of having a sister is 52%. The probability of not having a sister and low cholesterol is 22%. The probability of having a sister and low cholesterol is 28%.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.28
0.28/0.52 - 0.22/0.48 = 0.08
0.08 > 0",IV,cholesterol,1,correlation,P(Y | X)
17024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a sister and cholesterol level. Treatment assignment has a direct effect on having a sister. Having a sister has a direct effect on cholesterol level. Unobserved confounders is unobserved. For patients not assigned the drug treatment, the probability of low cholesterol is 75%. For patients assigned the drug treatment, the probability of low cholesterol is 86%. For patients not assigned the drug treatment, the probability of having a sister is 55%. For patients assigned the drug treatment, the probability of having a sister is 17%.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = having a sister; Y = cholesterol level.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.75
P(Y=1 | V2=1) = 0.86
P(X=1 | V2=0) = 0.55
P(X=1 | V2=1) = 0.17
(0.86 - 0.75) / (0.17 - 0.55) = -0.27
-0.27 < 0",IV,cholesterol,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 22%. For people who have a brother, the probability of high salary is 51%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.51
0.51 - 0.22 = 0.29
0.29 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 22%. For people who have a brother, the probability of high salary is 51%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.51
0.51 - 0.22 = 0.29
0.29 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 22%. For people who have a brother, the probability of high salary is 51%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.22
P(Y=1 | X=1) = 0.51
0.51 - 0.22 = 0.29
0.29 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 97%. The probability of not having a brother and high salary is 1%. The probability of having a brother and high salary is 49%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.49
0.49/0.97 - 0.01/0.03 = 0.29
0.29 > 0",chain,college_salary,1,correlation,P(Y | X)
17050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 55%. For people who have a brother, the probability of high salary is 64%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.64
0.64 - 0.55 = 0.09
0.09 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 55%. For people who have a brother, the probability of high salary is 64%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.64
0.64 - 0.55 = 0.09
0.09 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17058,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 96%. For people who do not have a brother, the probability of high salary is 55%. For people who have a brother, the probability of high salary is 64%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.64
0.96*0.64 - 0.04*0.55 = 0.64
0.64 > 0",chain,college_salary,1,marginal,P(Y)
17059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 96%. For people who do not have a brother, the probability of high salary is 55%. For people who have a brother, the probability of high salary is 64%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.64
0.96*0.64 - 0.04*0.55 = 0.64
0.64 > 0",chain,college_salary,1,marginal,P(Y)
17061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 96%. The probability of not having a brother and high salary is 2%. The probability of having a brother and high salary is 62%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.62
0.62/0.96 - 0.02/0.04 = 0.09
0.09 > 0",chain,college_salary,1,correlation,P(Y | X)
17062,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 24%. For people who have a brother, the probability of high salary is 61%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.61
0.61 - 0.24 = 0.37
0.37 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 84%. The probability of not having a brother and high salary is 4%. The probability of having a brother and high salary is 51%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.51
0.51/0.84 - 0.04/0.16 = 0.37
0.37 > 0",chain,college_salary,1,correlation,P(Y | X)
17075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 24%. For people who have a brother, the probability of high salary is 47%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.47
0.47 - 0.24 = 0.23
0.23 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 24%. For people who have a brother, the probability of high salary is 47%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.47
0.47 - 0.24 = 0.23
0.23 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 24%. For people who have a brother, the probability of high salary is 47%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.47
0.47 - 0.24 = 0.23
0.23 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17083,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 82%. For people who do not have a brother, the probability of high salary is 24%. For people who have a brother, the probability of high salary is 47%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.47
0.82*0.47 - 0.18*0.24 = 0.43
0.43 > 0",chain,college_salary,1,marginal,P(Y)
17084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 82%. The probability of not having a brother and high salary is 4%. The probability of having a brother and high salary is 39%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.39
0.39/0.82 - 0.04/0.18 = 0.23
0.23 > 0",chain,college_salary,1,correlation,P(Y | X)
17085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 82%. The probability of not having a brother and high salary is 4%. The probability of having a brother and high salary is 39%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.39
0.39/0.82 - 0.04/0.18 = 0.23
0.23 > 0",chain,college_salary,1,correlation,P(Y | X)
17090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 34%. For people who have a brother, the probability of high salary is 60%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.60
0.60 - 0.34 = 0.26
0.26 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 34%. For people who have a brother, the probability of high salary is 60%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.60
0.60 - 0.34 = 0.26
0.26 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 93%. For people who do not have a brother, the probability of high salary is 34%. For people who have a brother, the probability of high salary is 60%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.60
0.93*0.60 - 0.07*0.34 = 0.58
0.58 > 0",chain,college_salary,1,marginal,P(Y)
17099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 54%. For people who have a brother, the probability of high salary is 74%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.74
0.74 - 0.54 = 0.20
0.20 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 54%. For people who have a brother, the probability of high salary is 74%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.74
0.74 - 0.54 = 0.20
0.20 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 46%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.46
0.46 - 0.37 = 0.09
0.09 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 46%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.46
0.46 - 0.37 = 0.09
0.09 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 92%. The probability of not having a brother and high salary is 3%. The probability of having a brother and high salary is 42%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.42
0.42/0.92 - 0.03/0.08 = 0.09
0.09 > 0",chain,college_salary,1,correlation,P(Y | X)
17122,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 88%. The probability of not having a brother and high salary is 5%. The probability of having a brother and high salary is 50%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.50
0.50/0.88 - 0.05/0.12 = 0.13
0.13 > 0",chain,college_salary,1,correlation,P(Y | X)
17134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 81%. For people who do not have a brother, the probability of high salary is 43%. For people who have a brother, the probability of high salary is 72%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.72
0.81*0.72 - 0.19*0.43 = 0.67
0.67 > 0",chain,college_salary,1,marginal,P(Y)
17145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 81%. The probability of not having a brother and high salary is 8%. The probability of having a brother and high salary is 59%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.59
0.59/0.81 - 0.08/0.19 = 0.29
0.29 > 0",chain,college_salary,1,correlation,P(Y | X)
17148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 41%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.13
0.13 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 41%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.13
0.13 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 41%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.13
0.13 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 41%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.41 - 0.27 = 0.13
0.13 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 92%. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 41%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.92*0.41 - 0.08*0.27 = 0.40
0.40 > 0",chain,college_salary,1,marginal,P(Y)
17155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 92%. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 41%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.41
0.92*0.41 - 0.08*0.27 = 0.40
0.40 > 0",chain,college_salary,1,marginal,P(Y)
17158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 29%. For people who have a brother, the probability of high salary is 52%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.52
0.52 - 0.29 = 0.22
0.22 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17166,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 89%. For people who do not have a brother, the probability of high salary is 29%. For people who have a brother, the probability of high salary is 52%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.52
0.89*0.52 - 0.11*0.29 = 0.49
0.49 > 0",chain,college_salary,1,marginal,P(Y)
17167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 89%. For people who do not have a brother, the probability of high salary is 29%. For people who have a brother, the probability of high salary is 52%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.52
0.89*0.52 - 0.11*0.29 = 0.49
0.49 > 0",chain,college_salary,1,marginal,P(Y)
17170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 12%. For people who have a brother, the probability of high salary is 26%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.26
0.26 - 0.12 = 0.14
0.14 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 12%. For people who have a brother, the probability of high salary is 26%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.26
0.26 - 0.12 = 0.14
0.14 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 12%. For people who have a brother, the probability of high salary is 26%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.26
0.26 - 0.12 = 0.14
0.14 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 88%. For people who do not have a brother, the probability of high salary is 12%. For people who have a brother, the probability of high salary is 26%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.26
0.88*0.26 - 0.12*0.12 = 0.25
0.25 > 0",chain,college_salary,1,marginal,P(Y)
17181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 88%. The probability of not having a brother and high salary is 1%. The probability of having a brother and high salary is 23%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.23
0.23/0.88 - 0.01/0.12 = 0.14
0.14 > 0",chain,college_salary,1,correlation,P(Y | X)
17183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 67%. For people who have a brother, the probability of high salary is 80%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.80
0.80 - 0.67 = 0.13
0.13 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17187,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 67%. For people who have a brother, the probability of high salary is 80%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.80
0.80 - 0.67 = 0.13
0.13 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 67%. For people who have a brother, the probability of high salary is 80%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.80
0.80 - 0.67 = 0.13
0.13 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 82%. For people who do not have a brother, the probability of high salary is 67%. For people who have a brother, the probability of high salary is 80%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.80
0.82*0.80 - 0.18*0.67 = 0.77
0.77 > 0",chain,college_salary,1,marginal,P(Y)
17194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17195,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17197,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 65%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.65
0.65 - 0.27 = 0.38
0.38 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17198,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 65%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.65
0.65 - 0.27 = 0.38
0.38 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 27%. For people who have a brother, the probability of high salary is 65%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.65
0.65 - 0.27 = 0.38
0.38 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 89%. The probability of not having a brother and high salary is 3%. The probability of having a brother and high salary is 58%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.58
0.58/0.89 - 0.03/0.11 = 0.38
0.38 > 0",chain,college_salary,1,correlation,P(Y | X)
17206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17208,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 51%. For people who have a brother, the probability of high salary is 86%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.86
0.86 - 0.51 = 0.34
0.34 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 51%. For people who have a brother, the probability of high salary is 86%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.86
0.86 - 0.51 = 0.34
0.34 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 97%. The probability of not having a brother and high salary is 1%. The probability of having a brother and high salary is 83%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.83
0.83/0.97 - 0.01/0.03 = 0.34
0.34 > 0",chain,college_salary,1,correlation,P(Y | X)
17218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 46%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.46
0.46 - 0.37 = 0.09
0.09 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 46%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.46
0.46 - 0.37 = 0.09
0.09 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 46%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.46
0.46 - 0.37 = 0.09
0.09 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 97%. The probability of not having a brother and high salary is 1%. The probability of having a brother and high salary is 45%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.45
0.45/0.97 - 0.01/0.03 = 0.09
0.09 > 0",chain,college_salary,1,correlation,P(Y | X)
17230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 29%. For people who have a brother, the probability of high salary is 56%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.56
0.56 - 0.29 = 0.28
0.28 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 29%. For people who have a brother, the probability of high salary is 56%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.56
0.56 - 0.29 = 0.28
0.28 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 29%. For people who have a brother, the probability of high salary is 56%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.56
0.56 - 0.29 = 0.28
0.28 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 92%. For people who do not have a brother, the probability of high salary is 29%. For people who have a brother, the probability of high salary is 56%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.56
0.92*0.56 - 0.08*0.29 = 0.54
0.54 > 0",chain,college_salary,1,marginal,P(Y)
17239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 92%. For people who do not have a brother, the probability of high salary is 29%. For people who have a brother, the probability of high salary is 56%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.56
0.92*0.56 - 0.08*0.29 = 0.54
0.54 > 0",chain,college_salary,1,marginal,P(Y)
17240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 92%. The probability of not having a brother and high salary is 2%. The probability of having a brother and high salary is 52%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.52
0.52/0.92 - 0.02/0.08 = 0.28
0.28 > 0",chain,college_salary,1,correlation,P(Y | X)
17242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 18%. For people who have a brother, the probability of high salary is 38%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.38
0.38 - 0.18 = 0.20
0.20 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 18%. For people who have a brother, the probability of high salary is 38%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.38
0.38 - 0.18 = 0.20
0.20 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 18%. For people who have a brother, the probability of high salary is 38%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.38
0.38 - 0.18 = 0.20
0.20 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 92%. For people who do not have a brother, the probability of high salary is 18%. For people who have a brother, the probability of high salary is 38%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.38
0.92*0.38 - 0.08*0.18 = 0.36
0.36 > 0",chain,college_salary,1,marginal,P(Y)
17255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 19%. For people who have a brother, the probability of high salary is 69%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.69
0.69 - 0.19 = 0.50
0.50 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 19%. For people who have a brother, the probability of high salary is 69%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.69
0.69 - 0.19 = 0.50
0.50 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 90%. For people who do not have a brother, the probability of high salary is 19%. For people who have a brother, the probability of high salary is 69%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.69
0.90*0.69 - 0.10*0.19 = 0.64
0.64 > 0",chain,college_salary,1,marginal,P(Y)
17265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 90%. The probability of not having a brother and high salary is 2%. The probability of having a brother and high salary is 62%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.62
0.62/0.90 - 0.02/0.10 = 0.50
0.50 > 0",chain,college_salary,1,correlation,P(Y | X)
17270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 45%. For people who have a brother, the probability of high salary is 61%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.61
0.61 - 0.45 = 0.17
0.17 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 45%. For people who have a brother, the probability of high salary is 61%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.61
0.61 - 0.45 = 0.17
0.17 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 82%. For people who do not have a brother, the probability of high salary is 45%. For people who have a brother, the probability of high salary is 61%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.61
0.82*0.61 - 0.18*0.45 = 0.58
0.58 > 0",chain,college_salary,1,marginal,P(Y)
17275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 82%. For people who do not have a brother, the probability of high salary is 45%. For people who have a brother, the probability of high salary is 61%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.61
0.82*0.61 - 0.18*0.45 = 0.58
0.58 > 0",chain,college_salary,1,marginal,P(Y)
17280,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 24%. For people who have a brother, the probability of high salary is 50%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.50
0.50 - 0.24 = 0.26
0.26 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 24%. For people who have a brother, the probability of high salary is 50%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.50
0.50 - 0.24 = 0.26
0.26 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 93%. The probability of not having a brother and high salary is 2%. The probability of having a brother and high salary is 46%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.46
0.46/0.93 - 0.02/0.07 = 0.26
0.26 > 0",chain,college_salary,1,correlation,P(Y | X)
17289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 93%. The probability of not having a brother and high salary is 2%. The probability of having a brother and high salary is 46%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.46
0.46/0.93 - 0.02/0.07 = 0.26
0.26 > 0",chain,college_salary,1,correlation,P(Y | X)
17296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 44%. For people who have a brother, the probability of high salary is 54%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.54
0.54 - 0.44 = 0.10
0.10 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17298,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 90%. For people who do not have a brother, the probability of high salary is 44%. For people who have a brother, the probability of high salary is 54%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.54
0.90*0.54 - 0.10*0.44 = 0.53
0.53 > 0",chain,college_salary,1,marginal,P(Y)
17299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 90%. For people who do not have a brother, the probability of high salary is 44%. For people who have a brother, the probability of high salary is 54%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.54
0.90*0.54 - 0.10*0.44 = 0.53
0.53 > 0",chain,college_salary,1,marginal,P(Y)
17302,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17303,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 64%. For people who have a brother, the probability of high salary is 79%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.79
0.79 - 0.64 = 0.16
0.16 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 64%. For people who have a brother, the probability of high salary is 79%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.79
0.79 - 0.64 = 0.16
0.16 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 64%. For people who have a brother, the probability of high salary is 79%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.79
0.79 - 0.64 = 0.16
0.16 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 64%. For people who have a brother, the probability of high salary is 79%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.79
0.79 - 0.64 = 0.16
0.16 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 98%. For people who do not have a brother, the probability of high salary is 64%. For people who have a brother, the probability of high salary is 79%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.79
0.98*0.79 - 0.02*0.64 = 0.79
0.79 > 0",chain,college_salary,1,marginal,P(Y)
17313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 98%. The probability of not having a brother and high salary is 1%. The probability of having a brother and high salary is 78%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.78
0.78/0.98 - 0.01/0.02 = 0.16
0.16 > 0",chain,college_salary,1,correlation,P(Y | X)
17314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17315,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 57%. For people who have a brother, the probability of high salary is 84%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.84
0.84 - 0.57 = 0.27
0.27 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 57%. For people who have a brother, the probability of high salary is 84%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.84
0.84 - 0.57 = 0.27
0.27 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 57%. For people who have a brother, the probability of high salary is 84%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.84
0.84 - 0.57 = 0.27
0.27 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17321,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 57%. For people who have a brother, the probability of high salary is 84%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.84
0.84 - 0.57 = 0.27
0.27 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 94%. For people who do not have a brother, the probability of high salary is 57%. For people who have a brother, the probability of high salary is 84%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.84
0.94*0.84 - 0.06*0.57 = 0.83
0.83 > 0",chain,college_salary,1,marginal,P(Y)
17324,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 94%. The probability of not having a brother and high salary is 4%. The probability of having a brother and high salary is 79%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.94
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.79
0.79/0.94 - 0.04/0.06 = 0.27
0.27 > 0",chain,college_salary,1,correlation,P(Y | X)
17325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 94%. The probability of not having a brother and high salary is 4%. The probability of having a brother and high salary is 79%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.94
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.79
0.79/0.94 - 0.04/0.06 = 0.27
0.27 > 0",chain,college_salary,1,correlation,P(Y | X)
17327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 61%. For people who have a brother, the probability of high salary is 81%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.81
0.81 - 0.61 = 0.20
0.20 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 61%. For people who have a brother, the probability of high salary is 81%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.81
0.81 - 0.61 = 0.20
0.20 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 61%. For people who have a brother, the probability of high salary is 81%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.81
0.81 - 0.61 = 0.20
0.20 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 61%. For people who have a brother, the probability of high salary is 81%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.81
0.81 - 0.61 = 0.20
0.20 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 61%. For people who have a brother, the probability of high salary is 81%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.81
0.81 - 0.61 = 0.20
0.20 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 80%. The probability of not having a brother and high salary is 12%. The probability of having a brother and high salary is 65%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.80
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.65
0.65/0.80 - 0.12/0.20 = 0.20
0.20 > 0",chain,college_salary,1,correlation,P(Y | X)
17338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17339,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 39%. For people who have a brother, the probability of high salary is 57%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.57
0.57 - 0.39 = 0.18
0.18 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 39%. For people who have a brother, the probability of high salary is 57%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.57
0.57 - 0.39 = 0.18
0.18 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 39%. For people who have a brother, the probability of high salary is 57%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.57
0.57 - 0.39 = 0.18
0.18 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17349,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 91%. The probability of not having a brother and high salary is 3%. The probability of having a brother and high salary is 52%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.52
0.52/0.91 - 0.03/0.09 = 0.18
0.18 > 0",chain,college_salary,1,correlation,P(Y | X)
17352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 51%. For people who have a brother, the probability of high salary is 75%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.75
0.75 - 0.51 = 0.24
0.24 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 51%. For people who have a brother, the probability of high salary is 75%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.75
0.75 - 0.51 = 0.24
0.24 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 51%. For people who have a brother, the probability of high salary is 75%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.75
0.75 - 0.51 = 0.24
0.24 > 0",chain,college_salary,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17365,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 56%. For people who have a brother, the probability of high salary is 70%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.70
0.70 - 0.56 = 0.14
0.14 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 56%. For people who have a brother, the probability of high salary is 70%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.70
0.70 - 0.56 = 0.14
0.14 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 82%. For people who do not have a brother, the probability of high salary is 56%. For people who have a brother, the probability of high salary is 70%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.70
0.82*0.70 - 0.18*0.56 = 0.68
0.68 > 0",chain,college_salary,1,marginal,P(Y)
17373,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 82%. The probability of not having a brother and high salary is 10%. The probability of having a brother and high salary is 58%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.58
0.58/0.82 - 0.10/0.18 = 0.14
0.14 > 0",chain,college_salary,1,correlation,P(Y | X)
17375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 54%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.54
0.54 - 0.37 = 0.17
0.17 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 54%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.54
0.54 - 0.37 = 0.17
0.17 > 0",chain,college_salary,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 54%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.54
0.54 - 0.37 = 0.17
0.17 > 0",chain,college_salary,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 84%. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 54%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.54
0.84*0.54 - 0.16*0.37 = 0.51
0.51 > 0",chain,college_salary,1,marginal,P(Y)
17383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 84%. For people who do not have a brother, the probability of high salary is 37%. For people who have a brother, the probability of high salary is 54%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.54
0.84*0.54 - 0.16*0.37 = 0.51
0.51 > 0",chain,college_salary,1,marginal,P(Y)
17384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 84%. The probability of not having a brother and high salary is 6%. The probability of having a brother and high salary is 46%.",yes,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.46
0.46/0.84 - 0.06/0.16 = 0.17
0.17 > 0",chain,college_salary,1,correlation,P(Y | X)
17385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 84%. The probability of not having a brother and high salary is 6%. The probability of having a brother and high salary is 46%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.46
0.46/0.84 - 0.06/0.16 = 0.17
0.17 > 0",chain,college_salary,1,correlation,P(Y | X)
17387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look directly at how having a brother correlates with salary in general. Method 2: We look at this correlation case by case according to skill.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 81%. For people who do not have a brother, the probability of high salary is 60%. For people who have a brother, the probability of high salary is 66%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.66
0.81*0.66 - 0.19*0.60 = 0.65
0.65 > 0",chain,college_salary,1,marginal,P(Y)
17397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. The overall probability of having a brother is 81%. The probability of not having a brother and high salary is 11%. The probability of having a brother and high salary is 54%.",no,"Let X = having a brother; V2 = skill; Y = salary.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.54
0.54/0.81 - 0.11/0.19 = 0.07
0.07 > 0",chain,college_salary,1,correlation,P(Y | X)
17398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on skill. Skill has a direct effect on salary. Method 1: We look at how having a brother correlates with salary case by case according to skill. Method 2: We look directly at how having a brother correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,college_salary,2,backadj,[backdoor adjustment set for Y given X]
17401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 63%. For people living close to a college, the probability of large feet is 78%. For people living far from a college, the probability of college degree or higher is 59%. For people living close to a college, the probability of college degree or higher is 19%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.63
P(Y=1 | V2=1) = 0.78
P(X=1 | V2=0) = 0.59
P(X=1 | V2=1) = 0.19
(0.78 - 0.63) / (0.19 - 0.59) = -0.36
-0.36 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 24%. For people without a college degree, the probability of large feet is 85%. For people with a college degree or higher, the probability of large feet is 48%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.48
0.24*0.48 - 0.76*0.85 = 0.76
0.76 > 0",IV,college_wage,1,marginal,P(Y)
17404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 24%. The probability of high school degree or lower and large feet is 65%. The probability of college degree or higher and large feet is 11%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.11
0.11/0.24 - 0.65/0.76 = -0.37
-0.37 < 0",IV,college_wage,1,correlation,P(Y | X)
17406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 49%. The probability of high school degree or lower and large feet is 26%. The probability of college degree or higher and large feet is 7%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.07
0.07/0.49 - 0.26/0.51 = -0.37
-0.37 < 0",IV,college_wage,1,correlation,P(Y | X)
17423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 59%. For people without a college degree, the probability of large feet is 76%. For people with a college degree or higher, the probability of large feet is 10%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.10
0.59*0.10 - 0.41*0.76 = 0.37
0.37 > 0",IV,college_wage,1,marginal,P(Y)
17428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 59%. The probability of high school degree or lower and large feet is 31%. The probability of college degree or higher and large feet is 6%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.06
0.06/0.59 - 0.31/0.41 = -0.66
-0.66 < 0",IV,college_wage,1,correlation,P(Y | X)
17430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17432,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 37%. For people living close to a college, the probability of large feet is 52%. For people living far from a college, the probability of college degree or higher is 87%. For people living close to a college, the probability of college degree or higher is 43%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.37
P(Y=1 | V2=1) = 0.52
P(X=1 | V2=0) = 0.87
P(X=1 | V2=1) = 0.43
(0.52 - 0.37) / (0.43 - 0.87) = -0.35
-0.35 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 50%. The probability of high school degree or lower and large feet is 34%. The probability of college degree or higher and large feet is 16%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.16
0.16/0.50 - 0.34/0.50 = -0.35
-0.35 < 0",IV,college_wage,1,correlation,P(Y | X)
17437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 50%. The probability of high school degree or lower and large feet is 34%. The probability of college degree or higher and large feet is 16%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.16
0.16/0.50 - 0.34/0.50 = -0.35
-0.35 < 0",IV,college_wage,1,correlation,P(Y | X)
17438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 55%. For people without a college degree, the probability of large feet is 87%. For people with a college degree or higher, the probability of large feet is 52%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.52
0.55*0.52 - 0.45*0.87 = 0.68
0.68 > 0",IV,college_wage,1,marginal,P(Y)
17444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 55%. The probability of high school degree or lower and large feet is 39%. The probability of college degree or higher and large feet is 29%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.29
0.29/0.55 - 0.39/0.45 = -0.35
-0.35 < 0",IV,college_wage,1,correlation,P(Y | X)
17447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 39%. For people living close to a college, the probability of large feet is 51%. For people living far from a college, the probability of college degree or higher is 89%. For people living close to a college, the probability of college degree or higher is 50%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.39
P(Y=1 | V2=1) = 0.51
P(X=1 | V2=0) = 0.89
P(X=1 | V2=1) = 0.50
(0.51 - 0.39) / (0.50 - 0.89) = -0.32
-0.32 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 57%. For people without a college degree, the probability of large feet is 67%. For people with a college degree or higher, the probability of large feet is 35%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.35
0.57*0.35 - 0.43*0.67 = 0.49
0.49 > 0",IV,college_wage,1,marginal,P(Y)
17461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 65%. The probability of high school degree or lower and large feet is 20%. The probability of college degree or higher and large feet is 14%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.14
0.14/0.65 - 0.20/0.35 = -0.36
-0.36 < 0",IV,college_wage,1,correlation,P(Y | X)
17463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17465,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 40%. For people living close to a college, the probability of large feet is 51%. For people living far from a college, the probability of college degree or higher is 78%. For people living close to a college, the probability of college degree or higher is 37%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.40
P(Y=1 | V2=1) = 0.51
P(X=1 | V2=0) = 0.78
P(X=1 | V2=1) = 0.37
(0.51 - 0.40) / (0.37 - 0.78) = -0.27
-0.27 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17466,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 43%. For people without a college degree, the probability of large feet is 61%. For people with a college degree or higher, the probability of large feet is 34%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.34
0.43*0.34 - 0.57*0.61 = 0.49
0.49 > 0",IV,college_wage,1,marginal,P(Y)
17467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 43%. For people without a college degree, the probability of large feet is 61%. For people with a college degree or higher, the probability of large feet is 34%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.34
0.43*0.34 - 0.57*0.61 = 0.49
0.49 > 0",IV,college_wage,1,marginal,P(Y)
17468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 43%. The probability of high school degree or lower and large feet is 34%. The probability of college degree or higher and large feet is 15%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.15
0.15/0.43 - 0.34/0.57 = -0.27
-0.27 < 0",IV,college_wage,1,correlation,P(Y | X)
17472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 53%. For people living close to a college, the probability of large feet is 64%. For people living far from a college, the probability of college degree or higher is 80%. For people living close to a college, the probability of college degree or higher is 50%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.53
P(Y=1 | V2=1) = 0.64
P(X=1 | V2=0) = 0.80
P(X=1 | V2=1) = 0.50
(0.64 - 0.53) / (0.50 - 0.80) = -0.34
-0.34 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17475,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 77%. For people without a college degree, the probability of large feet is 80%. For people with a college degree or higher, the probability of large feet is 46%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.77
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.46
0.77*0.46 - 0.23*0.80 = 0.55
0.55 > 0",IV,college_wage,1,marginal,P(Y)
17476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 77%. The probability of high school degree or lower and large feet is 19%. The probability of college degree or higher and large feet is 36%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.77
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.36
0.36/0.77 - 0.19/0.23 = -0.34
-0.34 < 0",IV,college_wage,1,correlation,P(Y | X)
17480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 45%. For people living close to a college, the probability of large feet is 63%. For people living far from a college, the probability of college degree or higher is 39%. For people living close to a college, the probability of college degree or higher is 13%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.45
P(Y=1 | V2=1) = 0.63
P(X=1 | V2=0) = 0.39
P(X=1 | V2=1) = 0.13
(0.63 - 0.45) / (0.13 - 0.39) = -0.69
-0.69 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17493,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 47%. The probability of high school degree or lower and large feet is 32%. The probability of college degree or higher and large feet is 10%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.32
P(Y=1, X=1=1) = 0.10
0.10/0.47 - 0.32/0.53 = -0.39
-0.39 < 0",IV,college_wage,1,correlation,P(Y | X)
17494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17497,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 41%. For people living close to a college, the probability of large feet is 56%. For people living far from a college, the probability of college degree or higher is 65%. For people living close to a college, the probability of college degree or higher is 29%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.41
P(Y=1 | V2=1) = 0.56
P(X=1 | V2=0) = 0.65
P(X=1 | V2=1) = 0.29
(0.56 - 0.41) / (0.29 - 0.65) = -0.42
-0.42 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 36%. For people without a college degree, the probability of large feet is 67%. For people with a college degree or higher, the probability of large feet is 27%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.27
0.36*0.27 - 0.64*0.67 = 0.53
0.53 > 0",IV,college_wage,1,marginal,P(Y)
17500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 36%. The probability of high school degree or lower and large feet is 43%. The probability of college degree or higher and large feet is 10%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.36
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.10
0.10/0.36 - 0.43/0.64 = -0.40
-0.40 < 0",IV,college_wage,1,correlation,P(Y | X)
17502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 46%. For people without a college degree, the probability of large feet is 88%. For people with a college degree or higher, the probability of large feet is 43%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.43
0.46*0.43 - 0.54*0.88 = 0.68
0.68 > 0",IV,college_wage,1,marginal,P(Y)
17513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 22%. For people living close to a college, the probability of large feet is 39%. For people living far from a college, the probability of college degree or higher is 84%. For people living close to a college, the probability of college degree or higher is 47%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.22
P(Y=1 | V2=1) = 0.39
P(X=1 | V2=0) = 0.84
P(X=1 | V2=1) = 0.47
(0.39 - 0.22) / (0.47 - 0.84) = -0.46
-0.46 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 50%. The probability of high school degree or lower and large feet is 30%. The probability of college degree or higher and large feet is 7%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.07
0.07/0.50 - 0.30/0.50 = -0.46
-0.46 < 0",IV,college_wage,1,correlation,P(Y | X)
17517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 50%. The probability of high school degree or lower and large feet is 30%. The probability of college degree or higher and large feet is 7%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.07
0.07/0.50 - 0.30/0.50 = -0.46
-0.46 < 0",IV,college_wage,1,correlation,P(Y | X)
17519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 41%. For people living close to a college, the probability of large feet is 59%. For people living far from a college, the probability of college degree or higher is 49%. For people living close to a college, the probability of college degree or higher is 9%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.41
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.49
P(X=1 | V2=1) = 0.09
(0.59 - 0.41) / (0.09 - 0.49) = -0.44
-0.44 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 41%. For people living close to a college, the probability of large feet is 59%. For people living far from a college, the probability of college degree or higher is 49%. For people living close to a college, the probability of college degree or higher is 9%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.41
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.49
P(X=1 | V2=1) = 0.09
(0.59 - 0.41) / (0.09 - 0.49) = -0.44
-0.44 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 23%. For people without a college degree, the probability of large feet is 79%. For people with a college degree or higher, the probability of large feet is 29%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.29
0.23*0.29 - 0.77*0.79 = 0.68
0.68 > 0",IV,college_wage,1,marginal,P(Y)
17532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 23%. The probability of high school degree or lower and large feet is 61%. The probability of college degree or higher and large feet is 7%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.23
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.07
0.07/0.23 - 0.61/0.77 = -0.50
-0.50 < 0",IV,college_wage,1,correlation,P(Y | X)
17533,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 23%. The probability of high school degree or lower and large feet is 61%. The probability of college degree or higher and large feet is 7%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.23
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.07
0.07/0.23 - 0.61/0.77 = -0.50
-0.50 < 0",IV,college_wage,1,correlation,P(Y | X)
17538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 52%. For people without a college degree, the probability of large feet is 68%. For people with a college degree or higher, the probability of large feet is 39%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.39
0.52*0.39 - 0.48*0.68 = 0.53
0.53 > 0",IV,college_wage,1,marginal,P(Y)
17540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 52%. The probability of high school degree or lower and large feet is 33%. The probability of college degree or higher and large feet is 20%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.20
0.20/0.52 - 0.33/0.48 = -0.29
-0.29 < 0",IV,college_wage,1,correlation,P(Y | X)
17544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 11%. For people living close to a college, the probability of large feet is 27%. For people living far from a college, the probability of college degree or higher is 93%. For people living close to a college, the probability of college degree or higher is 52%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.11
P(Y=1 | V2=1) = 0.27
P(X=1 | V2=0) = 0.93
P(X=1 | V2=1) = 0.52
(0.27 - 0.11) / (0.52 - 0.93) = -0.38
-0.38 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 55%. For people without a college degree, the probability of large feet is 46%. For people with a college degree or higher, the probability of large feet is 8%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.08
0.55*0.08 - 0.45*0.46 = 0.25
0.25 > 0",IV,college_wage,1,marginal,P(Y)
17549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 55%. The probability of high school degree or lower and large feet is 21%. The probability of college degree or higher and large feet is 5%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.05
0.05/0.55 - 0.21/0.45 = -0.38
-0.38 < 0",IV,college_wage,1,correlation,P(Y | X)
17550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 39%. For people living close to a college, the probability of large feet is 49%. For people living far from a college, the probability of college degree or higher is 57%. For people living close to a college, the probability of college degree or higher is 30%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.39
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.57
P(X=1 | V2=1) = 0.30
(0.49 - 0.39) / (0.30 - 0.57) = -0.37
-0.37 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17558,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 9%. For people without a college degree, the probability of large feet is 67%. For people with a college degree or higher, the probability of large feet is 26%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.26
0.09*0.26 - 0.91*0.67 = 0.63
0.63 > 0",IV,college_wage,1,marginal,P(Y)
17564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 9%. The probability of high school degree or lower and large feet is 61%. The probability of college degree or higher and large feet is 2%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.02
0.02/0.09 - 0.61/0.91 = -0.41
-0.41 < 0",IV,college_wage,1,correlation,P(Y | X)
17568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 44%. For people living close to a college, the probability of large feet is 56%. For people living far from a college, the probability of college degree or higher is 88%. For people living close to a college, the probability of college degree or higher is 54%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.44
P(Y=1 | V2=1) = 0.56
P(X=1 | V2=0) = 0.88
P(X=1 | V2=1) = 0.54
(0.56 - 0.44) / (0.54 - 0.88) = -0.35
-0.35 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 44%. For people living close to a college, the probability of large feet is 56%. For people living far from a college, the probability of college degree or higher is 88%. For people living close to a college, the probability of college degree or higher is 54%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.44
P(Y=1 | V2=1) = 0.56
P(X=1 | V2=0) = 0.88
P(X=1 | V2=1) = 0.54
(0.56 - 0.44) / (0.54 - 0.88) = -0.35
-0.35 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17570,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 81%. For people without a college degree, the probability of large feet is 75%. For people with a college degree or higher, the probability of large feet is 40%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.40
0.81*0.40 - 0.19*0.75 = 0.46
0.46 > 0",IV,college_wage,1,marginal,P(Y)
17571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 81%. For people without a college degree, the probability of large feet is 75%. For people with a college degree or higher, the probability of large feet is 40%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.40
0.81*0.40 - 0.19*0.75 = 0.46
0.46 > 0",IV,college_wage,1,marginal,P(Y)
17576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 22%. For people living close to a college, the probability of large feet is 37%. For people living far from a college, the probability of college degree or higher is 56%. For people living close to a college, the probability of college degree or higher is 16%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.22
P(Y=1 | V2=1) = 0.37
P(X=1 | V2=0) = 0.56
P(X=1 | V2=1) = 0.16
(0.37 - 0.22) / (0.16 - 0.56) = -0.38
-0.38 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 18%. For people without a college degree, the probability of large feet is 42%. For people with a college degree or higher, the probability of large feet is 6%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.06
0.18*0.06 - 0.82*0.42 = 0.36
0.36 > 0",IV,college_wage,1,marginal,P(Y)
17580,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 18%. The probability of high school degree or lower and large feet is 35%. The probability of college degree or higher and large feet is 1%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.01
0.01/0.18 - 0.35/0.82 = -0.36
-0.36 < 0",IV,college_wage,1,correlation,P(Y | X)
17581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 18%. The probability of high school degree or lower and large feet is 35%. The probability of college degree or higher and large feet is 1%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.18
P(Y=1, X=0=1) = 0.35
P(Y=1, X=1=1) = 0.01
0.01/0.18 - 0.35/0.82 = -0.36
-0.36 < 0",IV,college_wage,1,correlation,P(Y | X)
17587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 73%. For people without a college degree, the probability of large feet is 90%. For people with a college degree or higher, the probability of large feet is 52%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.73
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.52
0.73*0.52 - 0.27*0.90 = 0.62
0.62 > 0",IV,college_wage,1,marginal,P(Y)
17588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 73%. The probability of high school degree or lower and large feet is 24%. The probability of college degree or higher and large feet is 38%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.73
P(Y=1, X=0=1) = 0.24
P(Y=1, X=1=1) = 0.38
0.38/0.73 - 0.24/0.27 = -0.38
-0.38 < 0",IV,college_wage,1,correlation,P(Y | X)
17594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 31%. For people without a college degree, the probability of large feet is 61%. For people with a college degree or higher, the probability of large feet is 33%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.33
0.31*0.33 - 0.69*0.61 = 0.52
0.52 > 0",IV,college_wage,1,marginal,P(Y)
17596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 31%. The probability of high school degree or lower and large feet is 42%. The probability of college degree or higher and large feet is 10%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.10
0.10/0.31 - 0.42/0.69 = -0.28
-0.28 < 0",IV,college_wage,1,correlation,P(Y | X)
17597,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 31%. The probability of high school degree or lower and large feet is 42%. The probability of college degree or higher and large feet is 10%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.10
0.10/0.31 - 0.42/0.69 = -0.28
-0.28 < 0",IV,college_wage,1,correlation,P(Y | X)
17601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 30%. For people living close to a college, the probability of large feet is 45%. For people living far from a college, the probability of college degree or higher is 68%. For people living close to a college, the probability of college degree or higher is 30%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.30
P(Y=1 | V2=1) = 0.45
P(X=1 | V2=0) = 0.68
P(X=1 | V2=1) = 0.30
(0.45 - 0.30) / (0.30 - 0.68) = -0.40
-0.40 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17602,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 66%. For people without a college degree, the probability of large feet is 56%. For people with a college degree or higher, the probability of large feet is 17%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.17
0.66*0.17 - 0.34*0.56 = 0.31
0.31 > 0",IV,college_wage,1,marginal,P(Y)
17606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 41%. For people living close to a college, the probability of large feet is 61%. For people living far from a college, the probability of college degree or higher is 73%. For people living close to a college, the probability of college degree or higher is 38%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.41
P(Y=1 | V2=1) = 0.61
P(X=1 | V2=0) = 0.73
P(X=1 | V2=1) = 0.38
(0.61 - 0.41) / (0.38 - 0.73) = -0.59
-0.59 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 44%. The probability of high school degree or lower and large feet is 47%. The probability of college degree or higher and large feet is 12%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.12
0.12/0.44 - 0.47/0.56 = -0.59
-0.59 < 0",IV,college_wage,1,correlation,P(Y | X)
17616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 42%. For people living close to a college, the probability of large feet is 60%. For people living far from a college, the probability of college degree or higher is 80%. For people living close to a college, the probability of college degree or higher is 26%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.42
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.80
P(X=1 | V2=1) = 0.26
(0.60 - 0.42) / (0.26 - 0.80) = -0.34
-0.34 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17617,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 42%. For people living close to a college, the probability of large feet is 60%. For people living far from a college, the probability of college degree or higher is 80%. For people living close to a college, the probability of college degree or higher is 26%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.42
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.80
P(X=1 | V2=1) = 0.26
(0.60 - 0.42) / (0.26 - 0.80) = -0.34
-0.34 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 80%. The probability of high school degree or lower and large feet is 14%. The probability of college degree or higher and large feet is 28%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.80
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.28
0.28/0.80 - 0.14/0.20 = -0.34
-0.34 < 0",IV,college_wage,1,correlation,P(Y | X)
17623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 42%. For people living close to a college, the probability of large feet is 53%. For people living far from a college, the probability of college degree or higher is 61%. For people living close to a college, the probability of college degree or higher is 34%.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.42
P(Y=1 | V2=1) = 0.53
P(X=1 | V2=0) = 0.61
P(X=1 | V2=1) = 0.34
(0.53 - 0.42) / (0.34 - 0.61) = -0.42
-0.42 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17625,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. For people living far from a college, the probability of large feet is 42%. For people living close to a college, the probability of large feet is 53%. For people living far from a college, the probability of college degree or higher is 61%. For people living close to a college, the probability of college degree or higher is 34%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.42
P(Y=1 | V2=1) = 0.53
P(X=1 | V2=0) = 0.61
P(X=1 | V2=1) = 0.34
(0.53 - 0.42) / (0.34 - 0.61) = -0.42
-0.42 < 0",IV,college_wage,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 59%. For people without a college degree, the probability of large feet is 67%. For people with a college degree or higher, the probability of large feet is 25%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.25
0.59*0.25 - 0.41*0.67 = 0.43
0.43 > 0",IV,college_wage,1,marginal,P(Y)
17631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look at how education level correlates with foot size case by case according to unobserved confounders. Method 2: We look directly at how education level correlates with foot size in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 38%. For people without a college degree, the probability of large feet is 70%. For people with a college degree or higher, the probability of large feet is 22%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.38
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.22
0.38*0.22 - 0.62*0.70 = 0.51
0.51 > 0",IV,college_wage,1,marginal,P(Y)
17637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. The overall probability of college degree or higher is 38%. The probability of high school degree or lower and large feet is 43%. The probability of college degree or higher and large feet is 8%.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = education level; Y = foot size.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.08
0.08/0.38 - 0.43/0.62 = -0.48
-0.48 < 0",IV,college_wage,1,correlation,P(Y | X)
17638,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on education level and foot size. Proximity to a college has a direct effect on education level. Education level has a direct effect on foot size. Unobserved confounders is unobserved. Method 1: We look directly at how education level correlates with foot size in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,college_wage,2,backadj,[backdoor adjustment set for Y given X]
17641,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 99%. For students who are not talented, the probability of brown eyes is 87%. For students who are talented, the probability of brown eyes is 87%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.87
0.99*0.87 - 0.01*0.87 = 0.87
0.87 > 0",collision,elite_students,1,marginal,P(Y)
17644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.02.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 99%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 95%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 81%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 93%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 74%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.99
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.81
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.99*0.74 + 0.01*0.81) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 99%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 95%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 81%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 93%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 74%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.99
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.81
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.99*0.74 + 0.01*0.81) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17656,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.07.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 97%. For students who are not talented, the probability of brown eyes is 95%. For students who are talented, the probability of brown eyes is 95%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.95
0.97*0.95 - 0.03*0.95 = 0.95
0.95 > 0",collision,elite_students,1,marginal,P(Y)
17665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.02.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 97%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 98%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 92%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 88%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.97
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.92
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.88
0.88 - (0.97*0.88 + 0.03*0.92) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17670,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 80%. For students who are not talented, the probability of brown eyes is 85%. For students who are talented, the probability of brown eyes is 85%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.85
0.80*0.85 - 0.20*0.85 = 0.85
0.85 > 0",collision,elite_students,1,marginal,P(Y)
17674,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.08.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17681,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 98%. For students who are not talented, the probability of brown eyes is 96%. For students who are talented, the probability of brown eyes is 96%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.96
P(Y=1 | X=1) = 0.96
0.98*0.96 - 0.02*0.96 = 0.96
0.96 > 0",collision,elite_students,1,marginal,P(Y)
17688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 98%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 99%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 94%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 98%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 93%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.98
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.94
P(Y=1 | X=1, V3=0) = 0.98
P(Y=1 | X=1, V3=1) = 0.93
0.93 - (0.98*0.93 + 0.02*0.94) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 83%. For students who are not talented, the probability of brown eyes is 82%. For students who are talented, the probability of brown eyes is 82%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.82
0.83*0.82 - 0.17*0.82 = 0.82
0.82 > 0",collision,elite_students,1,marginal,P(Y)
17697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.22.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 83%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 91%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 71%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 88%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 48%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.83
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.88
P(Y=1 | X=1, V3=1) = 0.48
0.48 - (0.83*0.48 + 0.17*0.71) = -0.08
-0.08 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.01.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 89%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 93%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 73%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 87%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 72%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.89
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.73
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.72
0.72 - (0.89*0.72 + 0.11*0.73) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 94%. For students who are not talented, the probability of brown eyes is 83%. For students who are talented, the probability of brown eyes is 83%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.83
0.94*0.83 - 0.06*0.83 = 0.83
0.83 > 0",collision,elite_students,1,marginal,P(Y)
17715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 94%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 93%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 75%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 90%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 69%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.94
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.75
P(Y=1 | X=1, V3=0) = 0.90
P(Y=1 | X=1, V3=1) = 0.69
0.69 - (0.94*0.69 + 0.06*0.75) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 94%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 93%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 75%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 90%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 69%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.94
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.75
P(Y=1 | X=1, V3=0) = 0.90
P(Y=1 | X=1, V3=1) = 0.69
0.69 - (0.94*0.69 + 0.06*0.75) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 90%. For students who are not talented, the probability of brown eyes is 93%. For students who are talented, the probability of brown eyes is 93%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.93
0.90*0.93 - 0.10*0.93 = 0.93
0.93 > 0",collision,elite_students,1,marginal,P(Y)
17724,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.05.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.05.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 95%. For students who are not talented, the probability of brown eyes is 94%. For students who are talented, the probability of brown eyes is 94%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.94
0.95*0.94 - 0.05*0.94 = 0.94
0.94 > 0",collision,elite_students,1,marginal,P(Y)
17731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 95%. For students who are not talented, the probability of brown eyes is 94%. For students who are talented, the probability of brown eyes is 94%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.94
0.95*0.94 - 0.05*0.94 = 0.94
0.94 > 0",collision,elite_students,1,marginal,P(Y)
17734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 95%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 98%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 91%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 96%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 84%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.95
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.96
P(Y=1 | X=1, V3=1) = 0.84
0.84 - (0.95*0.84 + 0.05*0.91) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.07.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 97%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 95%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 82%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 94%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 69%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.97
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.94
P(Y=1 | X=1, V3=1) = 0.69
0.69 - (0.97*0.69 + 0.03*0.82) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 97%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 95%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 82%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 94%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 69%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.97
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.94
P(Y=1 | X=1, V3=1) = 0.69
0.69 - (0.97*0.69 + 0.03*0.82) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 95%. For students who are not talented, the probability of brown eyes is 82%. For students who are talented, the probability of brown eyes is 82%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.82
0.95*0.82 - 0.05*0.82 = 0.82
0.82 > 0",collision,elite_students,1,marginal,P(Y)
17751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 95%. For students who are not talented, the probability of brown eyes is 82%. For students who are talented, the probability of brown eyes is 82%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.82
0.95*0.82 - 0.05*0.82 = 0.82
0.82 > 0",collision,elite_students,1,marginal,P(Y)
17760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 91%. For students who are not talented, the probability of brown eyes is 98%. For students who are talented, the probability of brown eyes is 98%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.98
P(Y=1 | X=1) = 0.98
0.91*0.98 - 0.09*0.98 = 0.98
0.98 > 0",collision,elite_students,1,marginal,P(Y)
17761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 91%. For students who are not talented, the probability of brown eyes is 98%. For students who are talented, the probability of brown eyes is 98%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.98
P(Y=1 | X=1) = 0.98
0.91*0.98 - 0.09*0.98 = 0.98
0.98 > 0",collision,elite_students,1,marginal,P(Y)
17767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.01.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17770,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 91%. For students who are not talented, the probability of brown eyes is 94%. For students who are talented, the probability of brown eyes is 94%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.94
0.91*0.94 - 0.09*0.94 = 0.94
0.94 > 0",collision,elite_students,1,marginal,P(Y)
17774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.33.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 91%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 89%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 96%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 60%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.91
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.96
P(Y=1 | X=1, V3=1) = 0.60
0.60 - (0.91*0.60 + 0.09*0.89) = -0.13
-0.13 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 93%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 100%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 99%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 99%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 98%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.93
P(Y=1 | X=0, V3=0) = 1.00
P(Y=1 | X=0, V3=1) = 0.99
P(Y=1 | X=1, V3=0) = 0.99
P(Y=1 | X=1, V3=1) = 0.98
0.98 - (0.93*0.98 + 0.07*0.99) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 91%. For students who are not talented, the probability of brown eyes is 95%. For students who are talented, the probability of brown eyes is 95%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.95
0.91*0.95 - 0.09*0.95 = 0.95
0.95 > 0",collision,elite_students,1,marginal,P(Y)
17800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 86%. For students who are not talented, the probability of brown eyes is 98%. For students who are talented, the probability of brown eyes is 98%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.98
P(Y=1 | X=1) = 0.98
0.86*0.98 - 0.14*0.98 = 0.98
0.98 > 0",collision,elite_students,1,marginal,P(Y)
17801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 86%. For students who are not talented, the probability of brown eyes is 98%. For students who are talented, the probability of brown eyes is 98%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.98
P(Y=1 | X=1) = 0.98
0.86*0.98 - 0.14*0.98 = 0.98
0.98 > 0",collision,elite_students,1,marginal,P(Y)
17811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 87%. For students who are not talented, the probability of brown eyes is 86%. For students who are talented, the probability of brown eyes is 86%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.86
0.87*0.86 - 0.13*0.86 = 0.86
0.86 > 0",collision,elite_students,1,marginal,P(Y)
17815,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 87%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 94%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 77%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 91%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 72%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.87
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.72
0.72 - (0.87*0.72 + 0.13*0.77) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 87%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 94%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 77%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 91%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 72%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.87
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.72
0.72 - (0.87*0.72 + 0.13*0.77) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.14.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 81%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 99%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 82%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 95%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 69%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.81
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.95
P(Y=1 | X=1, V3=1) = 0.69
0.69 - (0.81*0.69 + 0.19*0.82) = -0.05
-0.05 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 93%. For students who are not talented, the probability of brown eyes is 95%. For students who are talented, the probability of brown eyes is 95%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.95
0.93*0.95 - 0.07*0.95 = 0.95
0.95 > 0",collision,elite_students,1,marginal,P(Y)
17839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 93%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 99%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 93%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 92%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.93
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.93
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.92
0.92 - (0.93*0.92 + 0.07*0.93) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 82%. For students who are not talented, the probability of brown eyes is 96%. For students who are talented, the probability of brown eyes is 96%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.96
P(Y=1 | X=1) = 0.96
0.82*0.96 - 0.18*0.96 = 0.96
0.96 > 0",collision,elite_students,1,marginal,P(Y)
17844,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.06.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.06.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 82%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 99%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 94%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 90%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.82
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.94
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.90
0.90 - (0.82*0.90 + 0.18*0.94) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 95%. For students who are not talented, the probability of brown eyes is 88%. For students who are talented, the probability of brown eyes is 88%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.88
0.95*0.88 - 0.05*0.88 = 0.88
0.88 > 0",collision,elite_students,1,marginal,P(Y)
17854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17857,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.03.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17858,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 95%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 79%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 93%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 74%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.95
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.79
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.95*0.74 + 0.05*0.79) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 95%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 79%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 93%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 74%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.95
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.79
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.95*0.74 + 0.05*0.79) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 97%. For students who are not talented, the probability of brown eyes is 93%. For students who are talented, the probability of brown eyes is 93%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.93
P(Y=1 | X=1) = 0.93
0.97*0.93 - 0.03*0.93 = 0.93
0.93 > 0",collision,elite_students,1,marginal,P(Y)
17864,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 97%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 100%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 87%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 81%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.97
P(Y=1 | X=0, V3=0) = 1.00
P(Y=1 | X=0, V3=1) = 0.87
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.81
0.81 - (0.97*0.81 + 0.03*0.87) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17877,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.01.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 86%. For students who are not talented, the probability of brown eyes is 96%. For students who are talented, the probability of brown eyes is 96%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.96
P(Y=1 | X=1) = 0.96
0.86*0.96 - 0.14*0.96 = 0.96
0.96 > 0",collision,elite_students,1,marginal,P(Y)
17884,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.06.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 86%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 99%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 94%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 91%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.86
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.94
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.91
0.91 - (0.86*0.91 + 0.14*0.94) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 98%. For students who are not talented, the probability of brown eyes is 98%. For students who are talented, the probability of brown eyes is 98%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.98
P(Y=1 | X=1) = 0.98
0.98*0.98 - 0.02*0.98 = 0.98
0.98 > 0",collision,elite_students,1,marginal,P(Y)
17895,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.02.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17897,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.02.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17901,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 82%. For students who are not talented, the probability of brown eyes is 89%. For students who are talented, the probability of brown eyes is 89%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.89
0.82*0.89 - 0.18*0.89 = 0.89
0.89 > 0",collision,elite_students,1,marginal,P(Y)
17904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17905,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 82%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 99%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 82%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 96%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 53%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.82
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.96
P(Y=1 | X=1, V3=1) = 0.53
0.53 - (0.82*0.53 + 0.18*0.82) = -0.12
-0.12 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 98%. For students who are not talented, the probability of brown eyes is 90%. For students who are talented, the probability of brown eyes is 90%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.90
0.98*0.90 - 0.02*0.90 = 0.90
0.90 > 0",collision,elite_students,1,marginal,P(Y)
17917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.07.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 98%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 95%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 83%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 93%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 71%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.98
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.71
0.71 - (0.98*0.71 + 0.02*0.83) = -0.01
-0.01 < 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. For students accepted to elite institutions, the correlation between talent and brown eyes is -0.01.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,elite_students,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
17928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 99%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 99%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 91%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 97%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 88%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.99
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.88
0.88 - (0.99*0.88 + 0.01*0.91) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17930,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 86%. For students who are not talented, the probability of brown eyes is 96%. For students who are talented, the probability of brown eyes is 96%.",yes,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.96
P(Y=1 | X=1) = 0.96
0.86*0.96 - 0.14*0.96 = 0.96
0.96 > 0",collision,elite_students,1,marginal,P(Y)
17934,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look at how talent correlates with brown eyes case by case according to elite institution admission status. Method 2: We look directly at how talent correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. Method 1: We look directly at how talent correlates with brown eyes in general. Method 2: We look at this correlation case by case according to elite institution admission status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,elite_students,2,backadj,[backdoor adjustment set for Y given X]
17938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Talent has a direct effect on elite institution admission status. Brown eyes has a direct effect on elite institution admission status. The overall probability of talent is 86%. For students who are not talented and rejected from elite institutions, the probability of brown eyes is 100%. For students who are not talented and accepted to elite institutions, the probability of brown eyes is 94%. For students who are talented and rejected from elite institutions, the probability of brown eyes is 98%. For students who are talented and accepted to elite institutions, the probability of brown eyes is 92%.",no,"Let Y = brown eyes; X = talent; V3 = elite institution admission status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.86
P(Y=1 | X=0, V3=0) = 1.00
P(Y=1 | X=0, V3=1) = 0.94
P(Y=1 | X=1, V3=0) = 0.98
P(Y=1 | X=1, V3=1) = 0.92
0.92 - (0.86*0.92 + 0.14*0.94) = -0.00
0.00 = 0",collision,elite_students,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
17941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 58%. For students who are encouraged, the probability of brown eyes is 34%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.34
0.34 - 0.58 = -0.24
-0.24 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 58%. For students who are encouraged, the probability of brown eyes is 34%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.34
0.34 - 0.58 = -0.24
-0.24 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 58%. For students who are encouraged, the probability of brown eyes is 34%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.34
0.34 - 0.58 = -0.24
-0.24 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 67%. For students who are not encouraged and study hard, the probability of brown eyes is 42%. For students who are encouraged and do not study hard, the probability of brown eyes is 35%. For students who are encouraged and study hard, the probability of brown eyes is 5%. For students who are not encouraged, the probability of studying hard is 35%. For students who are encouraged, the probability of studying hard is 5%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.67
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.05
P(V2=1 | X=0) = 0.35
P(V2=1 | X=1) = 0.05
0.35 * (0.05 - 0.35) + 0.05 * (0.42 - 0.67) = -0.34
-0.34 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
17950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 90%. The probability of discouragement and brown eyes is 6%. The probability of encouragement and brown eyes is 31%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.31
0.31/0.90 - 0.06/0.10 = -0.24
-0.24 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
17953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
17959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 76%. For students who are not encouraged and study hard, the probability of brown eyes is 54%. For students who are encouraged and do not study hard, the probability of brown eyes is 56%. For students who are encouraged and study hard, the probability of brown eyes is 28%. For students who are not encouraged, the probability of studying hard is 77%. For students who are encouraged, the probability of studying hard is 36%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 0.28
P(V2=1 | X=0) = 0.77
P(V2=1 | X=1) = 0.36
0.36 * (0.54 - 0.76)+ 0.77 * (0.28 - 0.56)= 0.09
0.09 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 76%. For students who are not encouraged and study hard, the probability of brown eyes is 54%. For students who are encouraged and do not study hard, the probability of brown eyes is 56%. For students who are encouraged and study hard, the probability of brown eyes is 28%. For students who are not encouraged, the probability of studying hard is 77%. For students who are encouraged, the probability of studying hard is 36%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 0.28
P(V2=1 | X=0) = 0.77
P(V2=1 | X=1) = 0.36
0.77 * (0.28 - 0.56) + 0.36 * (0.54 - 0.76) = -0.25
-0.25 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
17961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 76%. For students who are not encouraged and study hard, the probability of brown eyes is 54%. For students who are encouraged and do not study hard, the probability of brown eyes is 56%. For students who are encouraged and study hard, the probability of brown eyes is 28%. For students who are not encouraged, the probability of studying hard is 77%. For students who are encouraged, the probability of studying hard is 36%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.56
P(Y=1 | X=1, V2=1) = 0.28
P(V2=1 | X=0) = 0.77
P(V2=1 | X=1) = 0.36
0.77 * (0.28 - 0.56) + 0.36 * (0.54 - 0.76) = -0.25
-0.25 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
17962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 88%. For students who are not encouraged, the probability of brown eyes is 59%. For students who are encouraged, the probability of brown eyes is 46%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.46
0.88*0.46 - 0.12*0.59 = 0.47
0.47 > 0",mediation,encouagement_program,1,marginal,P(Y)
17964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 88%. The probability of discouragement and brown eyes is 7%. The probability of encouragement and brown eyes is 41%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.41
0.41/0.88 - 0.07/0.12 = -0.13
-0.13 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
17968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 57%. For students who are encouraged, the probability of brown eyes is 34%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.34
0.34 - 0.57 = -0.23
-0.23 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 57%. For students who are encouraged, the probability of brown eyes is 34%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.34
0.34 - 0.57 = -0.23
-0.23 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 57%. For students who are encouraged, the probability of brown eyes is 34%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.34
0.34 - 0.57 = -0.23
-0.23 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 89%. For students who are not encouraged and study hard, the probability of brown eyes is 37%. For students who are encouraged and do not study hard, the probability of brown eyes is 50%. For students who are encouraged and study hard, the probability of brown eyes is 7%. For students who are not encouraged, the probability of studying hard is 61%. For students who are encouraged, the probability of studying hard is 36%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.89
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.07
P(V2=1 | X=0) = 0.61
P(V2=1 | X=1) = 0.36
0.36 * (0.37 - 0.89)+ 0.61 * (0.07 - 0.50)= 0.13
0.13 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 85%. The probability of discouragement and brown eyes is 9%. The probability of encouragement and brown eyes is 29%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.29
0.29/0.85 - 0.09/0.15 = -0.23
-0.23 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
17980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
17982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 69%. For students who are encouraged, the probability of brown eyes is 47%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.47
0.47 - 0.69 = -0.22
-0.22 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 69%. For students who are encouraged, the probability of brown eyes is 47%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.47
0.47 - 0.69 = -0.22
-0.22 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 86%. For students who are not encouraged and study hard, the probability of brown eyes is 57%. For students who are encouraged and do not study hard, the probability of brown eyes is 55%. For students who are encouraged and study hard, the probability of brown eyes is 28%. For students who are not encouraged, the probability of studying hard is 61%. For students who are encouraged, the probability of studying hard is 29%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.86
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.28
P(V2=1 | X=0) = 0.61
P(V2=1 | X=1) = 0.29
0.29 * (0.57 - 0.86)+ 0.61 * (0.28 - 0.55)= 0.09
0.09 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
17989,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 86%. For students who are not encouraged and study hard, the probability of brown eyes is 57%. For students who are encouraged and do not study hard, the probability of brown eyes is 55%. For students who are encouraged and study hard, the probability of brown eyes is 28%. For students who are not encouraged, the probability of studying hard is 61%. For students who are encouraged, the probability of studying hard is 29%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.86
P(Y=1 | X=0, V2=1) = 0.57
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.28
P(V2=1 | X=0) = 0.61
P(V2=1 | X=1) = 0.29
0.61 * (0.28 - 0.55) + 0.29 * (0.57 - 0.86) = -0.30
-0.30 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
17990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 85%. For students who are not encouraged, the probability of brown eyes is 69%. For students who are encouraged, the probability of brown eyes is 47%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.47
0.85*0.47 - 0.15*0.69 = 0.50
0.50 > 0",mediation,encouagement_program,1,marginal,P(Y)
17991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 85%. For students who are not encouraged, the probability of brown eyes is 69%. For students who are encouraged, the probability of brown eyes is 47%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.47
0.85*0.47 - 0.15*0.69 = 0.50
0.50 > 0",mediation,encouagement_program,1,marginal,P(Y)
17997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 59%. For students who are encouraged, the probability of brown eyes is 47%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.47
0.47 - 0.59 = -0.11
-0.11 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
17998,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 59%. For students who are encouraged, the probability of brown eyes is 47%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.47
0.47 - 0.59 = -0.11
-0.11 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
17999,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 59%. For students who are encouraged, the probability of brown eyes is 47%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.47
0.47 - 0.59 = -0.11
-0.11 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 84%. For students who are not encouraged and study hard, the probability of brown eyes is 50%. For students who are encouraged and do not study hard, the probability of brown eyes is 53%. For students who are encouraged and study hard, the probability of brown eyes is 23%. For students who are not encouraged, the probability of studying hard is 74%. For students who are encouraged, the probability of studying hard is 19%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.84
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.53
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.74
P(V2=1 | X=1) = 0.19
0.19 * (0.50 - 0.84)+ 0.74 * (0.23 - 0.53)= 0.19
0.19 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 82%. For students who are not encouraged, the probability of brown eyes is 59%. For students who are encouraged, the probability of brown eyes is 47%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.47
0.82*0.47 - 0.18*0.59 = 0.50
0.50 > 0",mediation,encouagement_program,1,marginal,P(Y)
18014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 90%. For students who are not encouraged and study hard, the probability of brown eyes is 54%. For students who are encouraged and do not study hard, the probability of brown eyes is 67%. For students who are encouraged and study hard, the probability of brown eyes is 33%. For students who are not encouraged, the probability of studying hard is 78%. For students who are encouraged, the probability of studying hard is 23%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.67
P(Y=1 | X=1, V2=1) = 0.33
P(V2=1 | X=0) = 0.78
P(V2=1 | X=1) = 0.23
0.23 * (0.54 - 0.90)+ 0.78 * (0.33 - 0.67)= 0.19
0.19 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 90%. For students who are not encouraged and study hard, the probability of brown eyes is 54%. For students who are encouraged and do not study hard, the probability of brown eyes is 67%. For students who are encouraged and study hard, the probability of brown eyes is 33%. For students who are not encouraged, the probability of studying hard is 78%. For students who are encouraged, the probability of studying hard is 23%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.90
P(Y=1 | X=0, V2=1) = 0.54
P(Y=1 | X=1, V2=0) = 0.67
P(Y=1 | X=1, V2=1) = 0.33
P(V2=1 | X=0) = 0.78
P(V2=1 | X=1) = 0.23
0.23 * (0.54 - 0.90)+ 0.78 * (0.33 - 0.67)= 0.19
0.19 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 95%. For students who are not encouraged, the probability of brown eyes is 62%. For students who are encouraged, the probability of brown eyes is 59%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.59
0.95*0.59 - 0.05*0.62 = 0.59
0.59 > 0",mediation,encouagement_program,1,marginal,P(Y)
18019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 95%. For students who are not encouraged, the probability of brown eyes is 62%. For students who are encouraged, the probability of brown eyes is 59%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.59
0.95*0.59 - 0.05*0.62 = 0.59
0.59 > 0",mediation,encouagement_program,1,marginal,P(Y)
18020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 95%. The probability of discouragement and brown eyes is 3%. The probability of encouragement and brown eyes is 56%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.56
0.56/0.95 - 0.03/0.05 = -0.03
-0.03 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 52%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.52
0.52 - 0.72 = -0.20
-0.20 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 52%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.52
0.52 - 0.72 = -0.20
-0.20 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18028,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 91%. For students who are not encouraged and study hard, the probability of brown eyes is 71%. For students who are encouraged and do not study hard, the probability of brown eyes is 66%. For students who are encouraged and study hard, the probability of brown eyes is 42%. For students who are not encouraged, the probability of studying hard is 95%. For students who are encouraged, the probability of studying hard is 61%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.91
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.42
P(V2=1 | X=0) = 0.95
P(V2=1 | X=1) = 0.61
0.61 * (0.71 - 0.91)+ 0.95 * (0.42 - 0.66)= 0.07
0.07 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 91%. For students who are not encouraged and study hard, the probability of brown eyes is 71%. For students who are encouraged and do not study hard, the probability of brown eyes is 66%. For students who are encouraged and study hard, the probability of brown eyes is 42%. For students who are not encouraged, the probability of studying hard is 95%. For students who are encouraged, the probability of studying hard is 61%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.91
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.42
P(V2=1 | X=0) = 0.95
P(V2=1 | X=1) = 0.61
0.61 * (0.71 - 0.91)+ 0.95 * (0.42 - 0.66)= 0.07
0.07 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 91%. For students who are not encouraged and study hard, the probability of brown eyes is 71%. For students who are encouraged and do not study hard, the probability of brown eyes is 66%. For students who are encouraged and study hard, the probability of brown eyes is 42%. For students who are not encouraged, the probability of studying hard is 95%. For students who are encouraged, the probability of studying hard is 61%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.91
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.42
P(V2=1 | X=0) = 0.95
P(V2=1 | X=1) = 0.61
0.95 * (0.42 - 0.66) + 0.61 * (0.71 - 0.91) = -0.29
-0.29 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 91%. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 52%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.52
0.91*0.52 - 0.09*0.72 = 0.53
0.53 > 0",mediation,encouagement_program,1,marginal,P(Y)
18036,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 36%. For students who are encouraged, the probability of brown eyes is 26%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.26
0.26 - 0.36 = -0.10
-0.10 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 74%. For students who are not encouraged and study hard, the probability of brown eyes is 36%. For students who are encouraged and do not study hard, the probability of brown eyes is 43%. For students who are encouraged and study hard, the probability of brown eyes is 9%. For students who are not encouraged, the probability of studying hard is 99%. For students who are encouraged, the probability of studying hard is 50%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.74
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.09
P(V2=1 | X=0) = 0.99
P(V2=1 | X=1) = 0.50
0.50 * (0.36 - 0.74)+ 0.99 * (0.09 - 0.43)= 0.19
0.19 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 50%. For students who are encouraged, the probability of brown eyes is 48%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.48
0.48 - 0.50 = -0.03
-0.03 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 76%. For students who are not encouraged and study hard, the probability of brown eyes is 35%. For students who are encouraged and do not study hard, the probability of brown eyes is 49%. For students who are encouraged and study hard, the probability of brown eyes is 4%. For students who are not encouraged, the probability of studying hard is 62%. For students who are encouraged, the probability of studying hard is 2%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.35
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.04
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.02
0.02 * (0.35 - 0.76)+ 0.62 * (0.04 - 0.49)= 0.24
0.24 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 76%. For students who are not encouraged and study hard, the probability of brown eyes is 35%. For students who are encouraged and do not study hard, the probability of brown eyes is 49%. For students who are encouraged and study hard, the probability of brown eyes is 4%. For students who are not encouraged, the probability of studying hard is 62%. For students who are encouraged, the probability of studying hard is 2%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.76
P(Y=1 | X=0, V2=1) = 0.35
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.04
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.02
0.02 * (0.35 - 0.76)+ 0.62 * (0.04 - 0.49)= 0.24
0.24 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 97%. For students who are not encouraged, the probability of brown eyes is 50%. For students who are encouraged, the probability of brown eyes is 48%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.48
0.97*0.48 - 0.03*0.50 = 0.48
0.48 > 0",mediation,encouagement_program,1,marginal,P(Y)
18065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 60%. For students who are encouraged, the probability of brown eyes is 44%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.44
0.44 - 0.60 = -0.16
-0.16 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 60%. For students who are encouraged, the probability of brown eyes is 44%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.44
0.44 - 0.60 = -0.16
-0.16 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 94%. For students who are not encouraged and study hard, the probability of brown eyes is 74%. For students who are encouraged and do not study hard, the probability of brown eyes is 65%. For students who are encouraged and study hard, the probability of brown eyes is 40%. For students who are not encouraged, the probability of studying hard is 59%. For students who are encouraged, the probability of studying hard is 2%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.74
P(Y=1 | X=1, V2=0) = 0.65
P(Y=1 | X=1, V2=1) = 0.40
P(V2=1 | X=0) = 0.59
P(V2=1 | X=1) = 0.02
0.02 * (0.74 - 0.94)+ 0.59 * (0.40 - 0.65)= 0.12
0.12 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 94%. For students who are not encouraged and study hard, the probability of brown eyes is 74%. For students who are encouraged and do not study hard, the probability of brown eyes is 65%. For students who are encouraged and study hard, the probability of brown eyes is 40%. For students who are not encouraged, the probability of studying hard is 59%. For students who are encouraged, the probability of studying hard is 2%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.74
P(Y=1 | X=1, V2=0) = 0.65
P(Y=1 | X=1, V2=1) = 0.40
P(V2=1 | X=0) = 0.59
P(V2=1 | X=1) = 0.02
0.02 * (0.74 - 0.94)+ 0.59 * (0.40 - 0.65)= 0.12
0.12 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 94%. For students who are not encouraged and study hard, the probability of brown eyes is 74%. For students who are encouraged and do not study hard, the probability of brown eyes is 65%. For students who are encouraged and study hard, the probability of brown eyes is 40%. For students who are not encouraged, the probability of studying hard is 59%. For students who are encouraged, the probability of studying hard is 2%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.74
P(Y=1 | X=1, V2=0) = 0.65
P(Y=1 | X=1, V2=1) = 0.40
P(V2=1 | X=0) = 0.59
P(V2=1 | X=1) = 0.02
0.59 * (0.40 - 0.65) + 0.02 * (0.74 - 0.94) = -0.32
-0.32 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 90%. The probability of discouragement and brown eyes is 8%. The probability of encouragement and brown eyes is 58%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.58
0.58/0.90 - 0.08/0.10 = -0.18
-0.18 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18092,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18094,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 53%. For students who are encouraged, the probability of brown eyes is 31%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.31
0.31 - 0.53 = -0.22
-0.22 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 53%. For students who are encouraged, the probability of brown eyes is 31%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.31
0.31 - 0.53 = -0.22
-0.22 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 53%. For students who are encouraged, the probability of brown eyes is 31%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.31
0.31 - 0.53 = -0.22
-0.22 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 53%. For students who are encouraged, the probability of brown eyes is 31%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.31
0.31 - 0.53 = -0.22
-0.22 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 92%. For students who are not encouraged, the probability of brown eyes is 53%. For students who are encouraged, the probability of brown eyes is 31%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.31
0.92*0.31 - 0.08*0.53 = 0.33
0.33 > 0",mediation,encouagement_program,1,marginal,P(Y)
18106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 78%. For students who are not encouraged and study hard, the probability of brown eyes is 44%. For students who are encouraged and do not study hard, the probability of brown eyes is 54%. For students who are encouraged and study hard, the probability of brown eyes is 22%. For students who are not encouraged, the probability of studying hard is 59%. For students who are encouraged, the probability of studying hard is 33%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.44
P(Y=1 | X=1, V2=0) = 0.54
P(Y=1 | X=1, V2=1) = 0.22
P(V2=1 | X=0) = 0.59
P(V2=1 | X=1) = 0.33
0.59 * (0.22 - 0.54) + 0.33 * (0.44 - 0.78) = -0.22
-0.22 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18117,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 84%. For students who are not encouraged, the probability of brown eyes is 58%. For students who are encouraged, the probability of brown eyes is 44%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.44
0.84*0.44 - 0.16*0.58 = 0.46
0.46 > 0",mediation,encouagement_program,1,marginal,P(Y)
18119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 84%. The probability of discouragement and brown eyes is 10%. The probability of encouragement and brown eyes is 37%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.37
0.37/0.84 - 0.10/0.16 = -0.14
-0.14 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 55%. For students who are encouraged, the probability of brown eyes is 33%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.33
0.33 - 0.55 = -0.22
-0.22 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 71%. For students who are not encouraged and study hard, the probability of brown eyes is 41%. For students who are encouraged and do not study hard, the probability of brown eyes is 35%. For students who are encouraged and study hard, the probability of brown eyes is 10%. For students who are not encouraged, the probability of studying hard is 52%. For students who are encouraged, the probability of studying hard is 5%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.41
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.10
P(V2=1 | X=0) = 0.52
P(V2=1 | X=1) = 0.05
0.05 * (0.41 - 0.71)+ 0.52 * (0.10 - 0.35)= 0.14
0.14 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 71%. For students who are not encouraged and study hard, the probability of brown eyes is 41%. For students who are encouraged and do not study hard, the probability of brown eyes is 35%. For students who are encouraged and study hard, the probability of brown eyes is 10%. For students who are not encouraged, the probability of studying hard is 52%. For students who are encouraged, the probability of studying hard is 5%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.71
P(Y=1 | X=0, V2=1) = 0.41
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.10
P(V2=1 | X=0) = 0.52
P(V2=1 | X=1) = 0.05
0.52 * (0.10 - 0.35) + 0.05 * (0.41 - 0.71) = -0.34
-0.34 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 95%. The probability of discouragement and brown eyes is 3%. The probability of encouragement and brown eyes is 32%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.32
0.32/0.95 - 0.03/0.05 = -0.22
-0.22 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 65%. For students who are encouraged, the probability of brown eyes is 62%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.62
0.62 - 0.65 = -0.03
-0.03 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 98%. For students who are not encouraged, the probability of brown eyes is 65%. For students who are encouraged, the probability of brown eyes is 62%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.62
0.98*0.62 - 0.02*0.65 = 0.62
0.62 > 0",mediation,encouagement_program,1,marginal,P(Y)
18145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 98%. For students who are not encouraged, the probability of brown eyes is 65%. For students who are encouraged, the probability of brown eyes is 62%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.62
0.98*0.62 - 0.02*0.65 = 0.62
0.62 > 0",mediation,encouagement_program,1,marginal,P(Y)
18148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 59%. For students who are encouraged, the probability of brown eyes is 41%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.41
0.41 - 0.59 = -0.18
-0.18 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 80%. For students who are not encouraged and study hard, the probability of brown eyes is 51%. For students who are encouraged and do not study hard, the probability of brown eyes is 47%. For students who are encouraged and study hard, the probability of brown eyes is 20%. For students who are not encouraged, the probability of studying hard is 72%. For students who are encouraged, the probability of studying hard is 22%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.80
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.20
P(V2=1 | X=0) = 0.72
P(V2=1 | X=1) = 0.22
0.72 * (0.20 - 0.47) + 0.22 * (0.51 - 0.80) = -0.32
-0.32 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18157,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 80%. For students who are not encouraged and study hard, the probability of brown eyes is 51%. For students who are encouraged and do not study hard, the probability of brown eyes is 47%. For students who are encouraged and study hard, the probability of brown eyes is 20%. For students who are not encouraged, the probability of studying hard is 72%. For students who are encouraged, the probability of studying hard is 22%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.80
P(Y=1 | X=0, V2=1) = 0.51
P(Y=1 | X=1, V2=0) = 0.47
P(Y=1 | X=1, V2=1) = 0.20
P(V2=1 | X=0) = 0.72
P(V2=1 | X=1) = 0.22
0.72 * (0.20 - 0.47) + 0.22 * (0.51 - 0.80) = -0.32
-0.32 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18163,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 61%. For students who are encouraged, the probability of brown eyes is 31%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.31
0.31 - 0.61 = -0.30
-0.30 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 61%. For students who are encouraged, the probability of brown eyes is 31%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.31
0.31 - 0.61 = -0.30
-0.30 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 68%. For students who are not encouraged and study hard, the probability of brown eyes is 46%. For students who are encouraged and do not study hard, the probability of brown eyes is 33%. For students who are encouraged and study hard, the probability of brown eyes is 2%. For students who are not encouraged, the probability of studying hard is 35%. For students who are encouraged, the probability of studying hard is 6%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.68
P(Y=1 | X=0, V2=1) = 0.46
P(Y=1 | X=1, V2=0) = 0.33
P(Y=1 | X=1, V2=1) = 0.02
P(V2=1 | X=0) = 0.35
P(V2=1 | X=1) = 0.06
0.06 * (0.46 - 0.68)+ 0.35 * (0.02 - 0.33)= 0.06
0.06 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 68%. For students who are not encouraged and study hard, the probability of brown eyes is 46%. For students who are encouraged and do not study hard, the probability of brown eyes is 33%. For students who are encouraged and study hard, the probability of brown eyes is 2%. For students who are not encouraged, the probability of studying hard is 35%. For students who are encouraged, the probability of studying hard is 6%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.68
P(Y=1 | X=0, V2=1) = 0.46
P(Y=1 | X=1, V2=0) = 0.33
P(Y=1 | X=1, V2=1) = 0.02
P(V2=1 | X=0) = 0.35
P(V2=1 | X=1) = 0.06
0.06 * (0.46 - 0.68)+ 0.35 * (0.02 - 0.33)= 0.06
0.06 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 65%. For students who are encouraged, the probability of brown eyes is 48%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.48
0.48 - 0.65 = -0.17
-0.17 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 65%. For students who are encouraged, the probability of brown eyes is 48%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.48
0.48 - 0.65 = -0.17
-0.17 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 65%. For students who are encouraged, the probability of brown eyes is 48%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.48
0.48 - 0.65 = -0.17
-0.17 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 88%. For students who are not encouraged and study hard, the probability of brown eyes is 58%. For students who are encouraged and do not study hard, the probability of brown eyes is 58%. For students who are encouraged and study hard, the probability of brown eyes is 23%. For students who are not encouraged, the probability of studying hard is 77%. For students who are encouraged, the probability of studying hard is 29%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.77
P(V2=1 | X=1) = 0.29
0.29 * (0.58 - 0.88)+ 0.77 * (0.23 - 0.58)= 0.14
0.14 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 88%. For students who are not encouraged and study hard, the probability of brown eyes is 58%. For students who are encouraged and do not study hard, the probability of brown eyes is 58%. For students who are encouraged and study hard, the probability of brown eyes is 23%. For students who are not encouraged, the probability of studying hard is 77%. For students who are encouraged, the probability of studying hard is 29%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.88
P(Y=1 | X=0, V2=1) = 0.58
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.77
P(V2=1 | X=1) = 0.29
0.77 * (0.23 - 0.58) + 0.29 * (0.58 - 0.88) = -0.34
-0.34 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 95%. The probability of discouragement and brown eyes is 3%. The probability of encouragement and brown eyes is 46%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.46
0.46/0.95 - 0.03/0.05 = -0.17
-0.17 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 50%. For students who are encouraged, the probability of brown eyes is 39%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.39
0.39 - 0.50 = -0.10
-0.10 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18197,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 73%. For students who are not encouraged and study hard, the probability of brown eyes is 36%. For students who are encouraged and do not study hard, the probability of brown eyes is 46%. For students who are encouraged and study hard, the probability of brown eyes is 1%. For students who are not encouraged, the probability of studying hard is 62%. For students who are encouraged, the probability of studying hard is 14%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.73
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.01
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.14
0.14 * (0.36 - 0.73)+ 0.62 * (0.01 - 0.46)= 0.18
0.18 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18198,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 73%. For students who are not encouraged and study hard, the probability of brown eyes is 36%. For students who are encouraged and do not study hard, the probability of brown eyes is 46%. For students who are encouraged and study hard, the probability of brown eyes is 1%. For students who are not encouraged, the probability of studying hard is 62%. For students who are encouraged, the probability of studying hard is 14%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.73
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.46
P(Y=1 | X=1, V2=1) = 0.01
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.14
0.62 * (0.01 - 0.46) + 0.14 * (0.36 - 0.73) = -0.32
-0.32 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 98%. For students who are not encouraged, the probability of brown eyes is 50%. For students who are encouraged, the probability of brown eyes is 39%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.39
0.98*0.39 - 0.02*0.50 = 0.40
0.40 > 0",mediation,encouagement_program,1,marginal,P(Y)
18201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 98%. For students who are not encouraged, the probability of brown eyes is 50%. For students who are encouraged, the probability of brown eyes is 39%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.39
0.98*0.39 - 0.02*0.50 = 0.40
0.40 > 0",mediation,encouagement_program,1,marginal,P(Y)
18205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 45%. For students who are encouraged, the probability of brown eyes is 40%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.40
0.40 - 0.45 = -0.05
-0.05 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 45%. For students who are encouraged, the probability of brown eyes is 40%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.40
0.40 - 0.45 = -0.05
-0.05 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 74%. For students who are not encouraged and study hard, the probability of brown eyes is 36%. For students who are encouraged and do not study hard, the probability of brown eyes is 50%. For students who are encouraged and study hard, the probability of brown eyes is 15%. For students who are not encouraged, the probability of studying hard is 76%. For students who are encouraged, the probability of studying hard is 28%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.74
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.15
P(V2=1 | X=0) = 0.76
P(V2=1 | X=1) = 0.28
0.76 * (0.15 - 0.50) + 0.28 * (0.36 - 0.74) = -0.22
-0.22 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 74%. For students who are not encouraged and study hard, the probability of brown eyes is 36%. For students who are encouraged and do not study hard, the probability of brown eyes is 50%. For students who are encouraged and study hard, the probability of brown eyes is 15%. For students who are not encouraged, the probability of studying hard is 76%. For students who are encouraged, the probability of studying hard is 28%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.74
P(Y=1 | X=0, V2=1) = 0.36
P(Y=1 | X=1, V2=0) = 0.50
P(Y=1 | X=1, V2=1) = 0.15
P(V2=1 | X=0) = 0.76
P(V2=1 | X=1) = 0.28
0.76 * (0.15 - 0.50) + 0.28 * (0.36 - 0.74) = -0.22
-0.22 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 60%. For students who are encouraged, the probability of brown eyes is 39%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.39 - 0.60 = -0.21
-0.21 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 60%. For students who are encouraged, the probability of brown eyes is 39%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.39 - 0.60 = -0.21
-0.21 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 80%. For students who are not encouraged and study hard, the probability of brown eyes is 55%. For students who are encouraged and do not study hard, the probability of brown eyes is 48%. For students who are encouraged and study hard, the probability of brown eyes is 25%. For students who are not encouraged, the probability of studying hard is 79%. For students who are encouraged, the probability of studying hard is 40%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.80
P(Y=1 | X=0, V2=1) = 0.55
P(Y=1 | X=1, V2=0) = 0.48
P(Y=1 | X=1, V2=1) = 0.25
P(V2=1 | X=0) = 0.79
P(V2=1 | X=1) = 0.40
0.40 * (0.55 - 0.80)+ 0.79 * (0.25 - 0.48)= 0.09
0.09 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 83%. For students who are not encouraged, the probability of brown eyes is 60%. For students who are encouraged, the probability of brown eyes is 39%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.83*0.39 - 0.17*0.60 = 0.43
0.43 > 0",mediation,encouagement_program,1,marginal,P(Y)
18234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 46%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.46
0.46 - 0.72 = -0.26
-0.26 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 46%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.46
0.46 - 0.72 = -0.26
-0.26 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 46%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.46
0.46 - 0.72 = -0.26
-0.26 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 46%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.46
0.46 - 0.72 = -0.26
-0.26 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 98%. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 46%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.46
0.98*0.46 - 0.02*0.72 = 0.46
0.46 > 0",mediation,encouagement_program,1,marginal,P(Y)
18243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 98%. For students who are not encouraged, the probability of brown eyes is 72%. For students who are encouraged, the probability of brown eyes is 46%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.46
0.98*0.46 - 0.02*0.72 = 0.46
0.46 > 0",mediation,encouagement_program,1,marginal,P(Y)
18246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 61%. For students who are encouraged, the probability of brown eyes is 45%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.45
0.45 - 0.61 = -0.16
-0.16 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 61%. For students who are encouraged, the probability of brown eyes is 45%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.45
0.45 - 0.61 = -0.16
-0.16 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 53%. For students who are encouraged, the probability of brown eyes is 39%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.39
0.39 - 0.53 = -0.14
-0.14 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 83%. For students who are not encouraged and study hard, the probability of brown eyes is 52%. For students who are encouraged and do not study hard, the probability of brown eyes is 45%. For students who are encouraged and study hard, the probability of brown eyes is 21%. For students who are not encouraged, the probability of studying hard is 99%. For students who are encouraged, the probability of studying hard is 28%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.83
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.99
P(V2=1 | X=1) = 0.28
0.28 * (0.52 - 0.83)+ 0.99 * (0.21 - 0.45)= 0.22
0.22 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 83%. For students who are not encouraged and study hard, the probability of brown eyes is 52%. For students who are encouraged and do not study hard, the probability of brown eyes is 45%. For students who are encouraged and study hard, the probability of brown eyes is 21%. For students who are not encouraged, the probability of studying hard is 99%. For students who are encouraged, the probability of studying hard is 28%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.83
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.99
P(V2=1 | X=1) = 0.28
0.99 * (0.21 - 0.45) + 0.28 * (0.52 - 0.83) = -0.32
-0.32 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 83%. For students who are not encouraged and study hard, the probability of brown eyes is 52%. For students who are encouraged and do not study hard, the probability of brown eyes is 45%. For students who are encouraged and study hard, the probability of brown eyes is 21%. For students who are not encouraged, the probability of studying hard is 99%. For students who are encouraged, the probability of studying hard is 28%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.83
P(Y=1 | X=0, V2=1) = 0.52
P(Y=1 | X=1, V2=0) = 0.45
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.99
P(V2=1 | X=1) = 0.28
0.99 * (0.21 - 0.45) + 0.28 * (0.52 - 0.83) = -0.32
-0.32 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 90%. For students who are not encouraged, the probability of brown eyes is 53%. For students who are encouraged, the probability of brown eyes is 39%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.39
0.90*0.39 - 0.10*0.53 = 0.40
0.40 > 0",mediation,encouagement_program,1,marginal,P(Y)
18271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 90%. For students who are not encouraged, the probability of brown eyes is 53%. For students who are encouraged, the probability of brown eyes is 39%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.39
0.90*0.39 - 0.10*0.53 = 0.40
0.40 > 0",mediation,encouagement_program,1,marginal,P(Y)
18273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 90%. The probability of discouragement and brown eyes is 5%. The probability of encouragement and brown eyes is 35%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.35
0.35/0.90 - 0.05/0.10 = -0.14
-0.14 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 54%. For students who are encouraged, the probability of brown eyes is 45%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.45
0.45 - 0.54 = -0.09
-0.09 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 54%. For students who are encouraged, the probability of brown eyes is 45%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.45
0.45 - 0.54 = -0.09
-0.09 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 91%. For students who are not encouraged, the probability of brown eyes is 54%. For students who are encouraged, the probability of brown eyes is 45%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.45
0.91*0.45 - 0.09*0.54 = 0.46
0.46 > 0",mediation,encouagement_program,1,marginal,P(Y)
18286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 91%. The probability of discouragement and brown eyes is 5%. The probability of encouragement and brown eyes is 41%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.41
0.41/0.91 - 0.05/0.09 = -0.09
-0.09 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 75%. For students who are encouraged, the probability of brown eyes is 48%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.48
0.48 - 0.75 = -0.27
-0.27 < 0",mediation,encouagement_program,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 75%. For students who are encouraged, the probability of brown eyes is 48%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.48
0.48 - 0.75 = -0.27
-0.27 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 75%. For students who are encouraged, the probability of brown eyes is 48%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.48
0.48 - 0.75 = -0.27
-0.27 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 98%. For students who are not encouraged and study hard, the probability of brown eyes is 62%. For students who are encouraged and do not study hard, the probability of brown eyes is 57%. For students who are encouraged and study hard, the probability of brown eyes is 29%. For students who are not encouraged, the probability of studying hard is 65%. For students who are encouraged, the probability of studying hard is 33%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.57
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.33
0.33 * (0.62 - 0.98)+ 0.65 * (0.29 - 0.57)= 0.11
0.11 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 98%. For students who are not encouraged and study hard, the probability of brown eyes is 62%. For students who are encouraged and do not study hard, the probability of brown eyes is 57%. For students who are encouraged and study hard, the probability of brown eyes is 29%. For students who are not encouraged, the probability of studying hard is 65%. For students who are encouraged, the probability of studying hard is 33%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.57
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.33
0.65 * (0.29 - 0.57) + 0.33 * (0.62 - 0.98) = -0.36
-0.36 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 98%. For students who are not encouraged and study hard, the probability of brown eyes is 62%. For students who are encouraged and do not study hard, the probability of brown eyes is 57%. For students who are encouraged and study hard, the probability of brown eyes is 29%. For students who are not encouraged, the probability of studying hard is 65%. For students who are encouraged, the probability of studying hard is 33%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.57
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.33
0.65 * (0.29 - 0.57) + 0.33 * (0.62 - 0.98) = -0.36
-0.36 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 98%. For students who are not encouraged, the probability of brown eyes is 75%. For students who are encouraged, the probability of brown eyes is 48%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.48
0.98*0.48 - 0.02*0.75 = 0.48
0.48 > 0",mediation,encouagement_program,1,marginal,P(Y)
18301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 98%. The probability of discouragement and brown eyes is 2%. The probability of encouragement and brown eyes is 46%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.46
0.46/0.98 - 0.02/0.02 = -0.27
-0.27 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18303,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 67%. For students who are encouraged, the probability of brown eyes is 61%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.61
0.61 - 0.67 = -0.06
-0.06 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 67%. For students who are encouraged, the probability of brown eyes is 61%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.61
0.61 - 0.67 = -0.06
-0.06 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 94%. For students who are not encouraged and study hard, the probability of brown eyes is 64%. For students who are encouraged and do not study hard, the probability of brown eyes is 70%. For students who are encouraged and study hard, the probability of brown eyes is 31%. For students who are not encouraged, the probability of studying hard is 91%. For students who are encouraged, the probability of studying hard is 25%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.94
P(Y=1 | X=0, V2=1) = 0.64
P(Y=1 | X=1, V2=0) = 0.70
P(Y=1 | X=1, V2=1) = 0.31
P(V2=1 | X=0) = 0.91
P(V2=1 | X=1) = 0.25
0.91 * (0.31 - 0.70) + 0.25 * (0.64 - 0.94) = -0.32
-0.32 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18315,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 81%. The probability of discouragement and brown eyes is 12%. The probability of encouragement and brown eyes is 49%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.49
0.49/0.81 - 0.12/0.19 = -0.06
-0.06 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 42%. For students who are encouraged, the probability of brown eyes is 25%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.25
0.25 - 0.42 = -0.17
-0.17 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18323,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 72%. For students who are not encouraged and study hard, the probability of brown eyes is 31%. For students who are encouraged and do not study hard, the probability of brown eyes is 30%. For students who are encouraged and study hard, the probability of brown eyes is 3%. For students who are not encouraged, the probability of studying hard is 74%. For students who are encouraged, the probability of studying hard is 21%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.72
P(Y=1 | X=0, V2=1) = 0.31
P(Y=1 | X=1, V2=0) = 0.30
P(Y=1 | X=1, V2=1) = 0.03
P(V2=1 | X=0) = 0.74
P(V2=1 | X=1) = 0.21
0.21 * (0.31 - 0.72)+ 0.74 * (0.03 - 0.30)= 0.22
0.22 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18324,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 72%. For students who are not encouraged and study hard, the probability of brown eyes is 31%. For students who are encouraged and do not study hard, the probability of brown eyes is 30%. For students who are encouraged and study hard, the probability of brown eyes is 3%. For students who are not encouraged, the probability of studying hard is 74%. For students who are encouraged, the probability of studying hard is 21%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.72
P(Y=1 | X=0, V2=1) = 0.31
P(Y=1 | X=1, V2=0) = 0.30
P(Y=1 | X=1, V2=1) = 0.03
P(V2=1 | X=0) = 0.74
P(V2=1 | X=1) = 0.21
0.74 * (0.03 - 0.30) + 0.21 * (0.31 - 0.72) = -0.32
-0.32 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 92%. For students who are not encouraged, the probability of brown eyes is 42%. For students who are encouraged, the probability of brown eyes is 25%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.25
0.92*0.25 - 0.08*0.42 = 0.27
0.27 > 0",mediation,encouagement_program,1,marginal,P(Y)
18328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 92%. The probability of discouragement and brown eyes is 3%. The probability of encouragement and brown eyes is 23%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.23
0.23/0.92 - 0.03/0.08 = -0.17
-0.17 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 92%. The probability of discouragement and brown eyes is 3%. The probability of encouragement and brown eyes is 23%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.23
0.23/0.92 - 0.03/0.08 = -0.17
-0.17 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 95%. For students who are not encouraged and study hard, the probability of brown eyes is 63%. For students who are encouraged and do not study hard, the probability of brown eyes is 59%. For students who are encouraged and study hard, the probability of brown eyes is 29%. For students who are not encouraged, the probability of studying hard is 62%. For students who are encouraged, the probability of studying hard is 11%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.59
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.11
0.11 * (0.63 - 0.95)+ 0.62 * (0.29 - 0.59)= 0.16
0.16 > 0",mediation,encouagement_program,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 95%. For students who are not encouraged and study hard, the probability of brown eyes is 63%. For students who are encouraged and do not study hard, the probability of brown eyes is 59%. For students who are encouraged and study hard, the probability of brown eyes is 29%. For students who are not encouraged, the probability of studying hard is 62%. For students who are encouraged, the probability of studying hard is 11%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.59
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.62
P(V2=1 | X=1) = 0.11
0.62 * (0.29 - 0.59) + 0.11 * (0.63 - 0.95) = -0.35
-0.35 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18340,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 84%. For students who are not encouraged, the probability of brown eyes is 75%. For students who are encouraged, the probability of brown eyes is 55%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.55
0.84*0.55 - 0.16*0.75 = 0.59
0.59 > 0",mediation,encouagement_program,1,marginal,P(Y)
18343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 84%. The probability of discouragement and brown eyes is 12%. The probability of encouragement and brown eyes is 47%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.47
0.47/0.84 - 0.12/0.16 = -0.20
-0.20 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18348,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged, the probability of brown eyes is 82%. For students who are encouraged, the probability of brown eyes is 64%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.64
0.64 - 0.82 = -0.18
-0.18 < 0",mediation,encouagement_program,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 95%. For students who are not encouraged and study hard, the probability of brown eyes is 74%. For students who are encouraged and do not study hard, the probability of brown eyes is 72%. For students who are encouraged and study hard, the probability of brown eyes is 45%. For students who are not encouraged, the probability of studying hard is 60%. For students who are encouraged, the probability of studying hard is 31%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.74
P(Y=1 | X=1, V2=0) = 0.72
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.60
P(V2=1 | X=1) = 0.31
0.60 * (0.45 - 0.72) + 0.31 * (0.74 - 0.95) = -0.27
-0.27 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. For students who are not encouraged and do not study hard, the probability of brown eyes is 95%. For students who are not encouraged and study hard, the probability of brown eyes is 74%. For students who are encouraged and do not study hard, the probability of brown eyes is 72%. For students who are encouraged and study hard, the probability of brown eyes is 45%. For students who are not encouraged, the probability of studying hard is 60%. For students who are encouraged, the probability of studying hard is 31%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.95
P(Y=1 | X=0, V2=1) = 0.74
P(Y=1 | X=1, V2=0) = 0.72
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.60
P(V2=1 | X=1) = 0.31
0.60 * (0.45 - 0.72) + 0.31 * (0.74 - 0.95) = -0.27
-0.27 < 0",mediation,encouagement_program,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 91%. For students who are not encouraged, the probability of brown eyes is 82%. For students who are encouraged, the probability of brown eyes is 64%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.64
0.91*0.64 - 0.09*0.82 = 0.65
0.65 > 0",mediation,encouagement_program,1,marginal,P(Y)
18356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 91%. The probability of discouragement and brown eyes is 7%. The probability of encouragement and brown eyes is 58%.",no,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.58
0.58/0.91 - 0.07/0.09 = -0.18
-0.18 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. The overall probability of encouragement is 91%. The probability of discouragement and brown eyes is 7%. The probability of encouragement and brown eyes is 58%.",yes,"Let X = encouragement level; V2 = studying habit; Y = brown eyes.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.58
0.58/0.91 - 0.07/0.09 = -0.18
-0.18 < 0",mediation,encouagement_program,1,correlation,P(Y | X)
18358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look at how encouragement level correlates with brown eyes case by case according to studying habit. Method 2: We look directly at how encouragement level correlates with brown eyes in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Encouragement level has a direct effect on studying habit and brown eyes. Studying habit has a direct effect on brown eyes. Method 1: We look directly at how encouragement level correlates with brown eyes in general. Method 2: We look at this correlation case by case according to studying habit.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,encouagement_program,2,backadj,[backdoor adjustment set for Y given X]
18360,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 85%. For individuals who are male, the probability of being lactose intolerant is 41%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.41
0.41 - 0.85 = -0.45
-0.45 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 85%. For individuals who are male, the probability of being lactose intolerant is 41%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.41
0.41 - 0.85 = -0.45
-0.45 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 85%. For individuals who are male, the probability of being lactose intolerant is 41%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.41
0.41 - 0.85 = -0.45
-0.45 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 8%. The probability of non-male gender and being lactose intolerant is 78%. The probability of male gender and being lactose intolerant is 3%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.78
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.78/0.92 = -0.45
-0.45 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 51%. For individuals who are male, the probability of being lactose intolerant is 45%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.45
0.45 - 0.51 = -0.06
-0.06 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 51%. For individuals who are male, the probability of being lactose intolerant is 45%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.45
0.45 - 0.51 = -0.06
-0.06 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 51%. For individuals who are male, the probability of being lactose intolerant is 45%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.45
0.45 - 0.51 = -0.06
-0.06 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18378,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 33%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 63%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 42%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are not male, the probability of competitive department is 59%. For individuals who are male, the probability of competitive department is 13%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.33
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.59
P(V2=1 | X=1) = 0.13
0.13 * (0.63 - 0.33)+ 0.59 * (0.65 - 0.42)= -0.14
-0.14 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 33%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 63%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 42%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are not male, the probability of competitive department is 59%. For individuals who are male, the probability of competitive department is 13%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.33
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.42
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.59
P(V2=1 | X=1) = 0.13
0.13 * (0.63 - 0.33)+ 0.59 * (0.65 - 0.42)= -0.14
-0.14 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 13%. For individuals who are not male, the probability of being lactose intolerant is 51%. For individuals who are male, the probability of being lactose intolerant is 45%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.45
0.13*0.45 - 0.87*0.51 = 0.50
0.50 > 0",mediation,gender_admission,1,marginal,P(Y)
18383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 13%. For individuals who are not male, the probability of being lactose intolerant is 51%. For individuals who are male, the probability of being lactose intolerant is 45%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.45
0.13*0.45 - 0.87*0.51 = 0.50
0.50 > 0",mediation,gender_admission,1,marginal,P(Y)
18385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 13%. The probability of non-male gender and being lactose intolerant is 44%. The probability of male gender and being lactose intolerant is 6%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.06
0.06/0.13 - 0.44/0.87 = -0.06
-0.06 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 90%. For individuals who are male, the probability of being lactose intolerant is 44%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.44
0.44 - 0.90 = -0.46
-0.46 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18390,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 90%. For individuals who are male, the probability of being lactose intolerant is 44%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.44
0.44 - 0.90 = -0.46
-0.46 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 90%. For individuals who are male, the probability of being lactose intolerant is 44%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.44
0.44 - 0.90 = -0.46
-0.46 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 53%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 97%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 31%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 68%. For individuals who are not male, the probability of competitive department is 86%. For individuals who are male, the probability of competitive department is 35%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.97
P(Y=1 | X=1, V2=0) = 0.31
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.86
P(V2=1 | X=1) = 0.35
0.35 * (0.97 - 0.53)+ 0.86 * (0.68 - 0.31)= -0.22
-0.22 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 53%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 97%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 31%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 68%. For individuals who are not male, the probability of competitive department is 86%. For individuals who are male, the probability of competitive department is 35%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.97
P(Y=1 | X=1, V2=0) = 0.31
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.86
P(V2=1 | X=1) = 0.35
0.86 * (0.68 - 0.31) + 0.35 * (0.97 - 0.53) = -0.28
-0.28 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 15%. The probability of non-male gender and being lactose intolerant is 77%. The probability of male gender and being lactose intolerant is 6%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.77
P(Y=1, X=1=1) = 0.06
0.06/0.15 - 0.77/0.85 = -0.46
-0.46 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 55%. For individuals who are male, the probability of being lactose intolerant is 50%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.50
0.50 - 0.55 = -0.05
-0.05 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 55%. For individuals who are male, the probability of being lactose intolerant is 50%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.50
0.50 - 0.55 = -0.05
-0.05 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 30%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 35%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 70%. For individuals who are male, the probability of competitive department is 47%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.30
P(Y=1 | X=0, V2=1) = 0.65
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.47
0.47 * (0.65 - 0.30)+ 0.70 * (0.67 - 0.35)= -0.08
-0.08 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18408,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 30%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 35%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 70%. For individuals who are male, the probability of competitive department is 47%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.30
P(Y=1 | X=0, V2=1) = 0.65
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.47
0.70 * (0.67 - 0.35) + 0.47 * (0.65 - 0.30) = 0.02
0.02 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 30%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 35%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 70%. For individuals who are male, the probability of competitive department is 47%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.30
P(Y=1 | X=0, V2=1) = 0.65
P(Y=1 | X=1, V2=0) = 0.35
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.47
0.70 * (0.67 - 0.35) + 0.47 * (0.65 - 0.30) = 0.02
0.02 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 3%. For individuals who are not male, the probability of being lactose intolerant is 55%. For individuals who are male, the probability of being lactose intolerant is 50%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.50
0.03*0.50 - 0.97*0.55 = 0.55
0.55 > 0",mediation,gender_admission,1,marginal,P(Y)
18414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 67%. For individuals who are male, the probability of being lactose intolerant is 22%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.22
0.22 - 0.67 = -0.46
-0.46 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 52%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 80%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 19%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 46%. For individuals who are not male, the probability of competitive department is 54%. For individuals who are male, the probability of competitive department is 10%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.52
P(Y=1 | X=0, V2=1) = 0.80
P(Y=1 | X=1, V2=0) = 0.19
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.10
0.10 * (0.80 - 0.52)+ 0.54 * (0.46 - 0.19)= -0.12
-0.12 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 3%. The probability of non-male gender and being lactose intolerant is 66%. The probability of male gender and being lactose intolerant is 1%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.66/0.97 = -0.46
-0.46 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 3%. The probability of non-male gender and being lactose intolerant is 66%. The probability of male gender and being lactose intolerant is 1%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.66/0.97 = -0.46
-0.46 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 37%. For individuals who are male, the probability of being lactose intolerant is 18%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.18
0.18 - 0.37 = -0.20
-0.20 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 37%. For individuals who are male, the probability of being lactose intolerant is 18%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.18
0.18 - 0.37 = -0.20
-0.20 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 37%. For individuals who are male, the probability of being lactose intolerant is 18%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.18
0.18 - 0.37 = -0.20
-0.20 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 11%. For individuals who are not male, the probability of being lactose intolerant is 37%. For individuals who are male, the probability of being lactose intolerant is 18%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.18
0.11*0.18 - 0.89*0.37 = 0.36
0.36 > 0",mediation,gender_admission,1,marginal,P(Y)
18450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 43%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 83%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 18%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 53%. For individuals who are not male, the probability of competitive department is 88%. For individuals who are male, the probability of competitive department is 30%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.83
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.53
P(V2=1 | X=0) = 0.88
P(V2=1 | X=1) = 0.30
0.88 * (0.53 - 0.18) + 0.30 * (0.83 - 0.43) = -0.30
-0.30 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 43%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 83%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 18%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 53%. For individuals who are not male, the probability of competitive department is 88%. For individuals who are male, the probability of competitive department is 30%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.83
P(Y=1 | X=1, V2=0) = 0.18
P(Y=1 | X=1, V2=1) = 0.53
P(V2=1 | X=0) = 0.88
P(V2=1 | X=1) = 0.30
0.88 * (0.53 - 0.18) + 0.30 * (0.83 - 0.43) = -0.30
-0.30 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 15%. The probability of non-male gender and being lactose intolerant is 67%. The probability of male gender and being lactose intolerant is 4%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.67
P(Y=1, X=1=1) = 0.04
0.04/0.15 - 0.67/0.85 = -0.50
-0.50 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 59%. For individuals who are male, the probability of being lactose intolerant is 44%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.44
0.44 - 0.59 = -0.15
-0.15 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 42%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 73%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 44%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are not male, the probability of competitive department is 55%. For individuals who are male, the probability of competitive department is 1%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.42
P(Y=1 | X=0, V2=1) = 0.73
P(Y=1 | X=1, V2=0) = 0.44
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.55
P(V2=1 | X=1) = 0.01
0.01 * (0.73 - 0.42)+ 0.55 * (0.65 - 0.44)= -0.17
-0.17 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 78%. For individuals who are male, the probability of being lactose intolerant is 42%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.42
0.42 - 0.78 = -0.37
-0.37 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 58%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 89%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 32%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are not male, the probability of competitive department is 65%. For individuals who are male, the probability of competitive department is 29%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.58
P(Y=1 | X=0, V2=1) = 0.89
P(Y=1 | X=1, V2=0) = 0.32
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.29
0.29 * (0.89 - 0.58)+ 0.65 * (0.65 - 0.32)= -0.11
-0.11 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 58%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 89%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 32%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are not male, the probability of competitive department is 65%. For individuals who are male, the probability of competitive department is 29%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.58
P(Y=1 | X=0, V2=1) = 0.89
P(Y=1 | X=1, V2=0) = 0.32
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.29
0.29 * (0.89 - 0.58)+ 0.65 * (0.65 - 0.32)= -0.11
-0.11 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 58%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 89%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 32%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are not male, the probability of competitive department is 65%. For individuals who are male, the probability of competitive department is 29%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.58
P(Y=1 | X=0, V2=1) = 0.89
P(Y=1 | X=1, V2=0) = 0.32
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.29
0.65 * (0.65 - 0.32) + 0.29 * (0.89 - 0.58) = -0.25
-0.25 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 1%. For individuals who are not male, the probability of being lactose intolerant is 78%. For individuals who are male, the probability of being lactose intolerant is 42%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.42
0.01*0.42 - 0.99*0.78 = 0.78
0.78 > 0",mediation,gender_admission,1,marginal,P(Y)
18482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 1%. The probability of non-male gender and being lactose intolerant is 77%. The probability of male gender and being lactose intolerant is 1%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.77
P(Y=1, X=1=1) = 0.01
0.01/0.01 - 0.77/0.99 = -0.37
-0.37 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18485,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 17%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 81%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 37%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 63%. For individuals who are not male, the probability of competitive department is 70%. For individuals who are male, the probability of competitive department is 9%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.17
P(Y=1 | X=0, V2=1) = 0.81
P(Y=1 | X=1, V2=0) = 0.37
P(Y=1 | X=1, V2=1) = 0.63
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.09
0.09 * (0.81 - 0.17)+ 0.70 * (0.63 - 0.37)= -0.39
-0.39 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 16%. For individuals who are not male, the probability of being lactose intolerant is 62%. For individuals who are male, the probability of being lactose intolerant is 39%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.39
0.16*0.39 - 0.84*0.62 = 0.55
0.55 > 0",mediation,gender_admission,1,marginal,P(Y)
18495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 16%. For individuals who are not male, the probability of being lactose intolerant is 62%. For individuals who are male, the probability of being lactose intolerant is 39%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.39
0.16*0.39 - 0.84*0.62 = 0.55
0.55 > 0",mediation,gender_admission,1,marginal,P(Y)
18496,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 16%. The probability of non-male gender and being lactose intolerant is 52%. The probability of male gender and being lactose intolerant is 6%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.06
0.06/0.16 - 0.52/0.84 = -0.23
-0.23 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 94%. For individuals who are male, the probability of being lactose intolerant is 51%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.51
0.51 - 0.94 = -0.43
-0.43 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 78%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 100%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 41%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 75%. For individuals who are male, the probability of competitive department is 37%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 1.00
P(Y=1 | X=1, V2=0) = 0.41
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.37
0.75 * (0.67 - 0.41) + 0.37 * (1.00 - 0.78) = -0.34
-0.34 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 15%. For individuals who are not male, the probability of being lactose intolerant is 94%. For individuals who are male, the probability of being lactose intolerant is 51%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.94
P(Y=1 | X=1) = 0.51
0.15*0.51 - 0.85*0.94 = 0.88
0.88 > 0",mediation,gender_admission,1,marginal,P(Y)
18510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 15%. The probability of non-male gender and being lactose intolerant is 80%. The probability of male gender and being lactose intolerant is 8%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.80
P(Y=1, X=1=1) = 0.08
0.08/0.15 - 0.80/0.85 = -0.43
-0.43 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18512,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 51%. For individuals who are male, the probability of being lactose intolerant is 33%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.33
0.33 - 0.51 = -0.18
-0.18 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 51%. For individuals who are male, the probability of being lactose intolerant is 33%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.33
0.33 - 0.51 = -0.18
-0.18 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 6%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 70%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 23%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 52%. For individuals who are not male, the probability of competitive department is 71%. For individuals who are male, the probability of competitive department is 35%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.70
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.35
0.35 * (0.70 - 0.06)+ 0.71 * (0.52 - 0.23)= -0.23
-0.23 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 6%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 70%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 23%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 52%. For individuals who are not male, the probability of competitive department is 71%. For individuals who are male, the probability of competitive department is 35%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.70
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.35
0.35 * (0.70 - 0.06)+ 0.71 * (0.52 - 0.23)= -0.23
-0.23 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 6%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 70%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 23%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 52%. For individuals who are not male, the probability of competitive department is 71%. For individuals who are male, the probability of competitive department is 35%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.06
P(Y=1 | X=0, V2=1) = 0.70
P(Y=1 | X=1, V2=0) = 0.23
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.71
P(V2=1 | X=1) = 0.35
0.71 * (0.52 - 0.23) + 0.35 * (0.70 - 0.06) = -0.08
-0.08 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 8%. For individuals who are not male, the probability of being lactose intolerant is 51%. For individuals who are male, the probability of being lactose intolerant is 33%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.33
0.08*0.33 - 0.92*0.51 = 0.49
0.49 > 0",mediation,gender_admission,1,marginal,P(Y)
18524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 8%. The probability of non-male gender and being lactose intolerant is 47%. The probability of male gender and being lactose intolerant is 3%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.47/0.92 = -0.18
-0.18 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 8%. The probability of non-male gender and being lactose intolerant is 47%. The probability of male gender and being lactose intolerant is 3%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.47
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.47/0.92 = -0.18
-0.18 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 60%. For individuals who are male, the probability of being lactose intolerant is 24%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.24
0.24 - 0.60 = -0.37
-0.37 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 35%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 15%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 41%. For individuals who are not male, the probability of competitive department is 80%. For individuals who are male, the probability of competitive department is 34%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.35
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.15
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.80
P(V2=1 | X=1) = 0.34
0.80 * (0.41 - 0.15) + 0.34 * (0.67 - 0.35) = -0.25
-0.25 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18535,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 35%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 15%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 41%. For individuals who are not male, the probability of competitive department is 80%. For individuals who are male, the probability of competitive department is 34%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.35
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.15
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.80
P(V2=1 | X=1) = 0.34
0.80 * (0.41 - 0.15) + 0.34 * (0.67 - 0.35) = -0.25
-0.25 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18539,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 9%. The probability of non-male gender and being lactose intolerant is 55%. The probability of male gender and being lactose intolerant is 2%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.55
P(Y=1, X=1=1) = 0.02
0.02/0.09 - 0.55/0.91 = -0.37
-0.37 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18542,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 53%. For individuals who are male, the probability of being lactose intolerant is 41%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.41
0.41 - 0.53 = -0.12
-0.12 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 53%. For individuals who are male, the probability of being lactose intolerant is 41%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.41
0.41 - 0.53 = -0.12
-0.12 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 53%. For individuals who are male, the probability of being lactose intolerant is 41%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.41
0.41 - 0.53 = -0.12
-0.12 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 26%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 38%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 63%. For individuals who are not male, the probability of competitive department is 65%. For individuals who are male, the probability of competitive department is 11%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.38
P(Y=1 | X=1, V2=1) = 0.63
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.11
0.11 * (0.67 - 0.26)+ 0.65 * (0.63 - 0.38)= -0.22
-0.22 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 26%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 38%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 63%. For individuals who are not male, the probability of competitive department is 65%. For individuals who are male, the probability of competitive department is 11%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.26
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.38
P(Y=1 | X=1, V2=1) = 0.63
P(V2=1 | X=0) = 0.65
P(V2=1 | X=1) = 0.11
0.65 * (0.63 - 0.38) + 0.11 * (0.67 - 0.26) = 0.02
0.02 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 14%. For individuals who are not male, the probability of being lactose intolerant is 53%. For individuals who are male, the probability of being lactose intolerant is 41%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.41
0.14*0.41 - 0.86*0.53 = 0.50
0.50 > 0",mediation,gender_admission,1,marginal,P(Y)
18560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 63%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 95%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 37%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 94%. For individuals who are male, the probability of competitive department is 48%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.95
P(Y=1 | X=1, V2=0) = 0.37
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.94
P(V2=1 | X=1) = 0.48
0.48 * (0.95 - 0.63)+ 0.94 * (0.67 - 0.37)= -0.15
-0.15 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 63%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 95%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 37%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 94%. For individuals who are male, the probability of competitive department is 48%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.95
P(Y=1 | X=1, V2=0) = 0.37
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.94
P(V2=1 | X=1) = 0.48
0.48 * (0.95 - 0.63)+ 0.94 * (0.67 - 0.37)= -0.15
-0.15 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 63%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 95%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 37%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 94%. For individuals who are male, the probability of competitive department is 48%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.63
P(Y=1 | X=0, V2=1) = 0.95
P(Y=1 | X=1, V2=0) = 0.37
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.94
P(V2=1 | X=1) = 0.48
0.94 * (0.67 - 0.37) + 0.48 * (0.95 - 0.63) = -0.28
-0.28 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 7%. The probability of non-male gender and being lactose intolerant is 86%. The probability of male gender and being lactose intolerant is 4%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.86
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.86/0.93 = -0.42
-0.42 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 7%. The probability of non-male gender and being lactose intolerant is 86%. The probability of male gender and being lactose intolerant is 4%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.86
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.86/0.93 = -0.42
-0.42 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 62%. For individuals who are male, the probability of being lactose intolerant is 30%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.30
0.30 - 0.62 = -0.32
-0.32 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 10%. For individuals who are not male, the probability of being lactose intolerant is 62%. For individuals who are male, the probability of being lactose intolerant is 30%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.30
0.10*0.30 - 0.90*0.62 = 0.57
0.57 > 0",mediation,gender_admission,1,marginal,P(Y)
18582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 68%. For individuals who are male, the probability of being lactose intolerant is 22%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.22
0.22 - 0.68 = -0.47
-0.47 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 68%. For individuals who are male, the probability of being lactose intolerant is 22%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.22
0.22 - 0.68 = -0.47
-0.47 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 68%. For individuals who are male, the probability of being lactose intolerant is 22%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.22
0.22 - 0.68 = -0.47
-0.47 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 37%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 68%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 7%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 33%. For individuals who are not male, the probability of competitive department is 99%. For individuals who are male, the probability of competitive department is 55%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.37
P(Y=1 | X=0, V2=1) = 0.68
P(Y=1 | X=1, V2=0) = 0.07
P(Y=1 | X=1, V2=1) = 0.33
P(V2=1 | X=0) = 0.99
P(V2=1 | X=1) = 0.55
0.55 * (0.68 - 0.37)+ 0.99 * (0.33 - 0.07)= -0.14
-0.14 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 1%. For individuals who are not male, the probability of being lactose intolerant is 68%. For individuals who are male, the probability of being lactose intolerant is 22%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.22
0.01*0.22 - 0.99*0.68 = 0.68
0.68 > 0",mediation,gender_admission,1,marginal,P(Y)
18596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18597,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 40%. For individuals who are male, the probability of being lactose intolerant is 31%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.31
0.31 - 0.40 = -0.09
-0.09 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 40%. For individuals who are male, the probability of being lactose intolerant is 31%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.31
0.31 - 0.40 = -0.09
-0.09 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 40%. For individuals who are male, the probability of being lactose intolerant is 31%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.31
0.31 - 0.40 = -0.09
-0.09 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18605,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 18%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 63%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 28%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 68%. For individuals who are not male, the probability of competitive department is 49%. For individuals who are male, the probability of competitive department is 7%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.18
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.28
P(Y=1 | X=1, V2=1) = 0.68
P(V2=1 | X=0) = 0.49
P(V2=1 | X=1) = 0.07
0.49 * (0.68 - 0.28) + 0.07 * (0.63 - 0.18) = 0.07
0.07 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 17%. For individuals who are not male, the probability of being lactose intolerant is 40%. For individuals who are male, the probability of being lactose intolerant is 31%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.31
0.17*0.31 - 0.83*0.40 = 0.38
0.38 > 0",mediation,gender_admission,1,marginal,P(Y)
18609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 17%. The probability of non-male gender and being lactose intolerant is 33%. The probability of male gender and being lactose intolerant is 5%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.05
0.05/0.17 - 0.33/0.83 = -0.09
-0.09 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 74%. For individuals who are male, the probability of being lactose intolerant is 34%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.34
0.34 - 0.74 = -0.40
-0.40 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18614,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 74%. For individuals who are male, the probability of being lactose intolerant is 34%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.34
0.34 - 0.74 = -0.40
-0.40 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 59%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 88%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 28%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 57%. For individuals who are not male, the probability of competitive department is 52%. For individuals who are male, the probability of competitive department is 22%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.88
P(Y=1 | X=1, V2=0) = 0.28
P(Y=1 | X=1, V2=1) = 0.57
P(V2=1 | X=0) = 0.52
P(V2=1 | X=1) = 0.22
0.52 * (0.57 - 0.28) + 0.22 * (0.88 - 0.59) = -0.31
-0.31 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18620,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 12%. For individuals who are not male, the probability of being lactose intolerant is 74%. For individuals who are male, the probability of being lactose intolerant is 34%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.34
0.12*0.34 - 0.88*0.74 = 0.69
0.69 > 0",mediation,gender_admission,1,marginal,P(Y)
18622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 12%. The probability of non-male gender and being lactose intolerant is 65%. The probability of male gender and being lactose intolerant is 4%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.65
P(Y=1, X=1=1) = 0.04
0.04/0.12 - 0.65/0.88 = -0.40
-0.40 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 68%. For individuals who are male, the probability of being lactose intolerant is 59%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.59
0.59 - 0.68 = -0.09
-0.09 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18630,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 47%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 71%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 40%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 69%. For individuals who are not male, the probability of competitive department is 88%. For individuals who are male, the probability of competitive department is 66%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.40
P(Y=1 | X=1, V2=1) = 0.69
P(V2=1 | X=0) = 0.88
P(V2=1 | X=1) = 0.66
0.66 * (0.71 - 0.47)+ 0.88 * (0.69 - 0.40)= -0.05
-0.05 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 47%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 71%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 40%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 69%. For individuals who are not male, the probability of competitive department is 88%. For individuals who are male, the probability of competitive department is 66%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.40
P(Y=1 | X=1, V2=1) = 0.69
P(V2=1 | X=0) = 0.88
P(V2=1 | X=1) = 0.66
0.66 * (0.71 - 0.47)+ 0.88 * (0.69 - 0.40)= -0.05
-0.05 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 47%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 71%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 40%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 69%. For individuals who are not male, the probability of competitive department is 88%. For individuals who are male, the probability of competitive department is 66%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.40
P(Y=1 | X=1, V2=1) = 0.69
P(V2=1 | X=0) = 0.88
P(V2=1 | X=1) = 0.66
0.88 * (0.69 - 0.40) + 0.66 * (0.71 - 0.47) = -0.03
-0.03 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18633,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 47%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 71%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 40%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 69%. For individuals who are not male, the probability of competitive department is 88%. For individuals who are male, the probability of competitive department is 66%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.71
P(Y=1 | X=1, V2=0) = 0.40
P(Y=1 | X=1, V2=1) = 0.69
P(V2=1 | X=0) = 0.88
P(V2=1 | X=1) = 0.66
0.88 * (0.69 - 0.40) + 0.66 * (0.71 - 0.47) = -0.03
-0.03 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 8%. For individuals who are not male, the probability of being lactose intolerant is 68%. For individuals who are male, the probability of being lactose intolerant is 59%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.59
0.08*0.59 - 0.92*0.68 = 0.67
0.67 > 0",mediation,gender_admission,1,marginal,P(Y)
18635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 8%. For individuals who are not male, the probability of being lactose intolerant is 68%. For individuals who are male, the probability of being lactose intolerant is 59%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.59
0.08*0.59 - 0.92*0.68 = 0.67
0.67 > 0",mediation,gender_admission,1,marginal,P(Y)
18642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 88%. For individuals who are male, the probability of being lactose intolerant is 13%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.13
0.13 - 0.88 = -0.76
-0.76 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 43%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 90%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 12%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 38%. For individuals who are not male, the probability of competitive department is 96%. For individuals who are male, the probability of competitive department is 3%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.90
P(Y=1 | X=1, V2=0) = 0.12
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.96
P(V2=1 | X=1) = 0.03
0.03 * (0.90 - 0.43)+ 0.96 * (0.38 - 0.12)= -0.44
-0.44 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 43%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 90%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 12%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 38%. For individuals who are not male, the probability of competitive department is 96%. For individuals who are male, the probability of competitive department is 3%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.43
P(Y=1 | X=0, V2=1) = 0.90
P(Y=1 | X=1, V2=0) = 0.12
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.96
P(V2=1 | X=1) = 0.03
0.03 * (0.90 - 0.43)+ 0.96 * (0.38 - 0.12)= -0.44
-0.44 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 11%. For individuals who are not male, the probability of being lactose intolerant is 88%. For individuals who are male, the probability of being lactose intolerant is 13%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.13
0.11*0.13 - 0.89*0.88 = 0.78
0.78 > 0",mediation,gender_admission,1,marginal,P(Y)
18649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 11%. For individuals who are not male, the probability of being lactose intolerant is 88%. For individuals who are male, the probability of being lactose intolerant is 13%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.13
0.11*0.13 - 0.89*0.88 = 0.78
0.78 > 0",mediation,gender_admission,1,marginal,P(Y)
18650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 11%. The probability of non-male gender and being lactose intolerant is 78%. The probability of male gender and being lactose intolerant is 1%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.78
P(Y=1, X=1=1) = 0.01
0.01/0.11 - 0.78/0.89 = -0.76
-0.76 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18652,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 52%. For individuals who are male, the probability of being lactose intolerant is 51%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.51
0.51 - 0.52 = -0.01
-0.01 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 28%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 43%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 65%. For individuals who are not male, the probability of competitive department is 60%. For individuals who are male, the probability of competitive department is 37%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.28
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.43
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.60
P(V2=1 | X=1) = 0.37
0.60 * (0.65 - 0.43) + 0.37 * (0.67 - 0.28) = 0.04
0.04 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 19%. For individuals who are not male, the probability of being lactose intolerant is 52%. For individuals who are male, the probability of being lactose intolerant is 51%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.51
0.19*0.51 - 0.81*0.52 = 0.51
0.51 > 0",mediation,gender_admission,1,marginal,P(Y)
18667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 60%. For individuals who are male, the probability of being lactose intolerant is 7%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.07
0.07 - 0.60 = -0.53
-0.53 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 16%. The probability of non-male gender and being lactose intolerant is 51%. The probability of male gender and being lactose intolerant is 1%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.51
P(Y=1, X=1=1) = 0.01
0.01/0.16 - 0.51/0.84 = -0.53
-0.53 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 16%. The probability of non-male gender and being lactose intolerant is 51%. The probability of male gender and being lactose intolerant is 1%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.51
P(Y=1, X=1=1) = 0.01
0.01/0.16 - 0.51/0.84 = -0.53
-0.53 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 42%. For individuals who are male, the probability of being lactose intolerant is 29%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.29
0.29 - 0.42 = -0.12
-0.12 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18687,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 25%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 60%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 21%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 72%. For individuals who are not male, the probability of competitive department is 48%. For individuals who are male, the probability of competitive department is 17%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.25
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.21
P(Y=1 | X=1, V2=1) = 0.72
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.17
0.17 * (0.60 - 0.25)+ 0.48 * (0.72 - 0.21)= -0.11
-0.11 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 25%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 60%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 21%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 72%. For individuals who are not male, the probability of competitive department is 48%. For individuals who are male, the probability of competitive department is 17%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.25
P(Y=1 | X=0, V2=1) = 0.60
P(Y=1 | X=1, V2=0) = 0.21
P(Y=1 | X=1, V2=1) = 0.72
P(V2=1 | X=0) = 0.48
P(V2=1 | X=1) = 0.17
0.48 * (0.72 - 0.21) + 0.17 * (0.60 - 0.25) = 0.04
0.04 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 3%. For individuals who are not male, the probability of being lactose intolerant is 42%. For individuals who are male, the probability of being lactose intolerant is 29%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.29
0.03*0.29 - 0.97*0.42 = 0.41
0.41 > 0",mediation,gender_admission,1,marginal,P(Y)
18692,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 3%. The probability of non-male gender and being lactose intolerant is 40%. The probability of male gender and being lactose intolerant is 1%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.40/0.97 = -0.12
-0.12 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 74%. For individuals who are male, the probability of being lactose intolerant is 21%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.21
0.21 - 0.74 = -0.53
-0.53 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 74%. For individuals who are male, the probability of being lactose intolerant is 21%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.21
0.21 - 0.74 = -0.53
-0.53 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 15%. For individuals who are not male, the probability of being lactose intolerant is 74%. For individuals who are male, the probability of being lactose intolerant is 21%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.21
0.15*0.21 - 0.85*0.74 = 0.66
0.66 > 0",mediation,gender_admission,1,marginal,P(Y)
18705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 15%. For individuals who are not male, the probability of being lactose intolerant is 74%. For individuals who are male, the probability of being lactose intolerant is 21%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.21
0.15*0.21 - 0.85*0.74 = 0.66
0.66 > 0",mediation,gender_admission,1,marginal,P(Y)
18709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18713,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 57%. For individuals who are male, the probability of being lactose intolerant is 14%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.14
0.14 - 0.57 = -0.42
-0.42 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 17%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 70%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 8%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 51%. For individuals who are not male, the probability of competitive department is 75%. For individuals who are male, the probability of competitive department is 14%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.17
P(Y=1 | X=0, V2=1) = 0.70
P(Y=1 | X=1, V2=0) = 0.08
P(Y=1 | X=1, V2=1) = 0.51
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.14
0.14 * (0.70 - 0.17)+ 0.75 * (0.51 - 0.08)= -0.33
-0.33 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18716,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 17%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 70%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 8%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 51%. For individuals who are not male, the probability of competitive department is 75%. For individuals who are male, the probability of competitive department is 14%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.17
P(Y=1 | X=0, V2=1) = 0.70
P(Y=1 | X=1, V2=0) = 0.08
P(Y=1 | X=1, V2=1) = 0.51
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.14
0.75 * (0.51 - 0.08) + 0.14 * (0.70 - 0.17) = -0.16
-0.16 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 17%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 70%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 8%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 51%. For individuals who are not male, the probability of competitive department is 75%. For individuals who are male, the probability of competitive department is 14%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.17
P(Y=1 | X=0, V2=1) = 0.70
P(Y=1 | X=1, V2=0) = 0.08
P(Y=1 | X=1, V2=1) = 0.51
P(V2=1 | X=0) = 0.75
P(V2=1 | X=1) = 0.14
0.75 * (0.51 - 0.08) + 0.14 * (0.70 - 0.17) = -0.16
-0.16 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 6%. The probability of non-male gender and being lactose intolerant is 53%. The probability of male gender and being lactose intolerant is 1%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.01
0.01/0.06 - 0.53/0.94 = -0.42
-0.42 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18721,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 6%. The probability of non-male gender and being lactose intolerant is 53%. The probability of male gender and being lactose intolerant is 1%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.01
0.01/0.06 - 0.53/0.94 = -0.42
-0.42 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 72%. For individuals who are male, the probability of being lactose intolerant is 28%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.28
0.28 - 0.72 = -0.45
-0.45 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 47%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 89%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 6%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 63%. For individuals who are not male, the probability of competitive department is 61%. For individuals who are male, the probability of competitive department is 38%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.89
P(Y=1 | X=1, V2=0) = 0.06
P(Y=1 | X=1, V2=1) = 0.63
P(V2=1 | X=0) = 0.61
P(V2=1 | X=1) = 0.38
0.61 * (0.63 - 0.06) + 0.38 * (0.89 - 0.47) = -0.31
-0.31 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 58%. For individuals who are male, the probability of being lactose intolerant is 45%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.45
0.45 - 0.58 = -0.13
-0.13 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 58%. For individuals who are male, the probability of being lactose intolerant is 45%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.45
0.45 - 0.58 = -0.13
-0.13 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18744,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 35%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 38%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 71%. For individuals who are not male, the probability of competitive department is 74%. For individuals who are male, the probability of competitive department is 20%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.35
P(Y=1 | X=0, V2=1) = 0.67
P(Y=1 | X=1, V2=0) = 0.38
P(Y=1 | X=1, V2=1) = 0.71
P(V2=1 | X=0) = 0.74
P(V2=1 | X=1) = 0.20
0.74 * (0.71 - 0.38) + 0.20 * (0.67 - 0.35) = 0.04
0.04 > 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18752,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 81%. For individuals who are male, the probability of being lactose intolerant is 42%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.42
0.42 - 0.81 = -0.40
-0.40 < 0",mediation,gender_admission,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 81%. For individuals who are male, the probability of being lactose intolerant is 42%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.42
0.42 - 0.81 = -0.40
-0.40 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 81%. For individuals who are male, the probability of being lactose intolerant is 42%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.42
0.42 - 0.81 = -0.40
-0.40 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 54%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 93%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 33%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 70%. For individuals who are male, the probability of competitive department is 25%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.54
P(Y=1 | X=0, V2=1) = 0.93
P(Y=1 | X=1, V2=0) = 0.33
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.25
0.25 * (0.93 - 0.54)+ 0.70 * (0.67 - 0.33)= -0.17
-0.17 < 0",mediation,gender_admission,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
18759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 54%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 93%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 33%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 67%. For individuals who are not male, the probability of competitive department is 70%. For individuals who are male, the probability of competitive department is 25%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.54
P(Y=1 | X=0, V2=1) = 0.93
P(Y=1 | X=1, V2=0) = 0.33
P(Y=1 | X=1, V2=1) = 0.67
P(V2=1 | X=0) = 0.70
P(V2=1 | X=1) = 0.25
0.70 * (0.67 - 0.33) + 0.25 * (0.93 - 0.54) = -0.24
-0.24 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 1%. For individuals who are not male, the probability of being lactose intolerant is 81%. For individuals who are male, the probability of being lactose intolerant is 42%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.42
0.01*0.42 - 0.99*0.81 = 0.81
0.81 > 0",mediation,gender_admission,1,marginal,P(Y)
18762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 1%. The probability of non-male gender and being lactose intolerant is 80%. The probability of male gender and being lactose intolerant is 1%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.80
P(Y=1, X=1=1) = 0.01
0.01/0.01 - 0.80/0.99 = -0.40
-0.40 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 1%. The probability of non-male gender and being lactose intolerant is 80%. The probability of male gender and being lactose intolerant is 1%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.01
P(Y=1, X=0=1) = 0.80
P(Y=1, X=1=1) = 0.01
0.01/0.01 - 0.80/0.99 = -0.40
-0.40 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look directly at how gender correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male, the probability of being lactose intolerant is 57%. For individuals who are male, the probability of being lactose intolerant is 28%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.28
0.28 - 0.57 = -0.29
-0.29 < 0",mediation,gender_admission,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18773,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. For individuals who are not male and applicants to a non-competitive department, the probability of being lactose intolerant is 19%. For individuals who are not male and applicants to a competitive department, the probability of being lactose intolerant is 62%. For individuals who are male and applicants to a non-competitive department, the probability of being lactose intolerant is 8%. For individuals who are male and applicants to a competitive department, the probability of being lactose intolerant is 59%. For individuals who are not male, the probability of competitive department is 87%. For individuals who are male, the probability of competitive department is 40%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.19
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.08
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.87
P(V2=1 | X=1) = 0.40
0.87 * (0.59 - 0.08) + 0.40 * (0.62 - 0.19) = -0.05
-0.05 < 0",mediation,gender_admission,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
18774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 19%. For individuals who are not male, the probability of being lactose intolerant is 57%. For individuals who are male, the probability of being lactose intolerant is 28%.",yes,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.28
0.19*0.28 - 0.81*0.57 = 0.52
0.52 > 0",mediation,gender_admission,1,marginal,P(Y)
18776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. The overall probability of male gender is 19%. The probability of non-male gender and being lactose intolerant is 46%. The probability of male gender and being lactose intolerant is 5%.",no,"Let X = gender; V2 = department competitiveness; Y = lactose intolerance.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.05
0.05/0.19 - 0.46/0.81 = -0.29
-0.29 < 0",mediation,gender_admission,1,correlation,P(Y | X)
18778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and lactose intolerance. Department competitiveness has a direct effect on lactose intolerance. Method 1: We look at how gender correlates with lactose intolerance case by case according to department competitiveness. Method 2: We look directly at how gender correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,gender_admission,2,backadj,[backdoor adjustment set for Y given X]
18786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 47%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 65%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 51%. For individuals who are male and applicants to a competitive department, the probability of freckles is 70%. For individuals who are not male and out-of-state residents, the probability of competitive department is 14%. For individuals who are not male and in-state residents, the probability of competitive department is 60%. For individuals who are male and out-of-state residents, the probability of competitive department is 28%. For individuals who are male and in-state residents, the probability of competitive department is 68%. The overall probability of in-state residency is 12%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.47
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0, V2=0) = 0.14
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.28
P(V3=1 | X=1, V2=1) = 0.68
P(V2=1) = 0.12
0.12 * (0.70 - 0.51) * 0.60 + 0.88 * (0.65 - 0.47) * 0.28 = 0.03
0.03 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 47%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 65%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 51%. For individuals who are male and applicants to a competitive department, the probability of freckles is 70%. For individuals who are not male and out-of-state residents, the probability of competitive department is 14%. For individuals who are not male and in-state residents, the probability of competitive department is 60%. For individuals who are male and out-of-state residents, the probability of competitive department is 28%. For individuals who are male and in-state residents, the probability of competitive department is 68%. The overall probability of in-state residency is 12%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.47
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.70
P(V3=1 | X=0, V2=0) = 0.14
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.28
P(V3=1 | X=1, V2=1) = 0.68
P(V2=1) = 0.12
0.12 * (0.70 - 0.51) * 0.60 + 0.88 * (0.65 - 0.47) * 0.28 = 0.03
0.03 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 10%. The probability of non-male gender and freckles is 46%. The probability of male gender and freckles is 6%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.06
0.06/0.10 - 0.46/0.90 = 0.06
0.06 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18792,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18794,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 50%. For individuals who are male, the probability of freckles is 82%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.82
0.82 - 0.50 = 0.32
0.32 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 50%. For individuals who are male, the probability of freckles is 82%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.82
0.82 - 0.50 = 0.32
0.32 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 45%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 72%. For individuals who are male and applicants to a competitive department, the probability of freckles is 90%. For individuals who are not male and out-of-state residents, the probability of competitive department is 27%. For individuals who are not male and in-state residents, the probability of competitive department is 55%. For individuals who are male and out-of-state residents, the probability of competitive department is 54%. For individuals who are male and in-state residents, the probability of competitive department is 82%. The overall probability of in-state residency is 15%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.72
P(Y=1 | X=1, V3=1) = 0.90
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.54
P(V3=1 | X=1, V2=1) = 0.82
P(V2=1) = 0.15
0.15 * 0.64 * (0.82 - 0.54)+ 0.85 * 0.64 * (0.55 - 0.27)= 0.06
0.06 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
18800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 45%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 72%. For individuals who are male and applicants to a competitive department, the probability of freckles is 90%. For individuals who are not male and out-of-state residents, the probability of competitive department is 27%. For individuals who are not male and in-state residents, the probability of competitive department is 55%. For individuals who are male and out-of-state residents, the probability of competitive department is 54%. For individuals who are male and in-state residents, the probability of competitive department is 82%. The overall probability of in-state residency is 15%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.72
P(Y=1 | X=1, V3=1) = 0.90
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.54
P(V3=1 | X=1, V2=1) = 0.82
P(V2=1) = 0.15
0.15 * (0.90 - 0.72) * 0.55 + 0.85 * (0.64 - 0.45) * 0.54 = 0.26
0.26 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 45%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 72%. For individuals who are male and applicants to a competitive department, the probability of freckles is 90%. For individuals who are not male and out-of-state residents, the probability of competitive department is 27%. For individuals who are not male and in-state residents, the probability of competitive department is 55%. For individuals who are male and out-of-state residents, the probability of competitive department is 54%. For individuals who are male and in-state residents, the probability of competitive department is 82%. The overall probability of in-state residency is 15%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.72
P(Y=1 | X=1, V3=1) = 0.90
P(V3=1 | X=0, V2=0) = 0.27
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.54
P(V3=1 | X=1, V2=1) = 0.82
P(V2=1) = 0.15
0.15 * (0.90 - 0.72) * 0.55 + 0.85 * (0.64 - 0.45) * 0.54 = 0.26
0.26 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 14%. For individuals who are not male, the probability of freckles is 50%. For individuals who are male, the probability of freckles is 82%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.82
0.14*0.82 - 0.86*0.50 = 0.55
0.55 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 63%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 80%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 34%. For individuals who are male and applicants to a competitive department, the probability of freckles is 56%. For individuals who are not male and out-of-state residents, the probability of competitive department is 78%. For individuals who are not male and in-state residents, the probability of competitive department is 100%. For individuals who are male and out-of-state residents, the probability of competitive department is 42%. For individuals who are male and in-state residents, the probability of competitive department is 70%. The overall probability of in-state residency is 20%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.63
P(Y=1 | X=0, V3=1) = 0.80
P(Y=1 | X=1, V3=0) = 0.34
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.78
P(V3=1 | X=0, V2=1) = 1.00
P(V3=1 | X=1, V2=0) = 0.42
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.20
0.20 * (0.56 - 0.34) * 1.00 + 0.80 * (0.80 - 0.63) * 0.42 = -0.23
-0.23 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 89%. For individuals who are not male, the probability of freckles is 77%. For individuals who are male, the probability of freckles is 45%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.45
0.89*0.45 - 0.11*0.77 = 0.49
0.49 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 89%. For individuals who are not male, the probability of freckles is 77%. For individuals who are male, the probability of freckles is 45%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.45
0.89*0.45 - 0.11*0.77 = 0.49
0.49 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 89%. The probability of non-male gender and freckles is 9%. The probability of male gender and freckles is 40%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.40
0.40/0.89 - 0.09/0.11 = -0.32
-0.32 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 40%. For individuals who are male, the probability of freckles is 32%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.32
0.32 - 0.40 = -0.08
-0.08 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 34%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 54%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 28%. For individuals who are male and applicants to a competitive department, the probability of freckles is 41%. For individuals who are not male and out-of-state residents, the probability of competitive department is 25%. For individuals who are not male and in-state residents, the probability of competitive department is 64%. For individuals who are male and out-of-state residents, the probability of competitive department is 9%. For individuals who are male and in-state residents, the probability of competitive department is 71%. The overall probability of in-state residency is 19%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.41
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.64
P(V3=1 | X=1, V2=0) = 0.09
P(V3=1 | X=1, V2=1) = 0.71
P(V2=1) = 0.19
0.19 * (0.41 - 0.28) * 0.64 + 0.81 * (0.54 - 0.34) * 0.09 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 34%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 54%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 28%. For individuals who are male and applicants to a competitive department, the probability of freckles is 41%. For individuals who are not male and out-of-state residents, the probability of competitive department is 25%. For individuals who are not male and in-state residents, the probability of competitive department is 64%. For individuals who are male and out-of-state residents, the probability of competitive department is 9%. For individuals who are male and in-state residents, the probability of competitive department is 71%. The overall probability of in-state residency is 19%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.41
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.64
P(V3=1 | X=1, V2=0) = 0.09
P(V3=1 | X=1, V2=1) = 0.71
P(V2=1) = 0.19
0.19 * (0.41 - 0.28) * 0.64 + 0.81 * (0.54 - 0.34) * 0.09 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 12%. For individuals who are not male, the probability of freckles is 40%. For individuals who are male, the probability of freckles is 32%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.32
0.12*0.32 - 0.88*0.40 = 0.39
0.39 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18831,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 12%. For individuals who are not male, the probability of freckles is 40%. For individuals who are male, the probability of freckles is 32%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.32
0.12*0.32 - 0.88*0.40 = 0.39
0.39 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18835,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 43%. For individuals who are male, the probability of freckles is 74%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.74
0.74 - 0.43 = 0.31
0.31 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 43%. For individuals who are male, the probability of freckles is 74%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.74
0.74 - 0.43 = 0.31
0.31 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 43%. For individuals who are male, the probability of freckles is 74%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.74
0.74 - 0.43 = 0.31
0.31 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18840,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 41%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a competitive department, the probability of freckles is 87%. For individuals who are not male and out-of-state residents, the probability of competitive department is 8%. For individuals who are not male and in-state residents, the probability of competitive department is 39%. For individuals who are male and out-of-state residents, the probability of competitive department is 44%. For individuals who are male and in-state residents, the probability of competitive department is 72%. The overall probability of in-state residency is 1%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.87
P(V3=1 | X=0, V2=0) = 0.08
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.44
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.01
0.01 * 0.64 * (0.72 - 0.44)+ 0.99 * 0.64 * (0.39 - 0.08)= 0.09
0.09 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
18841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 41%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a competitive department, the probability of freckles is 87%. For individuals who are not male and out-of-state residents, the probability of competitive department is 8%. For individuals who are not male and in-state residents, the probability of competitive department is 39%. For individuals who are male and out-of-state residents, the probability of competitive department is 44%. For individuals who are male and in-state residents, the probability of competitive department is 72%. The overall probability of in-state residency is 1%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.87
P(V3=1 | X=0, V2=0) = 0.08
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.44
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.01
0.01 * 0.64 * (0.72 - 0.44)+ 0.99 * 0.64 * (0.39 - 0.08)= 0.09
0.09 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
18842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 41%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a competitive department, the probability of freckles is 87%. For individuals who are not male and out-of-state residents, the probability of competitive department is 8%. For individuals who are not male and in-state residents, the probability of competitive department is 39%. For individuals who are male and out-of-state residents, the probability of competitive department is 44%. For individuals who are male and in-state residents, the probability of competitive department is 72%. The overall probability of in-state residency is 1%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.87
P(V3=1 | X=0, V2=0) = 0.08
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.44
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.01
0.01 * (0.87 - 0.64) * 0.39 + 0.99 * (0.64 - 0.41) * 0.44 = 0.23
0.23 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 41%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 64%. For individuals who are male and applicants to a competitive department, the probability of freckles is 87%. For individuals who are not male and out-of-state residents, the probability of competitive department is 8%. For individuals who are not male and in-state residents, the probability of competitive department is 39%. For individuals who are male and out-of-state residents, the probability of competitive department is 44%. For individuals who are male and in-state residents, the probability of competitive department is 72%. The overall probability of in-state residency is 1%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.87
P(V3=1 | X=0, V2=0) = 0.08
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.44
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.01
0.01 * (0.87 - 0.64) * 0.39 + 0.99 * (0.64 - 0.41) * 0.44 = 0.23
0.23 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 11%. The probability of non-male gender and freckles is 39%. The probability of male gender and freckles is 8%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.08
0.08/0.11 - 0.39/0.89 = 0.31
0.31 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 11%. The probability of non-male gender and freckles is 39%. The probability of male gender and freckles is 8%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.08
0.08/0.11 - 0.39/0.89 = 0.31
0.31 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 81%. For individuals who are male, the probability of freckles is 48%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.48
0.48 - 0.81 = -0.33
-0.33 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 70%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 87%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 40%. For individuals who are male and applicants to a competitive department, the probability of freckles is 62%. For individuals who are not male and out-of-state residents, the probability of competitive department is 65%. For individuals who are not male and in-state residents, the probability of competitive department is 94%. For individuals who are male and out-of-state residents, the probability of competitive department is 31%. For individuals who are male and in-state residents, the probability of competitive department is 63%. The overall probability of in-state residency is 17%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.87
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.62
P(V3=1 | X=0, V2=0) = 0.65
P(V3=1 | X=0, V2=1) = 0.94
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.63
P(V2=1) = 0.17
0.17 * (0.62 - 0.40) * 0.94 + 0.83 * (0.87 - 0.70) * 0.31 = -0.24
-0.24 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18857,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 70%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 87%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 40%. For individuals who are male and applicants to a competitive department, the probability of freckles is 62%. For individuals who are not male and out-of-state residents, the probability of competitive department is 65%. For individuals who are not male and in-state residents, the probability of competitive department is 94%. For individuals who are male and out-of-state residents, the probability of competitive department is 31%. For individuals who are male and in-state residents, the probability of competitive department is 63%. The overall probability of in-state residency is 17%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.87
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.62
P(V3=1 | X=0, V2=0) = 0.65
P(V3=1 | X=0, V2=1) = 0.94
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.63
P(V2=1) = 0.17
0.17 * (0.62 - 0.40) * 0.94 + 0.83 * (0.87 - 0.70) * 0.31 = -0.24
-0.24 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 97%. The probability of non-male gender and freckles is 2%. The probability of male gender and freckles is 47%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.47
0.47/0.97 - 0.02/0.03 = -0.33
-0.33 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18866,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 38%. For individuals who are male, the probability of freckles is 40%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.40
0.40 - 0.38 = 0.02
0.02 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 38%. For individuals who are male, the probability of freckles is 40%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.40
0.40 - 0.38 = 0.02
0.02 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 26%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 54%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 27%. For individuals who are male and applicants to a competitive department, the probability of freckles is 53%. For individuals who are not male and out-of-state residents, the probability of competitive department is 34%. For individuals who are not male and in-state residents, the probability of competitive department is 76%. For individuals who are male and out-of-state residents, the probability of competitive department is 46%. For individuals who are male and in-state residents, the probability of competitive department is 67%. The overall probability of in-state residency is 16%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.26
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.27
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0, V2=0) = 0.34
P(V3=1 | X=0, V2=1) = 0.76
P(V3=1 | X=1, V2=0) = 0.46
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.16
0.16 * 0.54 * (0.67 - 0.46)+ 0.84 * 0.54 * (0.76 - 0.34)= 0.03
0.03 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
18872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 7%. For individuals who are not male, the probability of freckles is 38%. For individuals who are male, the probability of freckles is 40%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.40
0.07*0.40 - 0.93*0.38 = 0.38
0.38 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 12%. The probability of non-male gender and freckles is 34%. The probability of male gender and freckles is 8%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.08
0.08/0.12 - 0.34/0.88 = 0.30
0.30 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 12%. The probability of non-male gender and freckles is 34%. The probability of male gender and freckles is 8%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.08
0.08/0.12 - 0.34/0.88 = 0.30
0.30 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 76%. For individuals who are male, the probability of freckles is 44%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.44
0.44 - 0.76 = -0.33
-0.33 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 76%. For individuals who are male, the probability of freckles is 44%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.44
0.44 - 0.76 = -0.33
-0.33 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18899,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 66%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 89%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 43%. For individuals who are male and applicants to a competitive department, the probability of freckles is 58%. For individuals who are not male and out-of-state residents, the probability of competitive department is 44%. For individuals who are not male and in-state residents, the probability of competitive department is 78%. For individuals who are male and out-of-state residents, the probability of competitive department is 4%. For individuals who are male and in-state residents, the probability of competitive department is 55%. The overall probability of in-state residency is 4%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.44
P(V3=1 | X=0, V2=1) = 0.78
P(V3=1 | X=1, V2=0) = 0.04
P(V3=1 | X=1, V2=1) = 0.55
P(V2=1) = 0.04
0.04 * (0.58 - 0.43) * 0.78 + 0.96 * (0.89 - 0.66) * 0.04 = -0.23
-0.23 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 82%. The probability of non-male gender and freckles is 14%. The probability of male gender and freckles is 36%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.36
0.36/0.82 - 0.14/0.18 = -0.33
-0.33 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 65%. For individuals who are male, the probability of freckles is 65%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.65
0.65 - 0.65 = -0.00
0.00 = 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 56%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 78%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 53%. For individuals who are male and applicants to a competitive department, the probability of freckles is 76%. For individuals who are not male and out-of-state residents, the probability of competitive department is 39%. For individuals who are not male and in-state residents, the probability of competitive department is 82%. For individuals who are male and out-of-state residents, the probability of competitive department is 51%. For individuals who are male and in-state residents, the probability of competitive department is 77%. The overall probability of in-state residency is 7%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.76
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.82
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.77
P(V2=1) = 0.07
0.07 * 0.78 * (0.77 - 0.51)+ 0.93 * 0.78 * (0.82 - 0.39)= 0.03
0.03 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
18911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 56%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 78%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 53%. For individuals who are male and applicants to a competitive department, the probability of freckles is 76%. For individuals who are not male and out-of-state residents, the probability of competitive department is 39%. For individuals who are not male and in-state residents, the probability of competitive department is 82%. For individuals who are male and out-of-state residents, the probability of competitive department is 51%. For individuals who are male and in-state residents, the probability of competitive department is 77%. The overall probability of in-state residency is 7%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.76
P(V3=1 | X=0, V2=0) = 0.39
P(V3=1 | X=0, V2=1) = 0.82
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.77
P(V2=1) = 0.07
0.07 * 0.78 * (0.77 - 0.51)+ 0.93 * 0.78 * (0.82 - 0.39)= 0.03
0.03 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
18914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 19%. For individuals who are not male, the probability of freckles is 65%. For individuals who are male, the probability of freckles is 65%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.65
0.19*0.65 - 0.81*0.65 = 0.65
0.65 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 34%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 59%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 60%. For individuals who are male and applicants to a competitive department, the probability of freckles is 84%. For individuals who are not male and out-of-state residents, the probability of competitive department is 31%. For individuals who are not male and in-state residents, the probability of competitive department is 52%. For individuals who are male and out-of-state residents, the probability of competitive department is 59%. For individuals who are male and in-state residents, the probability of competitive department is 92%. The overall probability of in-state residency is 1%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0, V2=0) = 0.31
P(V3=1 | X=0, V2=1) = 0.52
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.92
P(V2=1) = 0.01
0.01 * (0.84 - 0.60) * 0.52 + 0.99 * (0.59 - 0.34) * 0.59 = 0.25
0.25 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 68%. For individuals who are male, the probability of freckles is 38%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.38
0.38 - 0.68 = -0.30
-0.30 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 68%. For individuals who are male, the probability of freckles is 38%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.38
0.38 - 0.68 = -0.30
-0.30 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 97%. For individuals who are not male, the probability of freckles is 68%. For individuals who are male, the probability of freckles is 38%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.38
0.97*0.38 - 0.03*0.68 = 0.39
0.39 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 54%. For individuals who are male, the probability of freckles is 55%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.55
0.55 - 0.54 = 0.00
0.00 = 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 54%. For individuals who are male, the probability of freckles is 55%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.55
0.55 - 0.54 = 0.00
0.00 = 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 49%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 74%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 52%. For individuals who are male and applicants to a competitive department, the probability of freckles is 66%. For individuals who are not male and out-of-state residents, the probability of competitive department is 18%. For individuals who are not male and in-state residents, the probability of competitive department is 50%. For individuals who are male and out-of-state residents, the probability of competitive department is 8%. For individuals who are male and in-state residents, the probability of competitive department is 66%. The overall probability of in-state residency is 13%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.66
P(V3=1 | X=0, V2=0) = 0.18
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.08
P(V3=1 | X=1, V2=1) = 0.66
P(V2=1) = 0.13
0.13 * (0.66 - 0.52) * 0.50 + 0.87 * (0.74 - 0.49) * 0.08 = 0.02
0.02 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
18962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 56%. For individuals who are male, the probability of freckles is 88%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.88
0.88 - 0.56 = 0.32
0.32 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18965,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 56%. For individuals who are male, the probability of freckles is 88%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.88
0.88 - 0.56 = 0.32
0.32 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
18968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 44%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 75%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 67%. For individuals who are male and applicants to a competitive department, the probability of freckles is 97%. For individuals who are not male and out-of-state residents, the probability of competitive department is 37%. For individuals who are not male and in-state residents, the probability of competitive department is 72%. For individuals who are male and out-of-state residents, the probability of competitive department is 67%. For individuals who are male and in-state residents, the probability of competitive department is 92%. The overall probability of in-state residency is 3%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.75
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.97
P(V3=1 | X=0, V2=0) = 0.37
P(V3=1 | X=0, V2=1) = 0.72
P(V3=1 | X=1, V2=0) = 0.67
P(V3=1 | X=1, V2=1) = 0.92
P(V2=1) = 0.03
0.03 * (0.97 - 0.67) * 0.72 + 0.97 * (0.75 - 0.44) * 0.67 = 0.23
0.23 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
18971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 6%. For individuals who are not male, the probability of freckles is 56%. For individuals who are male, the probability of freckles is 88%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.88
0.06*0.88 - 0.94*0.56 = 0.57
0.57 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
18972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 6%. The probability of non-male gender and freckles is 52%. The probability of male gender and freckles is 5%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.05
0.05/0.06 - 0.52/0.94 = 0.32
0.32 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 6%. The probability of non-male gender and freckles is 52%. The probability of male gender and freckles is 5%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.05
0.05/0.06 - 0.52/0.94 = 0.32
0.32 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18987,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 93%. The probability of non-male gender and freckles is 5%. The probability of male gender and freckles is 34%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.34
0.34/0.93 - 0.05/0.07 = -0.34
-0.34 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
18991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 50%. For individuals who are male, the probability of freckles is 48%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.48
0.48 - 0.50 = -0.02
-0.02 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
18994,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 48%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 61%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 47%. For individuals who are male and applicants to a competitive department, the probability of freckles is 56%. For individuals who are not male and out-of-state residents, the probability of competitive department is 11%. For individuals who are not male and in-state residents, the probability of competitive department is 55%. For individuals who are male and out-of-state residents, the probability of competitive department is 3%. For individuals who are male and in-state residents, the probability of competitive department is 45%. The overall probability of in-state residency is 17%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.11
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.03
P(V3=1 | X=1, V2=1) = 0.45
P(V2=1) = 0.17
0.17 * 0.61 * (0.45 - 0.03)+ 0.83 * 0.61 * (0.55 - 0.11)= -0.02
-0.02 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
18995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 48%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 61%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 47%. For individuals who are male and applicants to a competitive department, the probability of freckles is 56%. For individuals who are not male and out-of-state residents, the probability of competitive department is 11%. For individuals who are not male and in-state residents, the probability of competitive department is 55%. For individuals who are male and out-of-state residents, the probability of competitive department is 3%. For individuals who are male and in-state residents, the probability of competitive department is 45%. The overall probability of in-state residency is 17%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.11
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.03
P(V3=1 | X=1, V2=1) = 0.45
P(V2=1) = 0.17
0.17 * 0.61 * (0.45 - 0.03)+ 0.83 * 0.61 * (0.55 - 0.11)= -0.02
-0.02 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
18998,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 11%. For individuals who are not male, the probability of freckles is 50%. For individuals who are male, the probability of freckles is 48%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.48
0.11*0.48 - 0.89*0.50 = 0.50
0.50 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 11%. The probability of non-male gender and freckles is 45%. The probability of male gender and freckles is 5%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.05
0.05/0.11 - 0.45/0.89 = -0.02
-0.02 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 26%. For individuals who are male, the probability of freckles is 64%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.64
0.64 - 0.26 = 0.37
0.37 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19006,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 26%. For individuals who are male, the probability of freckles is 64%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.64
0.64 - 0.26 = 0.37
0.37 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 26%. For individuals who are male, the probability of freckles is 64%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.64
0.64 - 0.26 = 0.37
0.37 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 21%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 51%. For individuals who are male and applicants to a competitive department, the probability of freckles is 74%. For individuals who are not male and out-of-state residents, the probability of competitive department is 21%. For individuals who are not male and in-state residents, the probability of competitive department is 73%. For individuals who are male and out-of-state residents, the probability of competitive department is 51%. For individuals who are male and in-state residents, the probability of competitive department is 94%. The overall probability of in-state residency is 11%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.21
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.73
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.94
P(V2=1) = 0.11
0.11 * 0.42 * (0.94 - 0.51)+ 0.89 * 0.42 * (0.73 - 0.21)= 0.08
0.08 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 21%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 51%. For individuals who are male and applicants to a competitive department, the probability of freckles is 74%. For individuals who are not male and out-of-state residents, the probability of competitive department is 21%. For individuals who are not male and in-state residents, the probability of competitive department is 73%. For individuals who are male and out-of-state residents, the probability of competitive department is 51%. For individuals who are male and in-state residents, the probability of competitive department is 94%. The overall probability of in-state residency is 11%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.21
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.73
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.94
P(V2=1) = 0.11
0.11 * (0.74 - 0.51) * 0.73 + 0.89 * (0.42 - 0.21) * 0.51 = 0.29
0.29 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 21%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 51%. For individuals who are male and applicants to a competitive department, the probability of freckles is 74%. For individuals who are not male and out-of-state residents, the probability of competitive department is 21%. For individuals who are not male and in-state residents, the probability of competitive department is 73%. For individuals who are male and out-of-state residents, the probability of competitive department is 51%. For individuals who are male and in-state residents, the probability of competitive department is 94%. The overall probability of in-state residency is 11%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.21
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.73
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.94
P(V2=1) = 0.11
0.11 * (0.74 - 0.51) * 0.73 + 0.89 * (0.42 - 0.21) * 0.51 = 0.29
0.29 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19012,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 9%. For individuals who are not male, the probability of freckles is 26%. For individuals who are male, the probability of freckles is 64%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.64
0.09*0.64 - 0.91*0.26 = 0.30
0.30 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19013,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 9%. For individuals who are not male, the probability of freckles is 26%. For individuals who are male, the probability of freckles is 64%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.64
0.09*0.64 - 0.91*0.26 = 0.30
0.30 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 82%. For individuals who are male, the probability of freckles is 49%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.49
0.49 - 0.82 = -0.32
-0.32 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 66%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 91%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a competitive department, the probability of freckles is 61%. For individuals who are not male and out-of-state residents, the probability of competitive department is 59%. For individuals who are not male and in-state residents, the probability of competitive department is 89%. For individuals who are male and out-of-state residents, the probability of competitive department is 30%. For individuals who are male and in-state residents, the probability of competitive department is 67%. The overall probability of in-state residency is 14%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.59
P(V3=1 | X=0, V2=1) = 0.89
P(V3=1 | X=1, V2=0) = 0.30
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.14
0.14 * 0.91 * (0.67 - 0.30)+ 0.86 * 0.91 * (0.89 - 0.59)= -0.08
-0.08 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 66%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 91%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a competitive department, the probability of freckles is 61%. For individuals who are not male and out-of-state residents, the probability of competitive department is 59%. For individuals who are not male and in-state residents, the probability of competitive department is 89%. For individuals who are male and out-of-state residents, the probability of competitive department is 30%. For individuals who are male and in-state residents, the probability of competitive department is 67%. The overall probability of in-state residency is 14%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.59
P(V3=1 | X=0, V2=1) = 0.89
P(V3=1 | X=1, V2=0) = 0.30
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.14
0.14 * (0.61 - 0.42) * 0.89 + 0.86 * (0.91 - 0.66) * 0.30 = -0.26
-0.26 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 66%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 91%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a competitive department, the probability of freckles is 61%. For individuals who are not male and out-of-state residents, the probability of competitive department is 59%. For individuals who are not male and in-state residents, the probability of competitive department is 89%. For individuals who are male and out-of-state residents, the probability of competitive department is 30%. For individuals who are male and in-state residents, the probability of competitive department is 67%. The overall probability of in-state residency is 14%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.59
P(V3=1 | X=0, V2=1) = 0.89
P(V3=1 | X=1, V2=0) = 0.30
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.14
0.14 * (0.61 - 0.42) * 0.89 + 0.86 * (0.91 - 0.66) * 0.30 = -0.26
-0.26 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 91%. The probability of non-male gender and freckles is 8%. The probability of male gender and freckles is 44%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.44
0.44/0.91 - 0.08/0.09 = -0.33
-0.33 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 57%. For individuals who are male, the probability of freckles is 57%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.57
0.57 - 0.57 = 0.00
0.00 = 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 51%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 83%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 53%. For individuals who are male and applicants to a competitive department, the probability of freckles is 80%. For individuals who are not male and out-of-state residents, the probability of competitive department is 18%. For individuals who are not male and in-state residents, the probability of competitive department is 45%. For individuals who are male and out-of-state residents, the probability of competitive department is 11%. For individuals who are male and in-state residents, the probability of competitive department is 54%. The overall probability of in-state residency is 8%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.51
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.80
P(V3=1 | X=0, V2=0) = 0.18
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.11
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.08
0.08 * (0.80 - 0.53) * 0.45 + 0.92 * (0.83 - 0.51) * 0.11 = 0.02
0.02 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 7%. For individuals who are not male, the probability of freckles is 57%. For individuals who are male, the probability of freckles is 57%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.57
0.07*0.57 - 0.93*0.57 = 0.57
0.57 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 7%. The probability of non-male gender and freckles is 53%. The probability of male gender and freckles is 4%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.53/0.93 = -0.00
0.00 = 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 7%. The probability of non-male gender and freckles is 53%. The probability of male gender and freckles is 4%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.04
0.04/0.07 - 0.53/0.93 = -0.00
0.00 = 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 49%. For individuals who are male, the probability of freckles is 78%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.78
0.78 - 0.49 = 0.30
0.30 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19052,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 45%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 66%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 69%. For individuals who are male and applicants to a competitive department, the probability of freckles is 88%. For individuals who are not male and out-of-state residents, the probability of competitive department is 17%. For individuals who are not male and in-state residents, the probability of competitive department is 57%. For individuals who are male and out-of-state residents, the probability of competitive department is 49%. For individuals who are male and in-state residents, the probability of competitive department is 78%. The overall probability of in-state residency is 3%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0, V2=0) = 0.17
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.49
P(V3=1 | X=1, V2=1) = 0.78
P(V2=1) = 0.03
0.03 * (0.88 - 0.69) * 0.57 + 0.97 * (0.66 - 0.45) * 0.49 = 0.23
0.23 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 45%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 66%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 69%. For individuals who are male and applicants to a competitive department, the probability of freckles is 88%. For individuals who are not male and out-of-state residents, the probability of competitive department is 17%. For individuals who are not male and in-state residents, the probability of competitive department is 57%. For individuals who are male and out-of-state residents, the probability of competitive department is 49%. For individuals who are male and in-state residents, the probability of competitive department is 78%. The overall probability of in-state residency is 3%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0, V2=0) = 0.17
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.49
P(V3=1 | X=1, V2=1) = 0.78
P(V2=1) = 0.03
0.03 * (0.88 - 0.69) * 0.57 + 0.97 * (0.66 - 0.45) * 0.49 = 0.23
0.23 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 19%. For individuals who are not male, the probability of freckles is 49%. For individuals who are male, the probability of freckles is 78%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.78
0.19*0.78 - 0.81*0.49 = 0.54
0.54 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 19%. The probability of non-male gender and freckles is 40%. The probability of male gender and freckles is 15%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.15
0.15/0.19 - 0.40/0.81 = 0.30
0.30 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19062,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 79%. For individuals who are male, the probability of freckles is 39%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.39
0.39 - 0.79 = -0.39
-0.39 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 60%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 90%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 34%. For individuals who are male and applicants to a competitive department, the probability of freckles is 58%. For individuals who are not male and out-of-state residents, the probability of competitive department is 61%. For individuals who are not male and in-state residents, the probability of competitive department is 91%. For individuals who are male and out-of-state residents, the probability of competitive department is 19%. For individuals who are male and in-state residents, the probability of competitive department is 48%. The overall probability of in-state residency is 6%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.90
P(Y=1 | X=1, V3=0) = 0.34
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.61
P(V3=1 | X=0, V2=1) = 0.91
P(V3=1 | X=1, V2=0) = 0.19
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.06
0.06 * 0.90 * (0.48 - 0.19)+ 0.94 * 0.90 * (0.91 - 0.61)= -0.13
-0.13 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 83%. For individuals who are not male, the probability of freckles is 79%. For individuals who are male, the probability of freckles is 39%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.39
0.83*0.39 - 0.17*0.79 = 0.46
0.46 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19074,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 59%. For individuals who are male, the probability of freckles is 55%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.55
0.55 - 0.59 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 59%. For individuals who are male, the probability of freckles is 55%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.55
0.55 - 0.59 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 59%. For individuals who are male, the probability of freckles is 55%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.55
0.55 - 0.59 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 45%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 68%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a competitive department, the probability of freckles is 69%. For individuals who are not male and out-of-state residents, the probability of competitive department is 56%. For individuals who are not male and in-state residents, the probability of competitive department is 85%. For individuals who are male and out-of-state residents, the probability of competitive department is 43%. For individuals who are male and in-state residents, the probability of competitive department is 80%. The overall probability of in-state residency is 13%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.68
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.69
P(V3=1 | X=0, V2=0) = 0.56
P(V3=1 | X=0, V2=1) = 0.85
P(V3=1 | X=1, V2=0) = 0.43
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.13
0.13 * 0.68 * (0.80 - 0.43)+ 0.87 * 0.68 * (0.85 - 0.56)= -0.03
-0.03 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 45%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 68%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a competitive department, the probability of freckles is 69%. For individuals who are not male and out-of-state residents, the probability of competitive department is 56%. For individuals who are not male and in-state residents, the probability of competitive department is 85%. For individuals who are male and out-of-state residents, the probability of competitive department is 43%. For individuals who are male and in-state residents, the probability of competitive department is 80%. The overall probability of in-state residency is 13%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.45
P(Y=1 | X=0, V3=1) = 0.68
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.69
P(V3=1 | X=0, V2=0) = 0.56
P(V3=1 | X=0, V2=1) = 0.85
P(V3=1 | X=1, V2=0) = 0.43
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.13
0.13 * (0.69 - 0.42) * 0.85 + 0.87 * (0.68 - 0.45) * 0.43 = -0.00
0.00 = 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 2%. For individuals who are not male, the probability of freckles is 59%. For individuals who are male, the probability of freckles is 55%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.55
0.02*0.55 - 0.98*0.59 = 0.59
0.59 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 2%. The probability of non-male gender and freckles is 58%. The probability of male gender and freckles is 1%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.58/0.98 = -0.04
-0.04 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 41%. For individuals who are male, the probability of freckles is 74%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.74
0.74 - 0.41 = 0.33
0.33 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 41%. For individuals who are male, the probability of freckles is 74%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.74
0.74 - 0.41 = 0.33
0.33 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19092,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 35%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 58%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 63%. For individuals who are male and applicants to a competitive department, the probability of freckles is 83%. For individuals who are not male and out-of-state residents, the probability of competitive department is 25%. For individuals who are not male and in-state residents, the probability of competitive department is 48%. For individuals who are male and out-of-state residents, the probability of competitive department is 51%. For individuals who are male and in-state residents, the probability of competitive department is 72%. The overall probability of in-state residency is 8%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.25
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.08
0.08 * 0.58 * (0.72 - 0.51)+ 0.92 * 0.58 * (0.48 - 0.25)= 0.06
0.06 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 13%. For individuals who are not male, the probability of freckles is 41%. For individuals who are male, the probability of freckles is 74%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.74
0.13*0.74 - 0.87*0.41 = 0.45
0.45 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 13%. The probability of non-male gender and freckles is 36%. The probability of male gender and freckles is 9%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.09
0.09/0.13 - 0.36/0.87 = 0.33
0.33 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 13%. The probability of non-male gender and freckles is 36%. The probability of male gender and freckles is 9%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.09
0.09/0.13 - 0.36/0.87 = 0.33
0.33 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 72%. For individuals who are male, the probability of freckles is 40%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.40
0.40 - 0.72 = -0.31
-0.31 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 72%. For individuals who are male, the probability of freckles is 40%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.40
0.40 - 0.72 = -0.31
-0.31 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 62%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 81%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 37%. For individuals who are male and applicants to a competitive department, the probability of freckles is 56%. For individuals who are not male and out-of-state residents, the probability of competitive department is 48%. For individuals who are not male and in-state residents, the probability of competitive department is 81%. For individuals who are male and out-of-state residents, the probability of competitive department is 14%. For individuals who are male and in-state residents, the probability of competitive department is 60%. The overall probability of in-state residency is 6%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.81
P(Y=1 | X=1, V3=0) = 0.37
P(Y=1 | X=1, V3=1) = 0.56
P(V3=1 | X=0, V2=0) = 0.48
P(V3=1 | X=0, V2=1) = 0.81
P(V3=1 | X=1, V2=0) = 0.14
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.06
0.06 * 0.81 * (0.60 - 0.14)+ 0.94 * 0.81 * (0.81 - 0.48)= -0.07
-0.07 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19110,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 80%. For individuals who are not male, the probability of freckles is 72%. For individuals who are male, the probability of freckles is 40%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.40
0.80*0.40 - 0.20*0.72 = 0.47
0.47 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19117,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 56%. For individuals who are male, the probability of freckles is 62%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.62
0.62 - 0.56 = 0.06
0.06 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 56%. For individuals who are male, the probability of freckles is 62%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.62
0.62 - 0.56 = 0.06
0.06 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 16%. The probability of non-male gender and freckles is 48%. The probability of male gender and freckles is 10%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.10
0.10/0.16 - 0.48/0.84 = 0.04
0.04 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 16%. The probability of non-male gender and freckles is 48%. The probability of male gender and freckles is 10%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.10
0.10/0.16 - 0.48/0.84 = 0.04
0.04 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 48%. For individuals who are male, the probability of freckles is 79%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.79
0.79 - 0.48 = 0.31
0.31 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 48%. For individuals who are male, the probability of freckles is 79%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.79
0.79 - 0.48 = 0.31
0.31 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 43%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 63%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 66%. For individuals who are male and applicants to a competitive department, the probability of freckles is 88%. For individuals who are not male and out-of-state residents, the probability of competitive department is 21%. For individuals who are not male and in-state residents, the probability of competitive department is 44%. For individuals who are male and out-of-state residents, the probability of competitive department is 57%. For individuals who are male and in-state residents, the probability of competitive department is 88%. The overall probability of in-state residency is 14%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.44
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.88
P(V2=1) = 0.14
0.14 * 0.63 * (0.88 - 0.57)+ 0.86 * 0.63 * (0.44 - 0.21)= 0.09
0.09 > 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 43%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 63%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 66%. For individuals who are male and applicants to a competitive department, the probability of freckles is 88%. For individuals who are not male and out-of-state residents, the probability of competitive department is 21%. For individuals who are not male and in-state residents, the probability of competitive department is 44%. For individuals who are male and out-of-state residents, the probability of competitive department is 57%. For individuals who are male and in-state residents, the probability of competitive department is 88%. The overall probability of in-state residency is 14%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0, V2=0) = 0.21
P(V3=1 | X=0, V2=1) = 0.44
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.88
P(V2=1) = 0.14
0.14 * (0.88 - 0.66) * 0.44 + 0.86 * (0.63 - 0.43) * 0.57 = 0.22
0.22 > 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 11%. For individuals who are not male, the probability of freckles is 48%. For individuals who are male, the probability of freckles is 79%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.79
0.11*0.79 - 0.89*0.48 = 0.51
0.51 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 11%. The probability of non-male gender and freckles is 43%. The probability of male gender and freckles is 9%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.09
0.09/0.11 - 0.43/0.89 = 0.31
0.31 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 74%. For individuals who are male, the probability of freckles is 42%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.42
0.42 - 0.74 = -0.31
-0.31 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 74%. For individuals who are male, the probability of freckles is 42%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.42
0.42 - 0.74 = -0.31
-0.31 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 66%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 89%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a competitive department, the probability of freckles is 43%. For individuals who are not male and out-of-state residents, the probability of competitive department is 33%. For individuals who are not male and in-state residents, the probability of competitive department is 66%. For individuals who are male and out-of-state residents, the probability of competitive department is 0%. For individuals who are male and in-state residents, the probability of competitive department is 33%. The overall probability of in-state residency is 6%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0, V2=0) = 0.33
P(V3=1 | X=0, V2=1) = 0.66
P(V3=1 | X=1, V2=0) = 0.00
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.06
0.06 * 0.89 * (0.33 - 0.00)+ 0.94 * 0.89 * (0.66 - 0.33)= -0.08
-0.08 < 0",arrowhead,gender_admission_state,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 66%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 89%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 42%. For individuals who are male and applicants to a competitive department, the probability of freckles is 43%. For individuals who are not male and out-of-state residents, the probability of competitive department is 33%. For individuals who are not male and in-state residents, the probability of competitive department is 66%. For individuals who are male and out-of-state residents, the probability of competitive department is 0%. For individuals who are male and in-state residents, the probability of competitive department is 33%. The overall probability of in-state residency is 6%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0, V2=0) = 0.33
P(V3=1 | X=0, V2=1) = 0.66
P(V3=1 | X=1, V2=0) = 0.00
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.06
0.06 * (0.43 - 0.42) * 0.66 + 0.94 * (0.89 - 0.66) * 0.00 = -0.25
-0.25 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 84%. For individuals who are not male, the probability of freckles is 74%. For individuals who are male, the probability of freckles is 42%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.42
0.84*0.42 - 0.16*0.74 = 0.47
0.47 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 84%. The probability of non-male gender and freckles is 12%. The probability of male gender and freckles is 36%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.36
0.36/0.84 - 0.12/0.16 = -0.31
-0.31 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 13%. For individuals who are not male, the probability of freckles is 61%. For individuals who are male, the probability of freckles is 65%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.65
0.13*0.65 - 0.87*0.61 = 0.61
0.61 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 13%. The probability of non-male gender and freckles is 53%. The probability of male gender and freckles is 8%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.08
0.08/0.13 - 0.53/0.87 = 0.04
0.04 > 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look at how gender correlates with freckles case by case according to department competitiveness. Method 2: We look directly at how gender correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. Method 1: We look directly at how gender correlates with freckles in general. Method 2: We look at this correlation case by case according to department competitiveness.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_admission_state,2,backadj,[backdoor adjustment set for Y given X]
19172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 68%. For individuals who are male, the probability of freckles is 38%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.38
0.38 - 0.68 = -0.29
-0.29 < 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 68%. For individuals who are male, the probability of freckles is 38%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.38
0.38 - 0.68 = -0.29
-0.29 < 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male and applicants to a non-competitive department, the probability of freckles is 59%. For individuals who are not male and applicants to a competitive department, the probability of freckles is 76%. For individuals who are male and applicants to a non-competitive department, the probability of freckles is 36%. For individuals who are male and applicants to a competitive department, the probability of freckles is 49%. For individuals who are not male and out-of-state residents, the probability of competitive department is 42%. For individuals who are not male and in-state residents, the probability of competitive department is 79%. For individuals who are male and out-of-state residents, the probability of competitive department is 10%. For individuals who are male and in-state residents, the probability of competitive department is 48%. The overall probability of in-state residency is 20%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.59
P(Y=1 | X=0, V3=1) = 0.76
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.79
P(V3=1 | X=1, V2=0) = 0.10
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.20
0.20 * (0.49 - 0.36) * 0.79 + 0.80 * (0.76 - 0.59) * 0.10 = -0.22
-0.22 < 0",arrowhead,gender_admission_state,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 83%. For individuals who are not male, the probability of freckles is 68%. For individuals who are male, the probability of freckles is 38%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.38
0.83*0.38 - 0.17*0.68 = 0.43
0.43 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 83%. For individuals who are not male, the probability of freckles is 68%. For individuals who are male, the probability of freckles is 38%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.38
0.83*0.38 - 0.17*0.68 = 0.43
0.43 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 83%. The probability of non-male gender and freckles is 11%. The probability of male gender and freckles is 32%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.32
0.32/0.83 - 0.11/0.17 = -0.29
-0.29 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 83%. The probability of non-male gender and freckles is 11%. The probability of male gender and freckles is 32%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.32
0.32/0.83 - 0.11/0.17 = -0.29
-0.29 < 0",arrowhead,gender_admission_state,1,correlation,P(Y | X)
19186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 37%. For individuals who are male, the probability of freckles is 68%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.68
0.68 - 0.37 = 0.31
0.31 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19187,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 37%. For individuals who are male, the probability of freckles is 68%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.68
0.68 - 0.37 = 0.31
0.31 > 0",arrowhead,gender_admission_state,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. For individuals who are not male, the probability of freckles is 37%. For individuals who are male, the probability of freckles is 68%.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.68
0.68 - 0.37 = 0.31
0.31 > 0",arrowhead,gender_admission_state,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and freckles. Residency status has a direct effect on department competitiveness and freckles. Department competitiveness has a direct effect on freckles. Residency status is unobserved. The overall probability of male gender is 2%. For individuals who are not male, the probability of freckles is 37%. For individuals who are male, the probability of freckles is 68%.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.68
0.02*0.68 - 0.98*0.37 = 0.37
0.37 > 0",arrowhead,gender_admission_state,1,marginal,P(Y)
19201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 60%. For individuals who like spicy food, the probability of high salary is 39%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.39 - 0.60 = -0.21
-0.21 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19203,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 60%. For individuals who like spicy food, the probability of high salary is 39%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.39
0.39 - 0.60 = -0.21
-0.21 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 70%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 48%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who like spicy food and white-collar workers, the probability of high salary is 17%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 74%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 45%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 49%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 18%. The overall probability of high skill level is 95%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.48
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.17
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.49
P(V3=1 | X=1, V2=1) = 0.18
P(V2=1) = 0.95
0.95 * 0.48 * (0.18 - 0.49)+ 0.05 * 0.48 * (0.45 - 0.74)= 0.06
0.06 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 70%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 48%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who like spicy food and white-collar workers, the probability of high salary is 17%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 74%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 45%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 49%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 18%. The overall probability of high skill level is 95%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.48
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.17
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.49
P(V3=1 | X=1, V2=1) = 0.18
P(V2=1) = 0.95
0.95 * (0.17 - 0.44) * 0.45 + 0.05 * (0.48 - 0.70) * 0.49 = -0.29
-0.29 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19211,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 2%. The probability of not liking spicy food and high salary is 58%. The probability of liking spicy food and high salary is 1%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.58/0.98 = -0.21
-0.21 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 36%. For individuals who like spicy food, the probability of high salary is 33%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.33
0.33 - 0.36 = -0.03
-0.03 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 40%. For individuals who like spicy food and white-collar workers, the probability of high salary is 16%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 64%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 29%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 63%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 30%. The overall probability of high skill level is 92%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0, V2=0) = 0.64
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.30
P(V2=1) = 0.92
0.92 * (0.16 - 0.40) * 0.29 + 0.08 * (0.19 - 0.44) * 0.63 = -0.03
-0.03 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 5%. The probability of not liking spicy food and high salary is 34%. The probability of liking spicy food and high salary is 2%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.02
0.02/0.05 - 0.34/0.95 = -0.04
-0.04 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 19%. For individuals who like spicy food, the probability of high salary is 40%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.40
0.40 - 0.19 = 0.21
0.21 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 23%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 1%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 48%. For individuals who like spicy food and white-collar workers, the probability of high salary is 28%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 49%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 19%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 75%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 40%. The overall probability of high skill level is 98%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.01
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.49
P(V3=1 | X=0, V2=1) = 0.19
P(V3=1 | X=1, V2=0) = 0.75
P(V3=1 | X=1, V2=1) = 0.40
P(V2=1) = 0.98
0.98 * (0.28 - 0.48) * 0.19 + 0.02 * (0.01 - 0.23) * 0.75 = 0.25
0.25 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 83%. For individuals who do not like spicy food, the probability of high salary is 19%. For individuals who like spicy food, the probability of high salary is 40%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.40
0.83*0.40 - 0.17*0.19 = 0.36
0.36 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 83%. For individuals who do not like spicy food, the probability of high salary is 19%. For individuals who like spicy food, the probability of high salary is 40%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.40
0.83*0.40 - 0.17*0.19 = 0.36
0.36 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 53%. For individuals who like spicy food, the probability of high salary is 35%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.35
0.35 - 0.53 = -0.17
-0.17 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 53%. For individuals who like spicy food, the probability of high salary is 35%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.35
0.35 - 0.53 = -0.17
-0.17 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 53%. For individuals who like spicy food, the probability of high salary is 35%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.35
0.35 - 0.53 = -0.17
-0.17 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 66%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 41%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 40%. For individuals who like spicy food and white-collar workers, the probability of high salary is 22%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 85%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 49%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 58%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 21%. The overall probability of high skill level is 85%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.85
P(V3=1 | X=0, V2=1) = 0.49
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.21
P(V2=1) = 0.85
0.85 * 0.41 * (0.21 - 0.58)+ 0.15 * 0.41 * (0.49 - 0.85)= 0.09
0.09 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 5%. For individuals who do not like spicy food, the probability of high salary is 53%. For individuals who like spicy food, the probability of high salary is 35%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.35
0.05*0.35 - 0.95*0.53 = 0.52
0.52 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 5%. The probability of not liking spicy food and high salary is 50%. The probability of liking spicy food and high salary is 2%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.02
0.02/0.05 - 0.50/0.95 = -0.18
-0.18 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 54%. For individuals who like spicy food, the probability of high salary is 41%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.41
0.41 - 0.54 = -0.12
-0.12 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 54%. For individuals who like spicy food, the probability of high salary is 41%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.41
0.41 - 0.54 = -0.12
-0.12 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 65%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 35%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 53%. For individuals who like spicy food and white-collar workers, the probability of high salary is 29%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 70%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 35%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 74%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 48%. The overall probability of high skill level is 92%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.29
P(V3=1 | X=0, V2=0) = 0.70
P(V3=1 | X=0, V2=1) = 0.35
P(V3=1 | X=1, V2=0) = 0.74
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.92
0.92 * 0.35 * (0.48 - 0.74)+ 0.08 * 0.35 * (0.35 - 0.70)= -0.04
-0.04 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 2%. The probability of not liking spicy food and high salary is 53%. The probability of liking spicy food and high salary is 1%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.53/0.98 = -0.13
-0.13 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 17%. For individuals who like spicy food, the probability of high salary is 31%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.31
0.31 - 0.17 = 0.14
0.14 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 17%. For individuals who like spicy food, the probability of high salary is 31%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.31
0.31 - 0.17 = 0.14
0.14 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 22%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 2%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 50%. For individuals who like spicy food and white-collar workers, the probability of high salary is 26%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 57%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 24%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 99%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 76%. The overall probability of high skill level is 96%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.22
P(Y=1 | X=0, V3=1) = 0.02
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.26
P(V3=1 | X=0, V2=0) = 0.57
P(V3=1 | X=0, V2=1) = 0.24
P(V3=1 | X=1, V2=0) = 0.99
P(V3=1 | X=1, V2=1) = 0.76
P(V2=1) = 0.96
0.96 * 0.02 * (0.76 - 0.99)+ 0.04 * 0.02 * (0.24 - 0.57)= -0.11
-0.11 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 22%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 2%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 50%. For individuals who like spicy food and white-collar workers, the probability of high salary is 26%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 57%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 24%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 99%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 76%. The overall probability of high skill level is 96%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.22
P(Y=1 | X=0, V3=1) = 0.02
P(Y=1 | X=1, V3=0) = 0.50
P(Y=1 | X=1, V3=1) = 0.26
P(V3=1 | X=0, V2=0) = 0.57
P(V3=1 | X=0, V2=1) = 0.24
P(V3=1 | X=1, V2=0) = 0.99
P(V3=1 | X=1, V2=1) = 0.76
P(V2=1) = 0.96
0.96 * (0.26 - 0.50) * 0.24 + 0.04 * (0.02 - 0.22) * 0.99 = 0.27
0.27 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19278,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 93%. For individuals who do not like spicy food, the probability of high salary is 17%. For individuals who like spicy food, the probability of high salary is 31%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.31
0.93*0.31 - 0.07*0.17 = 0.30
0.30 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 93%. For individuals who do not like spicy food, the probability of high salary is 17%. For individuals who like spicy food, the probability of high salary is 31%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.31
0.93*0.31 - 0.07*0.17 = 0.30
0.30 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19280,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 93%. The probability of not liking spicy food and high salary is 1%. The probability of liking spicy food and high salary is 29%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.29
0.29/0.93 - 0.01/0.07 = 0.14
0.14 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19281,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 93%. The probability of not liking spicy food and high salary is 1%. The probability of liking spicy food and high salary is 29%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.29
0.29/0.93 - 0.01/0.07 = 0.14
0.14 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 55%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 37%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 33%. For individuals who like spicy food and white-collar workers, the probability of high salary is 15%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 75%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 39%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 37%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 6%. The overall probability of high skill level is 90%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.55
P(Y=1 | X=0, V3=1) = 0.37
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.15
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.37
P(V3=1 | X=1, V2=1) = 0.06
P(V2=1) = 0.90
0.90 * (0.15 - 0.33) * 0.39 + 0.10 * (0.37 - 0.55) * 0.37 = -0.25
-0.25 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 55%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 37%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 33%. For individuals who like spicy food and white-collar workers, the probability of high salary is 15%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 75%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 39%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 37%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 6%. The overall probability of high skill level is 90%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.55
P(Y=1 | X=0, V3=1) = 0.37
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.15
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.37
P(V3=1 | X=1, V2=1) = 0.06
P(V2=1) = 0.90
0.90 * (0.15 - 0.33) * 0.39 + 0.10 * (0.37 - 0.55) * 0.37 = -0.25
-0.25 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 3%. The probability of not liking spicy food and high salary is 46%. The probability of liking spicy food and high salary is 1%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.01
0.01/0.03 - 0.46/0.97 = -0.17
-0.17 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19298,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 35%. For individuals who like spicy food, the probability of high salary is 33%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.33
0.33 - 0.35 = -0.01
-0.01 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 35%. For individuals who like spicy food, the probability of high salary is 33%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.33
0.33 - 0.35 = -0.01
-0.01 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 35%. For individuals who like spicy food, the probability of high salary is 33%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.33
0.33 - 0.35 = -0.01
-0.01 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19303,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 71%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 32%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 65%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 37%. The overall probability of high skill level is 86%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.71
P(V3=1 | X=0, V2=1) = 0.32
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 0.37
P(V2=1) = 0.86
0.86 * 0.19 * (0.37 - 0.65)+ 0.14 * 0.19 * (0.32 - 0.71)= -0.01
-0.01 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 71%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 32%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 65%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 37%. The overall probability of high skill level is 86%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.71
P(V3=1 | X=0, V2=1) = 0.32
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 0.37
P(V2=1) = 0.86
0.86 * (0.19 - 0.44) * 0.32 + 0.14 * (0.19 - 0.44) * 0.65 = -0.00
0.00 = 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 44%. For individuals who like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 71%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 32%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 65%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 37%. The overall probability of high skill level is 86%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.44
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.71
P(V3=1 | X=0, V2=1) = 0.32
P(V3=1 | X=1, V2=0) = 0.65
P(V3=1 | X=1, V2=1) = 0.37
P(V2=1) = 0.86
0.86 * (0.19 - 0.44) * 0.32 + 0.14 * (0.19 - 0.44) * 0.65 = -0.00
0.00 = 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 13%. For individuals who do not like spicy food, the probability of high salary is 35%. For individuals who like spicy food, the probability of high salary is 33%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.33
0.13*0.33 - 0.87*0.35 = 0.35
0.35 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 13%. For individuals who do not like spicy food, the probability of high salary is 35%. For individuals who like spicy food, the probability of high salary is 33%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.33
0.13*0.33 - 0.87*0.35 = 0.35
0.35 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 49%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 27%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 74%. For individuals who like spicy food and white-collar workers, the probability of high salary is 54%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 52%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 28%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 89%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 54%. The overall probability of high skill level is 96%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.74
P(Y=1 | X=1, V3=1) = 0.54
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.28
P(V3=1 | X=1, V2=0) = 0.89
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.96
0.96 * (0.54 - 0.74) * 0.28 + 0.04 * (0.27 - 0.49) * 0.89 = 0.25
0.25 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19321,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 81%. For individuals who do not like spicy food, the probability of high salary is 43%. For individuals who like spicy food, the probability of high salary is 63%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.63
0.81*0.63 - 0.19*0.43 = 0.59
0.59 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 81%. The probability of not liking spicy food and high salary is 8%. The probability of liking spicy food and high salary is 51%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.51
0.51/0.81 - 0.08/0.19 = 0.20
0.20 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 52%. For individuals who like spicy food, the probability of high salary is 37%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.37
0.37 - 0.52 = -0.15
-0.15 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 52%. For individuals who like spicy food, the probability of high salary is 37%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.37
0.37 - 0.52 = -0.15
-0.15 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 52%. For individuals who like spicy food, the probability of high salary is 37%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.37
0.37 - 0.52 = -0.15
-0.15 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 65%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 41%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 42%. For individuals who like spicy food and white-collar workers, the probability of high salary is 21%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 77%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 53%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 50%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 23%. The overall probability of high skill level is 97%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.21
P(V3=1 | X=0, V2=0) = 0.77
P(V3=1 | X=0, V2=1) = 0.53
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.23
P(V2=1) = 0.97
0.97 * 0.41 * (0.23 - 0.50)+ 0.03 * 0.41 * (0.53 - 0.77)= 0.07
0.07 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 19%. For individuals who do not like spicy food, the probability of high salary is 52%. For individuals who like spicy food, the probability of high salary is 37%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.37
0.19*0.37 - 0.81*0.52 = 0.49
0.49 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 19%. The probability of not liking spicy food and high salary is 42%. The probability of liking spicy food and high salary is 7%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.07
0.07/0.19 - 0.42/0.81 = -0.15
-0.15 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19339,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19340,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 50%. For individuals who like spicy food, the probability of high salary is 51%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.51
0.51 - 0.50 = 0.01
0.01 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 58%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 41%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 65%. For individuals who like spicy food and white-collar workers, the probability of high salary is 38%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 100%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 45%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 72%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 48%. The overall probability of high skill level is 91%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.58
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 1.00
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.91
0.91 * 0.41 * (0.48 - 0.72)+ 0.09 * 0.41 * (0.45 - 1.00)= -0.00
0.00 = 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 58%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 41%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 65%. For individuals who like spicy food and white-collar workers, the probability of high salary is 38%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 100%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 45%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 72%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 48%. The overall probability of high skill level is 91%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.58
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 1.00
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.91
0.91 * 0.41 * (0.48 - 0.72)+ 0.09 * 0.41 * (0.45 - 1.00)= -0.00
0.00 = 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 58%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 41%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 65%. For individuals who like spicy food and white-collar workers, the probability of high salary is 38%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 100%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 45%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 72%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 48%. The overall probability of high skill level is 91%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.58
P(Y=1 | X=0, V3=1) = 0.41
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 1.00
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.91
0.91 * (0.38 - 0.65) * 0.45 + 0.09 * (0.41 - 0.58) * 0.72 = 0.01
0.01 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19349,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 11%. For individuals who do not like spicy food, the probability of high salary is 50%. For individuals who like spicy food, the probability of high salary is 51%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.51
0.11*0.51 - 0.89*0.50 = 0.50
0.50 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 11%. The probability of not liking spicy food and high salary is 44%. The probability of liking spicy food and high salary is 6%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.06
0.06/0.11 - 0.44/0.89 = 0.01
0.01 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 29%. For individuals who like spicy food, the probability of high salary is 49%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.49
0.49 - 0.29 = 0.21
0.21 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 82%. For individuals who do not like spicy food, the probability of high salary is 29%. For individuals who like spicy food, the probability of high salary is 49%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.49
0.82*0.49 - 0.18*0.29 = 0.46
0.46 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19365,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 82%. The probability of not liking spicy food and high salary is 5%. The probability of liking spicy food and high salary is 41%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.41
0.41/0.82 - 0.05/0.18 = 0.21
0.21 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 52%. For individuals who like spicy food, the probability of high salary is 35%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.35
0.35 - 0.52 = -0.17
-0.17 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 67%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 46%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 42%. For individuals who like spicy food and white-collar workers, the probability of high salary is 23%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 99%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 70%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 64%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 38%. The overall probability of high skill level is 92%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.23
P(V3=1 | X=0, V2=0) = 0.99
P(V3=1 | X=0, V2=1) = 0.70
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.38
P(V2=1) = 0.92
0.92 * 0.46 * (0.38 - 0.64)+ 0.08 * 0.46 * (0.70 - 0.99)= 0.08
0.08 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19373,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 67%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 46%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 42%. For individuals who like spicy food and white-collar workers, the probability of high salary is 23%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 99%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 70%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 64%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 38%. The overall probability of high skill level is 92%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.23
P(V3=1 | X=0, V2=0) = 0.99
P(V3=1 | X=0, V2=1) = 0.70
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.38
P(V2=1) = 0.92
0.92 * 0.46 * (0.38 - 0.64)+ 0.08 * 0.46 * (0.70 - 0.99)= 0.08
0.08 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 44%. For individuals who like spicy food, the probability of high salary is 29%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.29
0.29 - 0.44 = -0.15
-0.15 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 44%. For individuals who like spicy food, the probability of high salary is 29%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.29
0.29 - 0.44 = -0.15
-0.15 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 60%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 14%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 48%. For individuals who like spicy food and white-collar workers, the probability of high salary is 6%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 84%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 29%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 96%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 41%. The overall probability of high skill level is 92%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.14
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.06
P(V3=1 | X=0, V2=0) = 0.84
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.96
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.92
0.92 * 0.14 * (0.41 - 0.96)+ 0.08 * 0.14 * (0.29 - 0.84)= -0.06
-0.06 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19389,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 60%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 14%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 48%. For individuals who like spicy food and white-collar workers, the probability of high salary is 6%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 84%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 29%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 96%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 41%. The overall probability of high skill level is 92%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.14
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.06
P(V3=1 | X=0, V2=0) = 0.84
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.96
P(V3=1 | X=1, V2=1) = 0.41
P(V2=1) = 0.92
0.92 * (0.06 - 0.48) * 0.29 + 0.08 * (0.14 - 0.60) * 0.96 = -0.09
-0.09 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 7%. For individuals who do not like spicy food, the probability of high salary is 44%. For individuals who like spicy food, the probability of high salary is 29%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.29
0.07*0.29 - 0.93*0.44 = 0.43
0.43 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 7%. The probability of not liking spicy food and high salary is 42%. The probability of liking spicy food and high salary is 2%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.02
0.02/0.07 - 0.42/0.93 = -0.16
-0.16 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 38%. For individuals who like spicy food, the probability of high salary is 48%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.48
0.48 - 0.38 = 0.10
0.10 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 38%. For individuals who like spicy food, the probability of high salary is 48%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.48
0.48 - 0.38 = 0.10
0.10 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 38%. For individuals who like spicy food, the probability of high salary is 48%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.48
0.48 - 0.38 = 0.10
0.10 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19400,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 40%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 20%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 61%. For individuals who like spicy food and white-collar workers, the probability of high salary is 39%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 42%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 9%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 89%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 58%. The overall probability of high skill level is 93%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.40
P(Y=1 | X=0, V3=1) = 0.20
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.09
P(V3=1 | X=1, V2=0) = 0.89
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.93
0.93 * 0.20 * (0.58 - 0.89)+ 0.07 * 0.20 * (0.09 - 0.42)= -0.12
-0.12 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19408,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 63%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 42%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 38%. For individuals who like spicy food and white-collar workers, the probability of high salary is 21%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 70%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 48%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 40%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 19%. The overall probability of high skill level is 82%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.63
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.38
P(Y=1 | X=1, V3=1) = 0.21
P(V3=1 | X=0, V2=0) = 0.70
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.40
P(V3=1 | X=1, V2=1) = 0.19
P(V2=1) = 0.82
0.82 * 0.42 * (0.19 - 0.40)+ 0.18 * 0.42 * (0.48 - 0.70)= 0.07
0.07 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19419,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 16%. For individuals who do not like spicy food, the probability of high salary is 52%. For individuals who like spicy food, the probability of high salary is 34%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.34
0.16*0.34 - 0.84*0.52 = 0.49
0.49 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 36%. For individuals who like spicy food, the probability of high salary is 31%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.31
0.31 - 0.36 = -0.05
-0.05 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 52%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 16%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 45%. For individuals who like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 74%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 42%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 82%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 52%. The overall probability of high skill level is 95%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.16
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.42
P(V3=1 | X=1, V2=0) = 0.82
P(V3=1 | X=1, V2=1) = 0.52
P(V2=1) = 0.95
0.95 * (0.19 - 0.45) * 0.42 + 0.05 * (0.16 - 0.52) * 0.82 = -0.03
-0.03 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 52%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 16%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 45%. For individuals who like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 74%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 42%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 82%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 52%. The overall probability of high skill level is 95%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.16
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.42
P(V3=1 | X=1, V2=0) = 0.82
P(V3=1 | X=1, V2=1) = 0.52
P(V2=1) = 0.95
0.95 * (0.19 - 0.45) * 0.42 + 0.05 * (0.16 - 0.52) * 0.82 = -0.03
-0.03 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 17%. For individuals who do not like spicy food, the probability of high salary is 36%. For individuals who like spicy food, the probability of high salary is 31%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.31
0.17*0.31 - 0.83*0.36 = 0.35
0.35 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 28%. For individuals who like spicy food, the probability of high salary is 51%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.51
0.51 - 0.28 = 0.23
0.23 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 28%. For individuals who like spicy food, the probability of high salary is 51%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.51
0.51 - 0.28 = 0.23
0.23 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 28%. For individuals who like spicy food, the probability of high salary is 51%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.51
0.51 - 0.28 = 0.23
0.23 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 28%. For individuals who like spicy food, the probability of high salary is 51%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.51
0.51 - 0.28 = 0.23
0.23 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 35%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 13%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 63%. For individuals who like spicy food and white-collar workers, the probability of high salary is 42%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 55%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 33%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 93%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 53%. The overall probability of high skill level is 92%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.13
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.42
P(V3=1 | X=0, V2=0) = 0.55
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.93
P(V3=1 | X=1, V2=1) = 0.53
P(V2=1) = 0.92
0.92 * (0.42 - 0.63) * 0.33 + 0.08 * (0.13 - 0.35) * 0.93 = 0.28
0.28 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 96%. For individuals who do not like spicy food, the probability of high salary is 28%. For individuals who like spicy food, the probability of high salary is 51%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.51
0.96*0.51 - 0.04*0.28 = 0.50
0.50 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 96%. The probability of not liking spicy food and high salary is 1%. The probability of liking spicy food and high salary is 49%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.49
0.49/0.96 - 0.01/0.04 = 0.23
0.23 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 56%. For individuals who like spicy food, the probability of high salary is 39%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.39
0.39 - 0.56 = -0.17
-0.17 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19459,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 67%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 45%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 42%. For individuals who like spicy food and white-collar workers, the probability of high salary is 25%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 66%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 44%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 39%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 9%. The overall probability of high skill level is 80%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.42
P(Y=1 | X=1, V3=1) = 0.25
P(V3=1 | X=0, V2=0) = 0.66
P(V3=1 | X=0, V2=1) = 0.44
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.80
0.80 * (0.25 - 0.42) * 0.44 + 0.20 * (0.45 - 0.67) * 0.39 = -0.25
-0.25 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 7%. The probability of not liking spicy food and high salary is 52%. The probability of liking spicy food and high salary is 3%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.03
0.03/0.07 - 0.52/0.93 = -0.17
-0.17 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19464,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19465,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19466,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 49%. For individuals who like spicy food, the probability of high salary is 36%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.36
0.36 - 0.49 = -0.13
-0.13 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 51%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 35%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 43%. For individuals who like spicy food and white-collar workers, the probability of high salary is 20%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 50%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 5%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 61%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 29%. The overall probability of high skill level is 87%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.51
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.20
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.05
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.29
P(V2=1) = 0.87
0.87 * 0.35 * (0.29 - 0.61)+ 0.13 * 0.35 * (0.05 - 0.50)= -0.07
-0.07 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 51%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 35%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 43%. For individuals who like spicy food and white-collar workers, the probability of high salary is 20%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 50%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 5%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 61%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 29%. The overall probability of high skill level is 87%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.51
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.20
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.05
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.29
P(V2=1) = 0.87
0.87 * 0.35 * (0.29 - 0.61)+ 0.13 * 0.35 * (0.05 - 0.50)= -0.07
-0.07 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 2%. For individuals who do not like spicy food, the probability of high salary is 49%. For individuals who like spicy food, the probability of high salary is 36%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.36
0.02*0.36 - 0.98*0.49 = 0.49
0.49 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 25%. For individuals who like spicy food, the probability of high salary is 44%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.44
0.44 - 0.25 = 0.19
0.19 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 25%. For individuals who like spicy food, the probability of high salary is 44%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.44
0.44 - 0.25 = 0.19
0.19 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19486,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 31%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 6%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 57%. For individuals who like spicy food and white-collar workers, the probability of high salary is 30%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 48%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 24%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 77%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 48%. The overall probability of high skill level is 97%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.06
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.48
P(V3=1 | X=0, V2=1) = 0.24
P(V3=1 | X=1, V2=0) = 0.77
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.97
0.97 * (0.30 - 0.57) * 0.24 + 0.03 * (0.06 - 0.31) * 0.77 = 0.26
0.26 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19487,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 31%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 6%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 57%. For individuals who like spicy food and white-collar workers, the probability of high salary is 30%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 48%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 24%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 77%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 48%. The overall probability of high skill level is 97%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.31
P(Y=1 | X=0, V3=1) = 0.06
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.48
P(V3=1 | X=0, V2=1) = 0.24
P(V3=1 | X=1, V2=0) = 0.77
P(V3=1 | X=1, V2=1) = 0.48
P(V2=1) = 0.97
0.97 * (0.30 - 0.57) * 0.24 + 0.03 * (0.06 - 0.31) * 0.77 = 0.26
0.26 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19491,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 96%. The probability of not liking spicy food and high salary is 1%. The probability of liking spicy food and high salary is 42%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.42
0.42/0.96 - 0.01/0.04 = 0.19
0.19 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 50%. For individuals who like spicy food, the probability of high salary is 32%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.32
0.32 - 0.50 = -0.18
-0.18 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 42%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 38%. For individuals who like spicy food and white-collar workers, the probability of high salary is 17%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 83%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 59%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 53%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 26%. The overall probability of high skill level is 96%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.38
P(Y=1 | X=1, V3=1) = 0.17
P(V3=1 | X=0, V2=0) = 0.83
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.96
0.96 * 0.42 * (0.26 - 0.53)+ 0.04 * 0.42 * (0.59 - 0.83)= 0.07
0.07 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 42%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 38%. For individuals who like spicy food and white-collar workers, the probability of high salary is 17%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 83%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 59%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 53%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 26%. The overall probability of high skill level is 96%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.38
P(Y=1 | X=1, V3=1) = 0.17
P(V3=1 | X=0, V2=0) = 0.83
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.96
0.96 * 0.42 * (0.26 - 0.53)+ 0.04 * 0.42 * (0.59 - 0.83)= 0.07
0.07 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 8%. For individuals who do not like spicy food, the probability of high salary is 50%. For individuals who like spicy food, the probability of high salary is 32%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.32
0.08*0.32 - 0.92*0.50 = 0.49
0.49 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19505,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 8%. The probability of not liking spicy food and high salary is 46%. The probability of liking spicy food and high salary is 3%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.03
0.03/0.08 - 0.46/0.92 = -0.18
-0.18 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 47%. For individuals who like spicy food, the probability of high salary is 40%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.40
0.40 - 0.47 = -0.07
-0.07 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 47%. For individuals who like spicy food, the probability of high salary is 40%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.40
0.40 - 0.47 = -0.07
-0.07 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 51%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 26%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 43%. For individuals who like spicy food and white-collar workers, the probability of high salary is 28%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 44%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 11%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 57%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 16%. The overall probability of high skill level is 85%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.51
P(Y=1 | X=0, V3=1) = 0.26
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.44
P(V3=1 | X=0, V2=1) = 0.11
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.16
P(V2=1) = 0.85
0.85 * (0.28 - 0.43) * 0.11 + 0.15 * (0.26 - 0.51) * 0.57 = -0.06
-0.06 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 13%. The probability of not liking spicy food and high salary is 41%. The probability of liking spicy food and high salary is 5%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.05
0.05/0.13 - 0.41/0.87 = -0.08
-0.08 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 13%. The probability of not liking spicy food and high salary is 41%. The probability of liking spicy food and high salary is 5%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.05
0.05/0.13 - 0.41/0.87 = -0.08
-0.08 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 32%. For individuals who like spicy food, the probability of high salary is 51%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.51
0.51 - 0.32 = 0.19
0.19 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 37%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 17%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who like spicy food and white-collar workers, the probability of high salary is 41%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 49%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 22%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 77%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 49%. The overall probability of high skill level is 92%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.17
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.41
P(V3=1 | X=0, V2=0) = 0.49
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.77
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.92
0.92 * 0.17 * (0.49 - 0.77)+ 0.08 * 0.17 * (0.22 - 0.49)= -0.06
-0.06 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 37%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 17%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who like spicy food and white-collar workers, the probability of high salary is 41%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 49%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 22%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 77%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 49%. The overall probability of high skill level is 92%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.37
P(Y=1 | X=0, V3=1) = 0.17
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.41
P(V3=1 | X=0, V2=0) = 0.49
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.77
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.92
0.92 * (0.41 - 0.62) * 0.22 + 0.08 * (0.17 - 0.37) * 0.77 = 0.25
0.25 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19536,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 46%. For individuals who like spicy food, the probability of high salary is 35%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.35
0.35 - 0.46 = -0.11
-0.11 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 39%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 41%. For individuals who like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 90%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 67%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 58%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 26%. The overall probability of high skill level is 92%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.41
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.90
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.92
0.92 * 0.39 * (0.26 - 0.58)+ 0.08 * 0.39 * (0.67 - 0.90)= 0.10
0.10 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 39%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 41%. For individuals who like spicy food and white-collar workers, the probability of high salary is 19%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 90%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 67%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 58%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 26%. The overall probability of high skill level is 92%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.41
P(Y=1 | X=1, V3=1) = 0.19
P(V3=1 | X=0, V2=0) = 0.90
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.92
0.92 * (0.19 - 0.41) * 0.67 + 0.08 * (0.39 - 0.62) * 0.58 = -0.21
-0.21 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 2%. The probability of not liking spicy food and high salary is 45%. The probability of liking spicy food and high salary is 1%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.45/0.98 = -0.11
-0.11 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 38%. For individuals who like spicy food, the probability of high salary is 34%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.34
0.34 - 0.38 = -0.05
-0.05 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 38%. For individuals who like spicy food, the probability of high salary is 34%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.34
0.34 - 0.38 = -0.05
-0.05 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 38%. For individuals who like spicy food, the probability of high salary is 34%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.34
0.34 - 0.38 = -0.05
-0.05 < 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 46%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 27%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 47%. For individuals who like spicy food and white-collar workers, the probability of high salary is 23%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 84%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 33%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 84%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 51%. The overall probability of high skill level is 84%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.23
P(V3=1 | X=0, V2=0) = 0.84
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.84
P(V3=1 | X=1, V2=1) = 0.51
P(V2=1) = 0.84
0.84 * 0.27 * (0.51 - 0.84)+ 0.16 * 0.27 * (0.33 - 0.84)= -0.04
-0.04 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 46%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 27%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 47%. For individuals who like spicy food and white-collar workers, the probability of high salary is 23%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 84%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 33%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 84%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 51%. The overall probability of high skill level is 84%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.23
P(V3=1 | X=0, V2=0) = 0.84
P(V3=1 | X=0, V2=1) = 0.33
P(V3=1 | X=1, V2=0) = 0.84
P(V3=1 | X=1, V2=1) = 0.51
P(V2=1) = 0.84
0.84 * (0.23 - 0.47) * 0.33 + 0.16 * (0.27 - 0.46) * 0.84 = -0.00
0.00 = 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 36%. For individuals who like spicy food, the probability of high salary is 50%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.50
0.50 - 0.36 = 0.15
0.15 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 40%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 18%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who like spicy food and white-collar workers, the probability of high salary is 40%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 58%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 18%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 79%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 51%. The overall probability of high skill level is 97%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.40
P(Y=1 | X=0, V3=1) = 0.18
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.58
P(V3=1 | X=0, V2=1) = 0.18
P(V3=1 | X=1, V2=0) = 0.79
P(V3=1 | X=1, V2=1) = 0.51
P(V2=1) = 0.97
0.97 * 0.18 * (0.51 - 0.79)+ 0.03 * 0.18 * (0.18 - 0.58)= -0.08
-0.08 < 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19575,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 95%. The probability of not liking spicy food and high salary is 2%. The probability of liking spicy food and high salary is 48%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.48
0.48/0.95 - 0.02/0.05 = 0.14
0.14 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 39%. For individuals who like spicy food, the probability of high salary is 56%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.56
0.56 - 0.39 = 0.17
0.17 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 39%. For individuals who like spicy food, the probability of high salary is 56%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.56
0.56 - 0.39 = 0.17
0.17 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 42%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 23%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 65%. For individuals who like spicy food and white-collar workers, the probability of high salary is 47%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 56%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 12%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 90%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 44%. The overall probability of high skill level is 93%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.23
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.56
P(V3=1 | X=0, V2=1) = 0.12
P(V3=1 | X=1, V2=0) = 0.90
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.93
0.93 * (0.47 - 0.65) * 0.12 + 0.07 * (0.23 - 0.42) * 0.90 = 0.24
0.24 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 90%. The probability of not liking spicy food and high salary is 4%. The probability of liking spicy food and high salary is 51%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.51
0.51/0.90 - 0.04/0.10 = 0.17
0.17 > 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 43%. For individuals who like spicy food, the probability of high salary is 47%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.47
0.47 - 0.43 = 0.05
0.05 > 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 43%. For individuals who like spicy food, the probability of high salary is 47%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.47
0.47 - 0.43 = 0.05
0.05 > 0",arrowhead,gender_pay,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
19598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 49%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 28%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 53%. For individuals who like spicy food and white-collar workers, the probability of high salary is 30%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 57%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 30%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 68%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 25%. The overall probability of high skill level is 95%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.49
P(Y=1 | X=0, V3=1) = 0.28
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.57
P(V3=1 | X=0, V2=1) = 0.30
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.95
0.95 * (0.30 - 0.53) * 0.30 + 0.05 * (0.28 - 0.49) * 0.68 = 0.03
0.03 > 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 18%. For individuals who do not like spicy food, the probability of high salary is 43%. For individuals who like spicy food, the probability of high salary is 47%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.47
0.18*0.47 - 0.82*0.43 = 0.43
0.43 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19604,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look at how liking spicy food correlates with salary case by case according to occupation. Method 2: We look directly at how liking spicy food correlates with salary in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19605,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. Method 1: We look directly at how liking spicy food correlates with salary in general. Method 2: We look at this correlation case by case according to occupation.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,gender_pay,2,backadj,[backdoor adjustment set for Y given X]
19607,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food, the probability of high salary is 46%. For individuals who like spicy food, the probability of high salary is 31%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.31
0.31 - 0.46 = -0.15
-0.15 < 0",arrowhead,gender_pay,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
19610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 38%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 37%. For individuals who like spicy food and white-collar workers, the probability of high salary is 16%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 92%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 63%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 45%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 25%. The overall probability of high skill level is 82%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.37
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0, V2=0) = 0.92
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.82
0.82 * 0.38 * (0.25 - 0.45)+ 0.18 * 0.38 * (0.63 - 0.92)= 0.11
0.11 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 38%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 37%. For individuals who like spicy food and white-collar workers, the probability of high salary is 16%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 92%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 63%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 45%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 25%. The overall probability of high skill level is 82%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.37
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0, V2=0) = 0.92
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.82
0.82 * 0.38 * (0.25 - 0.45)+ 0.18 * 0.38 * (0.63 - 0.92)= 0.11
0.11 > 0",arrowhead,gender_pay,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
19612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. For individuals who do not like spicy food and blue-collar workers, the probability of high salary is 62%. For individuals who do not like spicy food and white-collar workers, the probability of high salary is 38%. For individuals who like spicy food and blue-collar workers, the probability of high salary is 37%. For individuals who like spicy food and white-collar workers, the probability of high salary is 16%. For individuals who do not like spicy food and with low skill levels, the probability of white-collar job is 92%. For individuals who do not like spicy food and with high skill levels, the probability of white-collar job is 63%. For individuals who like spicy food and with low skill levels, the probability of white-collar job is 45%. For individuals who like spicy food and with high skill levels, the probability of white-collar job is 25%. The overall probability of high skill level is 82%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.37
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0, V2=0) = 0.92
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.82
0.82 * (0.16 - 0.37) * 0.63 + 0.18 * (0.38 - 0.62) * 0.45 = -0.25
-0.25 < 0",arrowhead,gender_pay,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
19614,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 13%. For individuals who do not like spicy food, the probability of high salary is 46%. For individuals who like spicy food, the probability of high salary is 31%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.31
0.13*0.31 - 0.87*0.46 = 0.44
0.44 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19615,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 13%. For individuals who do not like spicy food, the probability of high salary is 46%. For individuals who like spicy food, the probability of high salary is 31%.",yes,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.31
0.13*0.31 - 0.87*0.46 = 0.44
0.44 > 0",arrowhead,gender_pay,1,marginal,P(Y)
19616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. The overall probability of liking spicy food is 13%. The probability of not liking spicy food and high salary is 40%. The probability of liking spicy food and high salary is 4%.",no,"Let V2 = skill; X = liking spicy food; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.04
0.04/0.13 - 0.40/0.87 = -0.15
-0.15 < 0",arrowhead,gender_pay,1,correlation,P(Y | X)
19624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 91%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 89%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 68%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 84%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 59%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.91
P(Y=1 | X=0, V3=0) = 0.89
P(Y=1 | X=0, V3=1) = 0.68
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.59
0.59 - (0.91*0.59 + 0.09*0.68) = -0.02
-0.02 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 91%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 89%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 68%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 84%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 59%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.91
P(Y=1 | X=0, V3=0) = 0.89
P(Y=1 | X=0, V3=1) = 0.68
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.59
0.59 - (0.91*0.59 + 0.09*0.68) = -0.02
-0.02 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.02.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.02.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19655,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look directly at how drinking coffee correlates with broken bones in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 41%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 93%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 69%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 93%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 75%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.41
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.75
0.75 - (0.41*0.75 + 0.59*0.69) = 0.03
0.03 > 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look directly at how drinking coffee correlates with broken bones in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 94%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 93%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 70%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 89%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 24%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.94
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.70
P(Y=1 | X=1, V3=0) = 0.89
P(Y=1 | X=1, V3=1) = 0.24
0.24 - (0.94*0.24 + 0.06*0.70) = -0.11
-0.11 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 96%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 96%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 61%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 94%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 74%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.96
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.94
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.96*0.74 + 0.04*0.61) = 0.00
0.00 = 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 44%. For people who do not drink coffee, the probability of broken bones is 96%. For people who drink coffee, the probability of broken bones is 96%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.96
P(Y=1 | X=1) = 0.96
0.44*0.96 - 0.56*0.96 = 0.96
0.96 > 0",collision,hospitalization,1,marginal,P(Y)
19681,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 44%. For people who do not drink coffee, the probability of broken bones is 96%. For people who drink coffee, the probability of broken bones is 96%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.96
P(Y=1 | X=1) = 0.96
0.44*0.96 - 0.56*0.96 = 0.96
0.96 > 0",collision,hospitalization,1,marginal,P(Y)
19687,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.02.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 50%. For people who do not drink coffee, the probability of broken bones is 80%. For people who drink coffee, the probability of broken bones is 80%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.80
0.50*0.80 - 0.50*0.80 = 0.80
0.80 > 0",collision,hospitalization,1,marginal,P(Y)
19691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 50%. For people who do not drink coffee, the probability of broken bones is 80%. For people who drink coffee, the probability of broken bones is 80%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.80
0.50*0.80 - 0.50*0.80 = 0.80
0.80 > 0",collision,hospitalization,1,marginal,P(Y)
19696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is 0.10.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 94%. For people who do not drink coffee, the probability of broken bones is 95%. For people who drink coffee, the probability of broken bones is 95%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.95
0.94*0.95 - 0.06*0.95 = 0.95
0.95 > 0",collision,hospitalization,1,marginal,P(Y)
19704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look directly at how drinking coffee correlates with broken bones in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.06.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 88%. For people who do not drink coffee, the probability of broken bones is 87%. For people who drink coffee, the probability of broken bones is 87%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.87
0.88*0.87 - 0.12*0.87 = 0.87
0.87 > 0",collision,hospitalization,1,marginal,P(Y)
19714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is 0.03.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 88%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 94%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 77%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 93%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 81%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.88
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.81
0.81 - (0.88*0.81 + 0.12*0.77) = 0.00
0.00 = 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.25.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.25.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 44%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 92%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 84%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 92%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 57%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.44
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.84
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.57
0.57 - (0.44*0.57 + 0.56*0.84) = -0.23
-0.23 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 51%. For people who do not drink coffee, the probability of broken bones is 97%. For people who drink coffee, the probability of broken bones is 97%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.97
0.51*0.97 - 0.49*0.97 = 0.97
0.97 > 0",collision,hospitalization,1,marginal,P(Y)
19734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19736,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is 0.06.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is 0.06.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 51%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 98%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 91%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 99%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 94%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.51
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.99
P(Y=1 | X=1, V3=1) = 0.94
0.94 - (0.51*0.94 + 0.49*0.91) = 0.01
0.01 > 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19740,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 93%. For people who do not drink coffee, the probability of broken bones is 81%. For people who drink coffee, the probability of broken bones is 81%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.81
0.93*0.81 - 0.07*0.81 = 0.81
0.81 > 0",collision,hospitalization,1,marginal,P(Y)
19741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 93%. For people who do not drink coffee, the probability of broken bones is 81%. For people who drink coffee, the probability of broken bones is 81%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.81
0.93*0.81 - 0.07*0.81 = 0.81
0.81 > 0",collision,hospitalization,1,marginal,P(Y)
19745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look directly at how drinking coffee correlates with broken bones in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 93%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 99%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 74%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 91%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 69%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.93
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.69
0.69 - (0.93*0.69 + 0.07*0.74) = -0.00
0.00 = 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 93%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 99%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 74%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 91%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 69%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.93
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.69
0.69 - (0.93*0.69 + 0.07*0.74) = -0.00
0.00 = 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 89%. For people who do not drink coffee, the probability of broken bones is 85%. For people who drink coffee, the probability of broken bones is 85%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.85
0.89*0.85 - 0.11*0.85 = 0.85
0.85 > 0",collision,hospitalization,1,marginal,P(Y)
19756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is 0.09.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 59%. For people who do not drink coffee, the probability of broken bones is 82%. For people who drink coffee, the probability of broken bones is 82%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.82
0.59*0.82 - 0.41*0.82 = 0.82
0.82 > 0",collision,hospitalization,1,marginal,P(Y)
19769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 59%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 91%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 75%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 87%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 65%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.59
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.75
P(Y=1 | X=1, V3=0) = 0.87
P(Y=1 | X=1, V3=1) = 0.65
0.65 - (0.59*0.65 + 0.41*0.75) = -0.06
-0.06 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.25.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19777,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.25.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 59%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 91%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 72%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 91%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 47%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.59
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.47
0.47 - (0.59*0.47 + 0.41*0.72) = -0.15
-0.15 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 82%. For people who do not drink coffee, the probability of broken bones is 87%. For people who drink coffee, the probability of broken bones is 87%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.87
0.82*0.87 - 0.18*0.87 = 0.87
0.87 > 0",collision,hospitalization,1,marginal,P(Y)
19787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.15.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19790,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 89%. For people who do not drink coffee, the probability of broken bones is 85%. For people who drink coffee, the probability of broken bones is 85%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.85
0.89*0.85 - 0.11*0.85 = 0.85
0.85 > 0",collision,hospitalization,1,marginal,P(Y)
19798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 89%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 92%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 72%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 92%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 76%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.89
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.76
0.76 - (0.89*0.76 + 0.11*0.72) = 0.00
0.00 = 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 53%. For people who do not drink coffee, the probability of broken bones is 91%. For people who drink coffee, the probability of broken bones is 91%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.91
0.53*0.91 - 0.47*0.91 = 0.91
0.91 > 0",collision,hospitalization,1,marginal,P(Y)
19804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look directly at how drinking coffee correlates with broken bones in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.16.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 53%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 95%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 85%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 94%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 71%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.53
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.85
P(Y=1 | X=1, V3=0) = 0.94
P(Y=1 | X=1, V3=1) = 0.71
0.71 - (0.53*0.71 + 0.47*0.85) = -0.10
-0.10 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 53%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 95%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 85%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 94%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 71%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.53
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.85
P(Y=1 | X=1, V3=0) = 0.94
P(Y=1 | X=1, V3=1) = 0.71
0.71 - (0.53*0.71 + 0.47*0.85) = -0.10
-0.10 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 44%. For people who do not drink coffee, the probability of broken bones is 86%. For people who drink coffee, the probability of broken bones is 86%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.86
0.44*0.86 - 0.56*0.86 = 0.86
0.86 > 0",collision,hospitalization,1,marginal,P(Y)
19818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 44%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 97%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 65%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 93%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 79%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.44
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.79
0.79 - (0.44*0.79 + 0.56*0.65) = 0.06
0.06 > 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 94%. For people who do not drink coffee, the probability of broken bones is 95%. For people who drink coffee, the probability of broken bones is 95%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.95
0.94*0.95 - 0.06*0.95 = 0.95
0.95 > 0",collision,hospitalization,1,marginal,P(Y)
19824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.04.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.04.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 94%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 97%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 93%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 97%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 89%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.94
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.93
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.89
0.89 - (0.94*0.89 + 0.06*0.93) = -0.00
0.00 = 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19834,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.05.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19848,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 55%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 95%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 83%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 93%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 74%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.55
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.55*0.74 + 0.45*0.83) = -0.06
-0.06 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look directly at how drinking coffee correlates with broken bones in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 84%. For people who do not drink coffee, the probability of broken bones is 82%. For people who drink coffee, the probability of broken bones is 82%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.82
0.84*0.82 - 0.16*0.82 = 0.82
0.82 > 0",collision,hospitalization,1,marginal,P(Y)
19861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 84%. For people who do not drink coffee, the probability of broken bones is 82%. For people who drink coffee, the probability of broken bones is 82%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.82
P(Y=1 | X=1) = 0.82
0.84*0.82 - 0.16*0.82 = 0.82
0.82 > 0",collision,hospitalization,1,marginal,P(Y)
19867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.12.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 84%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 92%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 71%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 88%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 58%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.84
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.88
P(Y=1 | X=1, V3=1) = 0.58
0.58 - (0.84*0.58 + 0.16*0.71) = -0.04
-0.04 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 84%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 92%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 71%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 88%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 58%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.84
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.88
P(Y=1 | X=1, V3=1) = 0.58
0.58 - (0.84*0.58 + 0.16*0.71) = -0.04
-0.04 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19874,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 82%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 90%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 75%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 91%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 76%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.82
P(Y=1 | X=0, V3=0) = 0.90
P(Y=1 | X=0, V3=1) = 0.75
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.76
0.76 - (0.82*0.76 + 0.18*0.75) = 0.00
0.00 = 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 57%. For people who do not drink coffee, the probability of broken bones is 98%. For people who drink coffee, the probability of broken bones is 98%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.98
P(Y=1 | X=1) = 0.98
0.57*0.98 - 0.43*0.98 = 0.98
0.98 > 0",collision,hospitalization,1,marginal,P(Y)
19886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.13.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.13.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look at how drinking coffee correlates with broken bones case by case according to hospitalization status. Method 2: We look directly at how drinking coffee correlates with broken bones in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19895,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look directly at how drinking coffee correlates with broken bones in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 50%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 93%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 71%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 95%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 75%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.50
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.95
P(Y=1 | X=1, V3=1) = 0.75
0.75 - (0.50*0.75 + 0.50*0.71) = 0.01
0.01 > 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19901,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 45%. For people who do not drink coffee, the probability of broken bones is 97%. For people who drink coffee, the probability of broken bones is 97%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.97
0.45*0.97 - 0.55*0.97 = 0.97
0.97 > 0",collision,hospitalization,1,marginal,P(Y)
19908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 45%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 98%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 96%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 98%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 95%.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.96
P(Y=1 | X=1, V3=0) = 0.98
P(Y=1 | X=1, V3=1) = 0.95
0.95 - (0.45*0.95 + 0.55*0.96) = -0.01
-0.01 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. Method 1: We look directly at how drinking coffee correlates with broken bones in general. Method 2: We look at this correlation case by case according to hospitalization status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,hospitalization,2,backadj,[backdoor adjustment set for Y given X]
19916,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.18.",no,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. For hospitalized individuals, the correlation between drinking coffee and broken bones is -0.18.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,hospitalization,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on hospitalization status. Broken bones has a direct effect on hospitalization status. The overall probability of drinking coffee is 52%. For people who do not drink coffee and non-hospitalized individuals, the probability of broken bones is 92%. For people who do not drink coffee and hospitalized individuals, the probability of broken bones is 75%. For people who drink coffee and non-hospitalized individuals, the probability of broken bones is 89%. For people who drink coffee and hospitalized individuals, the probability of broken bones is 56%.",yes,"Let Y = broken bones; X = drinking coffee; V3 = hospitalization status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.52
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.75
P(Y=1 | X=1, V3=0) = 0.89
P(Y=1 | X=1, V3=1) = 0.56
0.56 - (0.52*0.56 + 0.48*0.75) = -0.13
-0.13 < 0",collision,hospitalization,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
19925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
19935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
19936,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.01.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.01.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 5%. For people who do not like spicy food and single people, the probability of attractive appearance is 92%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 73%. For people who like spicy food and single people, the probability of attractive appearance is 86%. For people who like spicy food and in a relationship, the probability of attractive appearance is 71%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.05
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.73
P(Y=1 | X=1, V3=0) = 0.86
P(Y=1 | X=1, V3=1) = 0.71
0.71 - (0.05*0.71 + 0.95*0.73) = -0.02
-0.02 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 80%. For people who do not like spicy food, the probability of attractive appearance is 85%. For people who like spicy food, the probability of attractive appearance is 85%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.85
0.80*0.85 - 0.20*0.85 = 0.85
0.85 > 0",collision,man_in_relationship,1,marginal,P(Y)
19945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
19948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 80%. For people who do not like spicy food and single people, the probability of attractive appearance is 93%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 73%. For people who like spicy food and single people, the probability of attractive appearance is 90%. For people who like spicy food and in a relationship, the probability of attractive appearance is 56%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.80
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.73
P(Y=1 | X=1, V3=0) = 0.90
P(Y=1 | X=1, V3=1) = 0.56
0.56 - (0.80*0.56 + 0.20*0.73) = -0.07
-0.07 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 5%. For people who do not like spicy food, the probability of attractive appearance is 88%. For people who like spicy food, the probability of attractive appearance is 88%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.88
0.05*0.88 - 0.95*0.88 = 0.88
0.88 > 0",collision,man_in_relationship,1,marginal,P(Y)
19951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 5%. For people who do not like spicy food, the probability of attractive appearance is 88%. For people who like spicy food, the probability of attractive appearance is 88%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.88
0.05*0.88 - 0.95*0.88 = 0.88
0.88 > 0",collision,man_in_relationship,1,marginal,P(Y)
19954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
19955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
19956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.04.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 19%. For people who do not like spicy food and single people, the probability of attractive appearance is 12%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 1%. For people who like spicy food and single people, the probability of attractive appearance is 2%. For people who like spicy food and in a relationship, the probability of attractive appearance is 1%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.19
P(Y=1 | X=0, V3=0) = 0.12
P(Y=1 | X=0, V3=1) = 0.01
P(Y=1 | X=1, V3=0) = 0.02
P(Y=1 | X=1, V3=1) = 0.01
0.01 - (0.19*0.01 + 0.81*0.01) = -0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
19971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 2%. For people who do not like spicy food, the probability of attractive appearance is 95%. For people who like spicy food, the probability of attractive appearance is 95%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.95
P(Y=1 | X=1) = 0.95
0.02*0.95 - 0.98*0.95 = 0.95
0.95 > 0",collision,man_in_relationship,1,marginal,P(Y)
19974,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
19986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.10.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 16%. For people who do not like spicy food, the probability of attractive appearance is 90%. For people who like spicy food, the probability of attractive appearance is 90%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.90
0.16*0.90 - 0.84*0.90 = 0.90
0.90 > 0",collision,man_in_relationship,1,marginal,P(Y)
19995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
19996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is 0.33.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
19997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is 0.33.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 8%. For people who do not like spicy food, the probability of attractive appearance is 17%. For people who like spicy food, the probability of attractive appearance is 17%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.17
0.08*0.17 - 0.92*0.17 = 0.17
0.17 > 0",collision,man_in_relationship,1,marginal,P(Y)
20005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20006,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.04.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 8%. For people who do not like spicy food and single people, the probability of attractive appearance is 47%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 6%. For people who like spicy food and single people, the probability of attractive appearance is 26%. For people who like spicy food and in a relationship, the probability of attractive appearance is 2%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.08
P(Y=1 | X=0, V3=0) = 0.47
P(Y=1 | X=0, V3=1) = 0.06
P(Y=1 | X=1, V3=0) = 0.26
P(Y=1 | X=1, V3=1) = 0.02
0.02 - (0.08*0.02 + 0.92*0.06) = -0.04
-0.04 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.07.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.07.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 17%. For people who do not like spicy food and single people, the probability of attractive appearance is 98%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 77%. For people who like spicy food and single people, the probability of attractive appearance is 94%. For people who like spicy food and in a relationship, the probability of attractive appearance is 67%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.17
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.94
P(Y=1 | X=1, V3=1) = 0.67
0.67 - (0.17*0.67 + 0.83*0.77) = -0.10
-0.10 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.11.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.11.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 1%. For people who do not like spicy food, the probability of attractive appearance is 84%. For people who like spicy food, the probability of attractive appearance is 84%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.01
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.84
0.01*0.84 - 0.99*0.84 = 0.84
0.84 > 0",collision,man_in_relationship,1,marginal,P(Y)
20034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is 0.02.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 1%. For people who do not like spicy food and single people, the probability of attractive appearance is 92%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 66%. For people who like spicy food and single people, the probability of attractive appearance is 91%. For people who like spicy food and in a relationship, the probability of attractive appearance is 74%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.01
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.91
P(Y=1 | X=1, V3=1) = 0.74
0.74 - (0.01*0.74 + 0.99*0.66) = 0.08
0.08 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 11%. For people who do not like spicy food, the probability of attractive appearance is 11%. For people who like spicy food, the probability of attractive appearance is 11%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.11
0.11*0.11 - 0.89*0.11 = 0.11
0.11 > 0",collision,man_in_relationship,1,marginal,P(Y)
20041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 11%. For people who do not like spicy food, the probability of attractive appearance is 11%. For people who like spicy food, the probability of attractive appearance is 11%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.11
P(Y=1 | X=1) = 0.11
0.11*0.11 - 0.89*0.11 = 0.11
0.11 > 0",collision,man_in_relationship,1,marginal,P(Y)
20045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.03.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.03.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 11%. For people who do not like spicy food and single people, the probability of attractive appearance is 24%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 7%. For people who like spicy food and single people, the probability of attractive appearance is 16%. For people who like spicy food and in a relationship, the probability of attractive appearance is 4%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.11
P(Y=1 | X=0, V3=0) = 0.24
P(Y=1 | X=0, V3=1) = 0.07
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.04
0.04 - (0.11*0.04 + 0.89*0.07) = -0.03
-0.03 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.03.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.07.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 18%. For people who do not like spicy food, the probability of attractive appearance is 96%. For people who like spicy food, the probability of attractive appearance is 96%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.96
P(Y=1 | X=1) = 0.96
0.18*0.96 - 0.82*0.96 = 0.96
0.96 > 0",collision,man_in_relationship,1,marginal,P(Y)
20075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20079,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 18%. For people who do not like spicy food and single people, the probability of attractive appearance is 98%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 87%. For people who like spicy food and single people, the probability of attractive appearance is 97%. For people who like spicy food and in a relationship, the probability of attractive appearance is 92%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.18
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.87
P(Y=1 | X=1, V3=0) = 0.97
P(Y=1 | X=1, V3=1) = 0.92
0.92 - (0.18*0.92 + 0.82*0.87) = 0.04
0.04 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.01.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 20%. For people who do not like spicy food and single people, the probability of attractive appearance is 27%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 5%. For people who like spicy food and single people, the probability of attractive appearance is 14%. For people who like spicy food and in a relationship, the probability of attractive appearance is 4%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.20
P(Y=1 | X=0, V3=0) = 0.27
P(Y=1 | X=0, V3=1) = 0.05
P(Y=1 | X=1, V3=0) = 0.14
P(Y=1 | X=1, V3=1) = 0.04
0.04 - (0.20*0.04 + 0.80*0.05) = -0.01
-0.01 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 16%. For people who do not like spicy food, the probability of attractive appearance is 92%. For people who like spicy food, the probability of attractive appearance is 92%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.92
0.16*0.92 - 0.84*0.92 = 0.92
0.92 > 0",collision,man_in_relationship,1,marginal,P(Y)
20095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.01.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 96%. For people who do not like spicy food and single people, the probability of attractive appearance is 96%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 78%. For people who like spicy food and single people, the probability of attractive appearance is 93%. For people who like spicy food and in a relationship, the probability of attractive appearance is 48%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.96
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.93
P(Y=1 | X=1, V3=1) = 0.48
0.48 - (0.96*0.48 + 0.04*0.78) = -0.04
-0.04 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20110,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 20%. For people who do not like spicy food, the probability of attractive appearance is 97%. For people who like spicy food, the probability of attractive appearance is 97%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.97
0.20*0.97 - 0.80*0.97 = 0.97
0.97 > 0",collision,man_in_relationship,1,marginal,P(Y)
20119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 20%. For people who do not like spicy food and single people, the probability of attractive appearance is 99%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 95%. For people who like spicy food and single people, the probability of attractive appearance is 99%. For people who like spicy food and in a relationship, the probability of attractive appearance is 93%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.20
P(Y=1 | X=0, V3=0) = 0.99
P(Y=1 | X=0, V3=1) = 0.95
P(Y=1 | X=1, V3=0) = 0.99
P(Y=1 | X=1, V3=1) = 0.93
0.93 - (0.20*0.93 + 0.80*0.95) = -0.01
-0.01 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.03.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.01.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 16%. For people who do not like spicy food and single people, the probability of attractive appearance is 100%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 96%. For people who like spicy food and single people, the probability of attractive appearance is 99%. For people who like spicy food and in a relationship, the probability of attractive appearance is 95%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.16
P(Y=1 | X=0, V3=0) = 1.00
P(Y=1 | X=0, V3=1) = 0.96
P(Y=1 | X=1, V3=0) = 0.99
P(Y=1 | X=1, V3=1) = 0.95
0.95 - (0.16*0.95 + 0.84*0.96) = -0.01
-0.01 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 95%. For people who do not like spicy food, the probability of attractive appearance is 89%. For people who like spicy food, the probability of attractive appearance is 89%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.89
P(Y=1 | X=1) = 0.89
0.95*0.89 - 0.05*0.89 = 0.89
0.89 > 0",collision,man_in_relationship,1,marginal,P(Y)
20150,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 14%. For people who do not like spicy food, the probability of attractive appearance is 92%. For people who like spicy food, the probability of attractive appearance is 92%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.92
0.14*0.92 - 0.86*0.92 = 0.92
0.92 > 0",collision,man_in_relationship,1,marginal,P(Y)
20151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 14%. For people who do not like spicy food, the probability of attractive appearance is 92%. For people who like spicy food, the probability of attractive appearance is 92%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.92
P(Y=1 | X=1) = 0.92
0.14*0.92 - 0.86*0.92 = 0.92
0.92 > 0",collision,man_in_relationship,1,marginal,P(Y)
20155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look directly at how liking spicy food correlates with appearance in general. Method 2: We look at this correlation case by case according to relationship status.",yes,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 14%. For people who do not like spicy food and single people, the probability of attractive appearance is 96%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 88%. For people who like spicy food and single people, the probability of attractive appearance is 98%. For people who like spicy food and in a relationship, the probability of attractive appearance is 84%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.14
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.88
P(Y=1 | X=1, V3=0) = 0.98
P(Y=1 | X=1, V3=1) = 0.84
0.84 - (0.14*0.84 + 0.86*0.88) = -0.03
-0.03 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 14%. For people who do not like spicy food and single people, the probability of attractive appearance is 96%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 88%. For people who like spicy food and single people, the probability of attractive appearance is 98%. For people who like spicy food and in a relationship, the probability of attractive appearance is 84%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.14
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.88
P(Y=1 | X=1, V3=0) = 0.98
P(Y=1 | X=1, V3=1) = 0.84
0.84 - (0.14*0.84 + 0.86*0.88) = -0.03
-0.03 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 17%. For people who do not like spicy food, the probability of attractive appearance is 10%. For people who like spicy food, the probability of attractive appearance is 10%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.10
P(Y=1 | X=1) = 0.10
0.17*0.10 - 0.83*0.10 = 0.10
0.10 > 0",collision,man_in_relationship,1,marginal,P(Y)
20167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.02.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 17%. For people who do not like spicy food and single people, the probability of attractive appearance is 22%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 7%. For people who like spicy food and single people, the probability of attractive appearance is 13%. For people who like spicy food and in a relationship, the probability of attractive appearance is 5%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.17
P(Y=1 | X=0, V3=0) = 0.22
P(Y=1 | X=0, V3=1) = 0.07
P(Y=1 | X=1, V3=0) = 0.13
P(Y=1 | X=1, V3=1) = 0.05
0.05 - (0.17*0.05 + 0.83*0.07) = -0.02
-0.02 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 17%. For people who do not like spicy food and single people, the probability of attractive appearance is 22%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 7%. For people who like spicy food and single people, the probability of attractive appearance is 13%. For people who like spicy food and in a relationship, the probability of attractive appearance is 5%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.17
P(Y=1 | X=0, V3=0) = 0.22
P(Y=1 | X=0, V3=1) = 0.07
P(Y=1 | X=1, V3=0) = 0.13
P(Y=1 | X=1, V3=1) = 0.05
0.05 - (0.17*0.05 + 0.83*0.07) = -0.02
-0.02 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 11%. For people who do not like spicy food, the probability of attractive appearance is 97%. For people who like spicy food, the probability of attractive appearance is 97%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.97
0.11*0.97 - 0.89*0.97 = 0.97
0.97 > 0",collision,man_in_relationship,1,marginal,P(Y)
20174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. Method 1: We look at how liking spicy food correlates with appearance case by case according to relationship status. Method 2: We look directly at how liking spicy food correlates with appearance in general.",no,"nan
nan
nan
nan
nan
nan
nan",collision,man_in_relationship,2,backadj,[backdoor adjustment set for Y given X]
20176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.01.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20177,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.01.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 94%. For people who do not like spicy food, the probability of attractive appearance is 97%. For people who like spicy food, the probability of attractive appearance is 97%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.97
P(Y=1 | X=1) = 0.97
0.94*0.97 - 0.06*0.97 = 0.97
0.97 > 0",collision,man_in_relationship,1,marginal,P(Y)
20186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.02.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20187,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.02.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
yes",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 94%. For people who do not like spicy food and single people, the probability of attractive appearance is 100%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 96%. For people who like spicy food and single people, the probability of attractive appearance is 99%. For people who like spicy food and in a relationship, the probability of attractive appearance is 95%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.94
P(Y=1 | X=0, V3=0) = 1.00
P(Y=1 | X=0, V3=1) = 0.96
P(Y=1 | X=1, V3=0) = 0.99
P(Y=1 | X=1, V3=1) = 0.95
0.95 - (0.94*0.95 + 0.06*0.96) = -0.00
0.00 = 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 19%. For people who do not like spicy food, the probability of attractive appearance is 88%. For people who like spicy food, the probability of attractive appearance is 88%.",yes,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.88
0.19*0.88 - 0.81*0.88 = 0.88
0.88 > 0",collision,man_in_relationship,1,marginal,P(Y)
20191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 19%. For people who do not like spicy food, the probability of attractive appearance is 88%. For people who like spicy food, the probability of attractive appearance is 88%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.88
0.19*0.88 - 0.81*0.88 = 0.88
0.88 > 0",collision,man_in_relationship,1,marginal,P(Y)
20199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 19%. For people who do not like spicy food and single people, the probability of attractive appearance is 94%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 74%. For people who like spicy food and single people, the probability of attractive appearance is 95%. For people who like spicy food and in a relationship, the probability of attractive appearance is 76%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.19
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.95
P(Y=1 | X=1, V3=1) = 0.76
0.76 - (0.19*0.76 + 0.81*0.74) = 0.02
0.02 > 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. For people in a relationship, the correlation between liking spicy food and attractive appearance is -0.05.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]
X and Y do not affect each other.

0
no",collision,man_in_relationship,2,collider_bias,"E[Y = 1 | do(X = 1), V3 = 1] - E[Y = 1 | do(X = 0), V3 = 1]"
20218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on relationship status. Appearance has a direct effect on relationship status. The overall probability of liking spicy food is 4%. For people who do not like spicy food and single people, the probability of attractive appearance is 95%. For people who do not like spicy food and in a relationship, the probability of attractive appearance is 82%. For people who like spicy food and single people, the probability of attractive appearance is 92%. For people who like spicy food and in a relationship, the probability of attractive appearance is 64%.",no,"Let Y = appearance; X = liking spicy food; V3 = relationship status.
X->V3,Y->V3
P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)
P(Y=1 | X=1, V3=1) - (P(X=1) * P(Y=1 | X=1, V3=1) + P(X=0) * P(Y=1 | X=0, V3=1))
P(X=1) = 0.04
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.64
0.64 - (0.04*0.64 + 0.96*0.82) = -0.19
-0.19 < 0",collision,man_in_relationship,1,exp_away,"P(Y = 1 | X = 1, V3 = 1] - P(Y = 1 | V3 = 1)"
20221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 90%. For children with intelligent parents, the probability of being lactose intolerant is 56%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.56
0.56 - 0.90 = -0.34
-0.34 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 90%. For children with intelligent parents, the probability of being lactose intolerant is 56%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.56
0.56 - 0.90 = -0.34
-0.34 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 88%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 89%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 57%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 49%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 78%. For children with unintelligent parents and confounder active, the probability of high parental social status is 41%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 50%. For children with intelligent parents and confounder active, the probability of high parental social status is 14%. The overall probability of confounder active is 48%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.78
P(V3=1 | X=0, V2=1) = 0.41
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.14
P(V2=1) = 0.48
0.48 * 0.89 * (0.14 - 0.50)+ 0.52 * 0.89 * (0.41 - 0.78)= 0.01
0.01 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 88%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 89%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 57%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 49%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 78%. For children with unintelligent parents and confounder active, the probability of high parental social status is 41%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 50%. For children with intelligent parents and confounder active, the probability of high parental social status is 14%. The overall probability of confounder active is 48%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.78
P(V3=1 | X=0, V2=1) = 0.41
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.14
P(V2=1) = 0.48
0.48 * 0.89 * (0.14 - 0.50)+ 0.52 * 0.89 * (0.41 - 0.78)= 0.01
0.01 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 88%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 89%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 57%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 49%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 78%. For children with unintelligent parents and confounder active, the probability of high parental social status is 41%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 50%. For children with intelligent parents and confounder active, the probability of high parental social status is 14%. The overall probability of confounder active is 48%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.78
P(V3=1 | X=0, V2=1) = 0.41
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.14
P(V2=1) = 0.48
0.48 * (0.49 - 0.57) * 0.41 + 0.52 * (0.89 - 0.88) * 0.50 = -0.35
-0.35 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 6%. For children with unintelligent parents, the probability of being lactose intolerant is 90%. For children with intelligent parents, the probability of being lactose intolerant is 56%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.56
0.06*0.56 - 0.94*0.90 = 0.88
0.88 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 6%. The probability of unintelligent parents and being lactose intolerant is 83%. The probability of intelligent parents and being lactose intolerant is 3%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.83
P(Y=1, X=1=1) = 0.03
0.03/0.06 - 0.83/0.94 = -0.34
-0.34 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 62%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.47
0.47 - 0.62 = -0.14
-0.14 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 62%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.47
0.47 - 0.62 = -0.14
-0.14 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 93%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 60%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 63%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 34%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 98%. For children with unintelligent parents and confounder active, the probability of high parental social status is 91%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 56%. For children with intelligent parents and confounder active, the probability of high parental social status is 51%. The overall probability of confounder active is 49%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.98
P(V3=1 | X=0, V2=1) = 0.91
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.51
P(V2=1) = 0.49
0.49 * 0.60 * (0.51 - 0.56)+ 0.51 * 0.60 * (0.91 - 0.98)= 0.14
0.14 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 93%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 60%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 63%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 34%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 98%. For children with unintelligent parents and confounder active, the probability of high parental social status is 91%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 56%. For children with intelligent parents and confounder active, the probability of high parental social status is 51%. The overall probability of confounder active is 49%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.98
P(V3=1 | X=0, V2=1) = 0.91
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.51
P(V2=1) = 0.49
0.49 * (0.34 - 0.63) * 0.91 + 0.51 * (0.60 - 0.93) * 0.56 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 3%. For children with unintelligent parents, the probability of being lactose intolerant is 62%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.47
0.03*0.47 - 0.97*0.62 = 0.61
0.61 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 3%. For children with unintelligent parents, the probability of being lactose intolerant is 62%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.47
0.03*0.47 - 0.97*0.62 = 0.61
0.61 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 3%. The probability of unintelligent parents and being lactose intolerant is 60%. The probability of intelligent parents and being lactose intolerant is 2%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.60
P(Y=1, X=1=1) = 0.02
0.02/0.03 - 0.60/0.97 = -0.14
-0.14 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 65%. For children with intelligent parents, the probability of being lactose intolerant is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.42
0.42 - 0.65 = -0.22
-0.22 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 65%. For children with intelligent parents, the probability of being lactose intolerant is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.42
0.42 - 0.65 = -0.22
-0.22 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 83%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 55%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 52%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 24%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 71%. For children with unintelligent parents and confounder active, the probability of high parental social status is 56%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 29%. For children with intelligent parents and confounder active, the probability of high parental social status is 47%. The overall probability of confounder active is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.24
P(V3=1 | X=0, V2=0) = 0.71
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.29
P(V3=1 | X=1, V2=1) = 0.47
P(V2=1) = 0.42
0.42 * (0.24 - 0.52) * 0.56 + 0.58 * (0.55 - 0.83) * 0.29 = -0.30
-0.30 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 19%. For children with unintelligent parents, the probability of being lactose intolerant is 65%. For children with intelligent parents, the probability of being lactose intolerant is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.42
0.19*0.42 - 0.81*0.65 = 0.61
0.61 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 19%. For children with unintelligent parents, the probability of being lactose intolerant is 65%. For children with intelligent parents, the probability of being lactose intolerant is 42%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.42
0.19*0.42 - 0.81*0.65 = 0.61
0.61 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 19%. The probability of unintelligent parents and being lactose intolerant is 53%. The probability of intelligent parents and being lactose intolerant is 8%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.08
0.08/0.19 - 0.53/0.81 = -0.23
-0.23 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 19%. The probability of unintelligent parents and being lactose intolerant is 53%. The probability of intelligent parents and being lactose intolerant is 8%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.08
0.08/0.19 - 0.53/0.81 = -0.23
-0.23 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 55%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 47%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 13%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 7%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 77%. For children with unintelligent parents and confounder active, the probability of high parental social status is 54%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 43%. For children with intelligent parents and confounder active, the probability of high parental social status is 20%. The overall probability of confounder active is 48%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.55
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.13
P(Y=1 | X=1, V3=1) = 0.07
P(V3=1 | X=0, V2=0) = 0.77
P(V3=1 | X=0, V2=1) = 0.54
P(V3=1 | X=1, V2=0) = 0.43
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.48
0.48 * 0.47 * (0.20 - 0.43)+ 0.52 * 0.47 * (0.54 - 0.77)= 0.02
0.02 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 55%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 47%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 13%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 7%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 77%. For children with unintelligent parents and confounder active, the probability of high parental social status is 54%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 43%. For children with intelligent parents and confounder active, the probability of high parental social status is 20%. The overall probability of confounder active is 48%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.55
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.13
P(Y=1 | X=1, V3=1) = 0.07
P(V3=1 | X=0, V2=0) = 0.77
P(V3=1 | X=0, V2=1) = 0.54
P(V3=1 | X=1, V2=0) = 0.43
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.48
0.48 * (0.07 - 0.13) * 0.54 + 0.52 * (0.47 - 0.55) * 0.43 = -0.41
-0.41 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 58%. For children with intelligent parents, the probability of being lactose intolerant is 39%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.39
0.39 - 0.58 = -0.19
-0.19 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 58%. For children with intelligent parents, the probability of being lactose intolerant is 39%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.39
0.39 - 0.58 = -0.19
-0.19 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20281,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 82%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 46%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 48%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 14%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 63%. For children with unintelligent parents and confounder active, the probability of high parental social status is 68%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 16%. For children with intelligent parents and confounder active, the probability of high parental social status is 30%. The overall probability of confounder active is 53%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.14
P(V3=1 | X=0, V2=0) = 0.63
P(V3=1 | X=0, V2=1) = 0.68
P(V3=1 | X=1, V2=0) = 0.16
P(V3=1 | X=1, V2=1) = 0.30
P(V2=1) = 0.53
0.53 * 0.46 * (0.30 - 0.16)+ 0.47 * 0.46 * (0.68 - 0.63)= 0.15
0.15 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 16%. For children with unintelligent parents, the probability of being lactose intolerant is 58%. For children with intelligent parents, the probability of being lactose intolerant is 39%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.39
0.16*0.39 - 0.84*0.58 = 0.55
0.55 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 16%. For children with unintelligent parents, the probability of being lactose intolerant is 58%. For children with intelligent parents, the probability of being lactose intolerant is 39%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.39
0.16*0.39 - 0.84*0.58 = 0.55
0.55 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 98%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 65%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 54%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 21%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 40%. For children with unintelligent parents and confounder active, the probability of high parental social status is 34%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 63%. For children with intelligent parents and confounder active, the probability of high parental social status is 51%. The overall probability of confounder active is 53%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.98
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.21
P(V3=1 | X=0, V2=0) = 0.40
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.51
P(V2=1) = 0.53
0.53 * 0.65 * (0.51 - 0.63)+ 0.47 * 0.65 * (0.34 - 0.40)= -0.06
-0.06 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20298,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 7%. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 35%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.07
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.35
0.07*0.35 - 0.93*0.86 = 0.82
0.82 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 7%. The probability of unintelligent parents and being lactose intolerant is 79%. The probability of intelligent parents and being lactose intolerant is 3%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.07
P(Y=1, X=0=1) = 0.79
P(Y=1, X=1=1) = 0.03
0.03/0.07 - 0.79/0.93 = -0.50
-0.50 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 48%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.48
0.48 - 0.86 = -0.38
-0.38 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20306,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 48%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.48
0.48 - 0.86 = -0.38
-0.38 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 48%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.48
0.48 - 0.86 = -0.38
-0.38 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 85%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 89%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 47%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 55%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 73%. For children with unintelligent parents and confounder active, the probability of high parental social status is 36%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 45%. For children with intelligent parents and confounder active, the probability of high parental social status is 6%. The overall probability of confounder active is 42%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.36
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.06
P(V2=1) = 0.42
0.42 * 0.89 * (0.06 - 0.45)+ 0.58 * 0.89 * (0.36 - 0.73)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 85%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 89%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 47%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 55%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 73%. For children with unintelligent parents and confounder active, the probability of high parental social status is 36%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 45%. For children with intelligent parents and confounder active, the probability of high parental social status is 6%. The overall probability of confounder active is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.36
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.06
P(V2=1) = 0.42
0.42 * 0.89 * (0.06 - 0.45)+ 0.58 * 0.89 * (0.36 - 0.73)= -0.01
-0.01 < 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 85%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 89%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 47%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 55%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 73%. For children with unintelligent parents and confounder active, the probability of high parental social status is 36%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 45%. For children with intelligent parents and confounder active, the probability of high parental social status is 6%. The overall probability of confounder active is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.47
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.36
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.06
P(V2=1) = 0.42
0.42 * (0.55 - 0.47) * 0.36 + 0.58 * (0.89 - 0.85) * 0.45 = -0.37
-0.37 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 9%. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 48%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.48
0.09*0.48 - 0.91*0.86 = 0.83
0.83 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20315,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 9%. The probability of unintelligent parents and being lactose intolerant is 79%. The probability of intelligent parents and being lactose intolerant is 5%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.79
P(Y=1, X=1=1) = 0.05
0.05/0.09 - 0.79/0.91 = -0.38
-0.38 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20317,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20318,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 73%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.46
0.46 - 0.73 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 73%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.46
0.46 - 0.73 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20321,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 73%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.46
0.46 - 0.73 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 95%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 70%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 59%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 33%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 91%. For children with unintelligent parents and confounder active, the probability of high parental social status is 88%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 59%. For children with intelligent parents and confounder active, the probability of high parental social status is 46%. The overall probability of confounder active is 55%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.70
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.33
P(V3=1 | X=0, V2=0) = 0.91
P(V3=1 | X=0, V2=1) = 0.88
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.55
0.55 * 0.70 * (0.46 - 0.59)+ 0.45 * 0.70 * (0.88 - 0.91)= 0.09
0.09 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. For children with unintelligent parents, the probability of being lactose intolerant is 73%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.46
0.14*0.46 - 0.86*0.73 = 0.69
0.69 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. For children with unintelligent parents, the probability of being lactose intolerant is 73%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.46
0.14*0.46 - 0.86*0.73 = 0.69
0.69 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. The probability of unintelligent parents and being lactose intolerant is 63%. The probability of intelligent parents and being lactose intolerant is 6%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.06
0.06/0.14 - 0.63/0.86 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 78%. For children with intelligent parents, the probability of being lactose intolerant is 54%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.54
0.54 - 0.78 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 78%. For children with intelligent parents, the probability of being lactose intolerant is 54%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.54
0.54 - 0.78 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 78%. For children with intelligent parents, the probability of being lactose intolerant is 54%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.54
0.54 - 0.78 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 2%. The probability of unintelligent parents and being lactose intolerant is 76%. The probability of intelligent parents and being lactose intolerant is 1%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.76
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.76/0.98 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 66%. For children with intelligent parents, the probability of being lactose intolerant is 23%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.23
0.23 - 0.66 = -0.43
-0.43 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 66%. For children with intelligent parents, the probability of being lactose intolerant is 23%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.23
0.23 - 0.66 = -0.43
-0.43 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20350,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 77%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 65%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 28%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 17%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 93%. For children with unintelligent parents and confounder active, the probability of high parental social status is 63%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 57%. For children with intelligent parents and confounder active, the probability of high parental social status is 29%. The overall probability of confounder active is 44%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.17
P(V3=1 | X=0, V2=0) = 0.93
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.29
P(V2=1) = 0.44
0.44 * 0.65 * (0.29 - 0.57)+ 0.56 * 0.65 * (0.63 - 0.93)= 0.04
0.04 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 77%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 65%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 28%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 17%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 93%. For children with unintelligent parents and confounder active, the probability of high parental social status is 63%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 57%. For children with intelligent parents and confounder active, the probability of high parental social status is 29%. The overall probability of confounder active is 44%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.17
P(V3=1 | X=0, V2=0) = 0.93
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.29
P(V2=1) = 0.44
0.44 * 0.65 * (0.29 - 0.57)+ 0.56 * 0.65 * (0.63 - 0.93)= 0.04
0.04 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 77%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 65%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 28%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 17%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 93%. For children with unintelligent parents and confounder active, the probability of high parental social status is 63%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 57%. For children with intelligent parents and confounder active, the probability of high parental social status is 29%. The overall probability of confounder active is 44%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.28
P(Y=1 | X=1, V3=1) = 0.17
P(V3=1 | X=0, V2=0) = 0.93
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.29
P(V2=1) = 0.44
0.44 * (0.17 - 0.28) * 0.63 + 0.56 * (0.65 - 0.77) * 0.57 = -0.47
-0.47 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. For children with unintelligent parents, the probability of being lactose intolerant is 66%. For children with intelligent parents, the probability of being lactose intolerant is 23%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.23
0.14*0.23 - 0.86*0.66 = 0.60
0.60 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. The probability of unintelligent parents and being lactose intolerant is 58%. The probability of intelligent parents and being lactose intolerant is 3%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.03
0.03/0.14 - 0.58/0.86 = -0.44
-0.44 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 71%. For children with intelligent parents, the probability of being lactose intolerant is 41%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.41
0.41 - 0.71 = -0.30
-0.30 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 71%. For children with intelligent parents, the probability of being lactose intolerant is 41%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.41
0.41 - 0.71 = -0.30
-0.30 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20364,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 95%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 54%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 48%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 20%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 56%. For children with unintelligent parents and confounder active, the probability of high parental social status is 62%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 31%. For children with intelligent parents and confounder active, the probability of high parental social status is 22%. The overall probability of confounder active is 49%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.20
P(V3=1 | X=0, V2=0) = 0.56
P(V3=1 | X=0, V2=1) = 0.62
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.49
0.49 * 0.54 * (0.22 - 0.31)+ 0.51 * 0.54 * (0.62 - 0.56)= 0.13
0.13 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 95%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 54%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 48%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 20%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 56%. For children with unintelligent parents and confounder active, the probability of high parental social status is 62%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 31%. For children with intelligent parents and confounder active, the probability of high parental social status is 22%. The overall probability of confounder active is 49%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.95
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.20
P(V3=1 | X=0, V2=0) = 0.56
P(V3=1 | X=0, V2=1) = 0.62
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.49
0.49 * (0.20 - 0.48) * 0.62 + 0.51 * (0.54 - 0.95) * 0.31 = -0.40
-0.40 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 11%. For children with unintelligent parents, the probability of being lactose intolerant is 71%. For children with intelligent parents, the probability of being lactose intolerant is 41%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.41
0.11*0.41 - 0.89*0.71 = 0.68
0.68 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 11%. The probability of unintelligent parents and being lactose intolerant is 63%. The probability of intelligent parents and being lactose intolerant is 4%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.63
P(Y=1, X=1=1) = 0.04
0.04/0.11 - 0.63/0.89 = -0.30
-0.30 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 58%. For children with intelligent parents, the probability of being lactose intolerant is 33%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.33
0.33 - 0.58 = -0.25
-0.25 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 58%. For children with intelligent parents, the probability of being lactose intolerant is 33%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.33
0.33 - 0.58 = -0.25
-0.25 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20378,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 67%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 42%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 40%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 16%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 22%. For children with unintelligent parents and confounder active, the probability of high parental social status is 59%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 35%. For children with intelligent parents and confounder active, the probability of high parental social status is 22%. The overall probability of confounder active is 46%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0, V2=0) = 0.22
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.46
0.46 * 0.42 * (0.22 - 0.35)+ 0.54 * 0.42 * (0.59 - 0.22)= 0.02
0.02 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 67%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 42%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 40%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 16%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 22%. For children with unintelligent parents and confounder active, the probability of high parental social status is 59%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 35%. For children with intelligent parents and confounder active, the probability of high parental social status is 22%. The overall probability of confounder active is 46%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0, V2=0) = 0.22
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.46
0.46 * (0.16 - 0.40) * 0.59 + 0.54 * (0.42 - 0.67) * 0.35 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 67%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 42%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 40%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 16%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 22%. For children with unintelligent parents and confounder active, the probability of high parental social status is 59%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 35%. For children with intelligent parents and confounder active, the probability of high parental social status is 22%. The overall probability of confounder active is 46%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.40
P(Y=1 | X=1, V3=1) = 0.16
P(V3=1 | X=0, V2=0) = 0.22
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.46
0.46 * (0.16 - 0.40) * 0.59 + 0.54 * (0.42 - 0.67) * 0.35 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. For children with unintelligent parents, the probability of being lactose intolerant is 58%. For children with intelligent parents, the probability of being lactose intolerant is 33%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.33
0.14*0.33 - 0.86*0.58 = 0.54
0.54 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. The probability of unintelligent parents and being lactose intolerant is 49%. The probability of intelligent parents and being lactose intolerant is 5%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.49
P(Y=1, X=1=1) = 0.05
0.05/0.14 - 0.49/0.86 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 88%. For children with intelligent parents, the probability of being lactose intolerant is 48%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.48
0.48 - 0.88 = -0.40
-0.40 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20392,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 92%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 85%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 51%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 47%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 80%. For children with unintelligent parents and confounder active, the probability of high parental social status is 34%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 44%. For children with intelligent parents and confounder active, the probability of high parental social status is 12%. The overall probability of confounder active is 52%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.92
P(Y=1 | X=0, V3=1) = 0.85
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.44
P(V3=1 | X=1, V2=1) = 0.12
P(V2=1) = 0.52
0.52 * 0.85 * (0.12 - 0.44)+ 0.48 * 0.85 * (0.34 - 0.80)= 0.01
0.01 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 17%. The probability of unintelligent parents and being lactose intolerant is 73%. The probability of intelligent parents and being lactose intolerant is 8%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.73
P(Y=1, X=1=1) = 0.08
0.08/0.17 - 0.73/0.83 = -0.39
-0.39 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 17%. The probability of unintelligent parents and being lactose intolerant is 73%. The probability of intelligent parents and being lactose intolerant is 8%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.73
P(Y=1, X=1=1) = 0.08
0.08/0.17 - 0.73/0.83 = -0.39
-0.39 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 53%. For children with intelligent parents, the probability of being lactose intolerant is 36%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.36
0.36 - 0.53 = -0.17
-0.17 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 53%. For children with intelligent parents, the probability of being lactose intolerant is 36%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.36
0.36 - 0.53 = -0.17
-0.17 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20408,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 68%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 43%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 43%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 20%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 67%. For children with unintelligent parents and confounder active, the probability of high parental social status is 56%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 36%. For children with intelligent parents and confounder active, the probability of high parental social status is 26%. The overall probability of confounder active is 47%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.43
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.20
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.36
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.47
0.47 * (0.20 - 0.43) * 0.56 + 0.53 * (0.43 - 0.68) * 0.36 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 13%. For children with unintelligent parents, the probability of being lactose intolerant is 53%. For children with intelligent parents, the probability of being lactose intolerant is 36%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.36
0.13*0.36 - 0.87*0.53 = 0.51
0.51 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 54%. For children with intelligent parents, the probability of being lactose intolerant is 19%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.19
0.19 - 0.54 = -0.35
-0.35 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 66%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 37%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 32%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 8%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 26%. For children with unintelligent parents and confounder active, the probability of high parental social status is 57%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 55%. For children with intelligent parents and confounder active, the probability of high parental social status is 54%. The overall probability of confounder active is 42%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.37
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.08
P(V3=1 | X=0, V2=0) = 0.26
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.55
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.42
0.42 * (0.08 - 0.32) * 0.57 + 0.58 * (0.37 - 0.66) * 0.55 = -0.31
-0.31 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 66%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 37%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 32%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 8%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 26%. For children with unintelligent parents and confounder active, the probability of high parental social status is 57%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 55%. For children with intelligent parents and confounder active, the probability of high parental social status is 54%. The overall probability of confounder active is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.37
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.08
P(V3=1 | X=0, V2=0) = 0.26
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.55
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.42
0.42 * (0.08 - 0.32) * 0.57 + 0.58 * (0.37 - 0.66) * 0.55 = -0.31
-0.31 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 11%. For children with unintelligent parents, the probability of being lactose intolerant is 54%. For children with intelligent parents, the probability of being lactose intolerant is 19%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.19
0.11*0.19 - 0.89*0.54 = 0.50
0.50 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20432,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 55%. For children with intelligent parents, the probability of being lactose intolerant is 17%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.17
0.17 - 0.55 = -0.38
-0.38 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20434,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 72%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 50%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 16%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 12%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 95%. For children with unintelligent parents and confounder active, the probability of high parental social status is 59%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 70%. For children with intelligent parents and confounder active, the probability of high parental social status is 25%. The overall probability of confounder active is 45%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.12
P(V3=1 | X=0, V2=0) = 0.95
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.70
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.45
0.45 * 0.50 * (0.25 - 0.70)+ 0.55 * 0.50 * (0.59 - 0.95)= 0.05
0.05 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 4%. For children with unintelligent parents, the probability of being lactose intolerant is 55%. For children with intelligent parents, the probability of being lactose intolerant is 17%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.17
0.04*0.17 - 0.96*0.55 = 0.53
0.53 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 37%. For children with intelligent parents, the probability of being lactose intolerant is 22%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.22
0.22 - 0.37 = -0.15
-0.15 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 59%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 29%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 33%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 4%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 74%. For children with unintelligent parents and confounder active, the probability of high parental social status is 72%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 45%. For children with intelligent parents and confounder active, the probability of high parental social status is 26%. The overall probability of confounder active is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.59
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.04
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.72
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.42
0.42 * 0.29 * (0.26 - 0.45)+ 0.58 * 0.29 * (0.72 - 0.74)= 0.11
0.11 > 0",arrowhead,nature_vs_nurture,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
20451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 59%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 29%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 33%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 4%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 74%. For children with unintelligent parents and confounder active, the probability of high parental social status is 72%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 45%. For children with intelligent parents and confounder active, the probability of high parental social status is 26%. The overall probability of confounder active is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.59
P(Y=1 | X=0, V3=1) = 0.29
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.04
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.72
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.42
0.42 * (0.04 - 0.33) * 0.72 + 0.58 * (0.29 - 0.59) * 0.45 = -0.26
-0.26 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 11%. For children with unintelligent parents, the probability of being lactose intolerant is 37%. For children with intelligent parents, the probability of being lactose intolerant is 22%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.11
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.22
0.11*0.22 - 0.89*0.37 = 0.36
0.36 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 11%. The probability of unintelligent parents and being lactose intolerant is 33%. The probability of intelligent parents and being lactose intolerant is 2%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.02
0.02/0.11 - 0.33/0.89 = -0.15
-0.15 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20464,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 66%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 34%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 35%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 8%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 50%. For children with unintelligent parents and confounder active, the probability of high parental social status is 76%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 70%. For children with intelligent parents and confounder active, the probability of high parental social status is 72%. The overall probability of confounder active is 49%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.66
P(Y=1 | X=0, V3=1) = 0.34
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.08
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.76
P(V3=1 | X=1, V2=0) = 0.70
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.49
0.49 * (0.08 - 0.35) * 0.76 + 0.51 * (0.34 - 0.66) * 0.70 = -0.29
-0.29 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20466,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 3%. For children with unintelligent parents, the probability of being lactose intolerant is 46%. For children with intelligent parents, the probability of being lactose intolerant is 16%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.16
0.03*0.16 - 0.97*0.46 = 0.46
0.46 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 3%. The probability of unintelligent parents and being lactose intolerant is 45%. The probability of intelligent parents and being lactose intolerant is 0%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.00
0.00/0.03 - 0.45/0.97 = -0.30
-0.30 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 3%. The probability of unintelligent parents and being lactose intolerant is 45%. The probability of intelligent parents and being lactose intolerant is 0%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.03
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.00
0.00/0.03 - 0.45/0.97 = -0.30
-0.30 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20473,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 90%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.47
0.47 - 0.90 = -0.42
-0.42 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 91%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 90%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 45%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 59%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 63%. For children with unintelligent parents and confounder active, the probability of high parental social status is 42%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 31%. For children with intelligent parents and confounder active, the probability of high parental social status is 9%. The overall probability of confounder active is 56%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.90
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.59
P(V3=1 | X=0, V2=0) = 0.63
P(V3=1 | X=0, V2=1) = 0.42
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.56
0.56 * (0.59 - 0.45) * 0.42 + 0.44 * (0.90 - 0.91) * 0.31 = -0.38
-0.38 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 91%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 90%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 45%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 59%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 63%. For children with unintelligent parents and confounder active, the probability of high parental social status is 42%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 31%. For children with intelligent parents and confounder active, the probability of high parental social status is 9%. The overall probability of confounder active is 56%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.90
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.59
P(V3=1 | X=0, V2=0) = 0.63
P(V3=1 | X=0, V2=1) = 0.42
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.56
0.56 * (0.59 - 0.45) * 0.42 + 0.44 * (0.90 - 0.91) * 0.31 = -0.38
-0.38 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 12%. For children with unintelligent parents, the probability of being lactose intolerant is 90%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.47
0.12*0.47 - 0.88*0.90 = 0.85
0.85 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 12%. For children with unintelligent parents, the probability of being lactose intolerant is 90%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.12
P(Y=1 | X=0) = 0.90
P(Y=1 | X=1) = 0.47
0.12*0.47 - 0.88*0.90 = 0.85
0.85 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 72%. For children with intelligent parents, the probability of being lactose intolerant is 58%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.58
0.58 - 0.72 = -0.15
-0.15 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 72%. For children with intelligent parents, the probability of being lactose intolerant is 58%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.58
0.58 - 0.72 = -0.15
-0.15 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20493,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 96%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 51%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 61%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 28%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 42%. For children with unintelligent parents and confounder active, the probability of high parental social status is 62%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 12%. For children with intelligent parents and confounder active, the probability of high parental social status is 6%. The overall probability of confounder active is 53%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.96
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.28
P(V3=1 | X=0, V2=0) = 0.42
P(V3=1 | X=0, V2=1) = 0.62
P(V3=1 | X=1, V2=0) = 0.12
P(V3=1 | X=1, V2=1) = 0.06
P(V2=1) = 0.53
0.53 * (0.28 - 0.61) * 0.62 + 0.47 * (0.51 - 0.96) * 0.12 = -0.29
-0.29 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20497,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 5%. The probability of unintelligent parents and being lactose intolerant is 68%. The probability of intelligent parents and being lactose intolerant is 3%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.68
P(Y=1, X=1=1) = 0.03
0.03/0.05 - 0.68/0.95 = -0.14
-0.14 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 76%. For children with intelligent parents, the probability of being lactose intolerant is 37%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.37
0.37 - 0.76 = -0.39
-0.39 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 83%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 46%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 55%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 20%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 24%. For children with unintelligent parents and confounder active, the probability of high parental social status is 6%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 40%. For children with intelligent parents and confounder active, the probability of high parental social status is 62%. The overall probability of confounder active is 44%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.20
P(V3=1 | X=0, V2=0) = 0.24
P(V3=1 | X=0, V2=1) = 0.06
P(V3=1 | X=1, V2=0) = 0.40
P(V3=1 | X=1, V2=1) = 0.62
P(V2=1) = 0.44
0.44 * (0.20 - 0.55) * 0.06 + 0.56 * (0.46 - 0.83) * 0.40 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. For children with unintelligent parents, the probability of being lactose intolerant is 76%. For children with intelligent parents, the probability of being lactose intolerant is 37%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.37
0.14*0.37 - 0.86*0.76 = 0.71
0.71 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. The probability of unintelligent parents and being lactose intolerant is 66%. The probability of intelligent parents and being lactose intolerant is 5%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.66
P(Y=1, X=1=1) = 0.05
0.05/0.14 - 0.66/0.86 = -0.39
-0.39 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 73%. For children with intelligent parents, the probability of being lactose intolerant is 42%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.42
0.42 - 0.73 = -0.31
-0.31 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20521,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 71%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 74%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 43%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 35%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 71%. For children with unintelligent parents and confounder active, the probability of high parental social status is 47%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 34%. For children with intelligent parents and confounder active, the probability of high parental social status is 8%. The overall probability of confounder active is 59%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.71
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.43
P(Y=1 | X=1, V3=1) = 0.35
P(V3=1 | X=0, V2=0) = 0.71
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.08
P(V2=1) = 0.59
0.59 * (0.35 - 0.43) * 0.47 + 0.41 * (0.74 - 0.71) * 0.34 = -0.34
-0.34 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 12%. The probability of unintelligent parents and being lactose intolerant is 64%. The probability of intelligent parents and being lactose intolerant is 5%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.64
P(Y=1, X=1=1) = 0.05
0.05/0.12 - 0.64/0.88 = -0.31
-0.31 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 49%. For children with intelligent parents, the probability of being lactose intolerant is 32%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.32
0.32 - 0.49 = -0.16
-0.16 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 49%. For children with intelligent parents, the probability of being lactose intolerant is 32%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.32
0.32 - 0.49 = -0.16
-0.16 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 68%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 38%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 41%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 10%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 66%. For children with unintelligent parents and confounder active, the probability of high parental social status is 61%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 23%. For children with intelligent parents and confounder active, the probability of high parental social status is 38%. The overall probability of confounder active is 41%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.41
P(Y=1 | X=1, V3=1) = 0.10
P(V3=1 | X=0, V2=0) = 0.66
P(V3=1 | X=0, V2=1) = 0.61
P(V3=1 | X=1, V2=0) = 0.23
P(V3=1 | X=1, V2=1) = 0.38
P(V2=1) = 0.41
0.41 * (0.10 - 0.41) * 0.61 + 0.59 * (0.38 - 0.68) * 0.23 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20536,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. For children with unintelligent parents, the probability of being lactose intolerant is 49%. For children with intelligent parents, the probability of being lactose intolerant is 32%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.32
0.14*0.32 - 0.86*0.49 = 0.46
0.46 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. The probability of unintelligent parents and being lactose intolerant is 42%. The probability of intelligent parents and being lactose intolerant is 5%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.05
0.05/0.14 - 0.42/0.86 = -0.16
-0.16 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20542,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.46
0.46 - 0.86 = -0.40
-0.40 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.46
0.46 - 0.86 = -0.40
-0.40 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.46
0.46 - 0.86 = -0.40
-0.40 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 91%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 67%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 64%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 39%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 31%. For children with unintelligent parents and confounder active, the probability of high parental social status is 10%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 63%. For children with intelligent parents and confounder active, the probability of high parental social status is 80%. The overall probability of confounder active is 53%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.91
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.31
P(V3=1 | X=0, V2=1) = 0.10
P(V3=1 | X=1, V2=0) = 0.63
P(V3=1 | X=1, V2=1) = 0.80
P(V2=1) = 0.53
0.53 * (0.39 - 0.64) * 0.10 + 0.47 * (0.67 - 0.91) * 0.63 = -0.27
-0.27 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 13%. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.46
0.13*0.46 - 0.87*0.86 = 0.81
0.81 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 13%. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 46%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.46
0.13*0.46 - 0.87*0.86 = 0.81
0.81 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 63%. For children with intelligent parents, the probability of being lactose intolerant is 29%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.29
0.29 - 0.63 = -0.34
-0.34 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20559,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 63%. For children with intelligent parents, the probability of being lactose intolerant is 29%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.29
0.29 - 0.63 = -0.34
-0.34 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 60%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 65%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 29%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 22%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 72%. For children with unintelligent parents and confounder active, the probability of high parental social status is 41%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 35%. For children with intelligent parents and confounder active, the probability of high parental social status is 12%. The overall probability of confounder active is 52%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.72
P(V3=1 | X=0, V2=1) = 0.41
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.12
P(V2=1) = 0.52
0.52 * (0.22 - 0.29) * 0.41 + 0.48 * (0.65 - 0.60) * 0.35 = -0.36
-0.36 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 60%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 65%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 29%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 22%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 72%. For children with unintelligent parents and confounder active, the probability of high parental social status is 41%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 35%. For children with intelligent parents and confounder active, the probability of high parental social status is 12%. The overall probability of confounder active is 52%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0, V2=0) = 0.72
P(V3=1 | X=0, V2=1) = 0.41
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.12
P(V2=1) = 0.52
0.52 * (0.22 - 0.29) * 0.41 + 0.48 * (0.65 - 0.60) * 0.35 = -0.36
-0.36 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 15%. For children with unintelligent parents, the probability of being lactose intolerant is 63%. For children with intelligent parents, the probability of being lactose intolerant is 29%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.29
0.15*0.29 - 0.85*0.63 = 0.57
0.57 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 15%. The probability of unintelligent parents and being lactose intolerant is 54%. The probability of intelligent parents and being lactose intolerant is 4%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.04
0.04/0.15 - 0.54/0.85 = -0.35
-0.35 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20570,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 52%. For children with intelligent parents, the probability of being lactose intolerant is 35%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.35
0.35 - 0.52 = -0.17
-0.17 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 52%. For children with intelligent parents, the probability of being lactose intolerant is 35%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.35
0.35 - 0.52 = -0.17
-0.17 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 75%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 50%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 48%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 21%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 96%. For children with unintelligent parents and confounder active, the probability of high parental social status is 90%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 50%. For children with intelligent parents and confounder active, the probability of high parental social status is 50%. The overall probability of confounder active is 49%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.50
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.21
P(V3=1 | X=0, V2=0) = 0.96
P(V3=1 | X=0, V2=1) = 0.90
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.49
0.49 * (0.21 - 0.48) * 0.90 + 0.51 * (0.50 - 0.75) * 0.50 = -0.29
-0.29 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 14%. For children with unintelligent parents, the probability of being lactose intolerant is 52%. For children with intelligent parents, the probability of being lactose intolerant is 35%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.35
0.14*0.35 - 0.86*0.52 = 0.49
0.49 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 49%. For children with intelligent parents, the probability of being lactose intolerant is 25%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.25
0.25 - 0.49 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 49%. For children with intelligent parents, the probability of being lactose intolerant is 25%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.25
0.25 - 0.49 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 17%. The probability of unintelligent parents and being lactose intolerant is 40%. The probability of intelligent parents and being lactose intolerant is 4%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.04
0.04/0.17 - 0.40/0.83 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20595,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 17%. The probability of unintelligent parents and being lactose intolerant is 40%. The probability of intelligent parents and being lactose intolerant is 4%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.04
0.04/0.17 - 0.40/0.83 = -0.24
-0.24 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20600,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 50%. For children with intelligent parents, the probability of being lactose intolerant is 28%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.28
0.28 - 0.50 = -0.22
-0.22 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 50%. For children with intelligent parents, the probability of being lactose intolerant is 28%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.28
0.28 - 0.50 = -0.22
-0.22 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 16%. The probability of unintelligent parents and being lactose intolerant is 42%. The probability of intelligent parents and being lactose intolerant is 4%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.04
0.04/0.16 - 0.42/0.84 = -0.21
-0.21 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look directly at how parents' intelligence correlates with lactose intolerance in general. Method 2: We look at this correlation case by case according to parents' social status.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 63%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 40%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 39%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 13%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 37%. For children with unintelligent parents and confounder active, the probability of high parental social status is 53%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 31%. For children with intelligent parents and confounder active, the probability of high parental social status is 60%. The overall probability of confounder active is 50%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.63
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.13
P(V3=1 | X=0, V2=0) = 0.37
P(V3=1 | X=0, V2=1) = 0.53
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.50
0.50 * (0.13 - 0.39) * 0.53 + 0.50 * (0.40 - 0.63) * 0.31 = -0.25
-0.25 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20619,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 63%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 40%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 39%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 13%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 37%. For children with unintelligent parents and confounder active, the probability of high parental social status is 53%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 31%. For children with intelligent parents and confounder active, the probability of high parental social status is 60%. The overall probability of confounder active is 50%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.63
P(Y=1 | X=0, V3=1) = 0.40
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.13
P(V3=1 | X=0, V2=0) = 0.37
P(V3=1 | X=0, V2=1) = 0.53
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.60
P(V2=1) = 0.50
0.50 * (0.13 - 0.39) * 0.53 + 0.50 * (0.40 - 0.63) * 0.31 = -0.25
-0.25 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20620,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 19%. For children with unintelligent parents, the probability of being lactose intolerant is 53%. For children with intelligent parents, the probability of being lactose intolerant is 28%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.28
0.19*0.28 - 0.81*0.53 = 0.48
0.48 > 0",arrowhead,nature_vs_nurture,1,marginal,P(Y)
20622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. The overall probability of intelligent parents is 19%. The probability of unintelligent parents and being lactose intolerant is 42%. The probability of intelligent parents and being lactose intolerant is 5%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.05
0.05/0.19 - 0.42/0.81 = -0.25
-0.25 < 0",arrowhead,nature_vs_nurture,1,correlation,P(Y | X)
20626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.47
0.47 - 0.86 = -0.39
-0.39 < 0",arrowhead,nature_vs_nurture,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents, the probability of being lactose intolerant is 86%. For children with intelligent parents, the probability of being lactose intolerant is 47%.",no,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.47
0.47 - 0.86 = -0.39
-0.39 < 0",arrowhead,nature_vs_nurture,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20633,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. For children with unintelligent parents and with low parental social status, the probability of being lactose intolerant is 89%. For children with unintelligent parents and with high parental social status, the probability of being lactose intolerant is 86%. For children with intelligent parents and with low parental social status, the probability of being lactose intolerant is 45%. For children with intelligent parents and with high parental social status, the probability of being lactose intolerant is 47%. For children with unintelligent parents and confounder inactive, the probability of high parental social status is 92%. For children with unintelligent parents and confounder active, the probability of high parental social status is 70%. For children with intelligent parents and confounder inactive, the probability of high parental social status is 55%. For children with intelligent parents and confounder active, the probability of high parental social status is 24%. The overall probability of confounder active is 49%.",yes,"Let V2 = other unobserved factors; X = parents' intelligence; V3 = parents' social status; Y = lactose intolerance.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.89
P(Y=1 | X=0, V3=1) = 0.86
P(Y=1 | X=1, V3=0) = 0.45
P(Y=1 | X=1, V3=1) = 0.47
P(V3=1 | X=0, V2=0) = 0.92
P(V3=1 | X=0, V2=1) = 0.70
P(V3=1 | X=1, V2=0) = 0.55
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.49
0.49 * (0.47 - 0.45) * 0.70 + 0.51 * (0.86 - 0.89) * 0.55 = -0.37
-0.37 < 0",arrowhead,nature_vs_nurture,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
20638,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Parents' intelligence has a direct effect on parents' social status and lactose intolerance. Other unobserved factors has a direct effect on parents' social status and lactose intolerance. Parents' social status has a direct effect on lactose intolerance. Other unobserved factors is unobserved. Method 1: We look at how parents' intelligence correlates with lactose intolerance case by case according to parents' social status. Method 2: We look directly at how parents' intelligence correlates with lactose intolerance in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,nature_vs_nurture,2,backadj,[backdoor adjustment set for Y given X]
20642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 40%. For smokers, the probability of freckles is 74%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.74
0.74 - 0.40 = 0.33
0.33 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 40%. For smokers, the probability of freckles is 74%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.74
0.74 - 0.40 = 0.33
0.33 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 53%. For nonsmokers and are hard-working, the probability of freckles is 20%. For smokers and are lazy, the probability of freckles is 89%. For smokers and are hard-working, the probability of freckles is 65%. For nonsmokers, the probability of being hard-working is 38%. For smokers, the probability of being hard-working is 63%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.20
P(Y=1 | X=1, V2=0) = 0.89
P(Y=1 | X=1, V2=1) = 0.65
P(V2=1 | X=0) = 0.38
P(V2=1 | X=1) = 0.63
0.63 * (0.20 - 0.53)+ 0.38 * (0.65 - 0.89)= -0.08
-0.08 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 93%. For nonsmokers, the probability of freckles is 40%. For smokers, the probability of freckles is 74%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.74
0.93*0.74 - 0.07*0.40 = 0.71
0.71 > 0",mediation,neg_mediation,1,marginal,P(Y)
20652,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20654,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 41%. For smokers, the probability of freckles is 31%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.31
0.31 - 0.41 = -0.10
-0.10 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 46%. For nonsmokers and are hard-working, the probability of freckles is 25%. For smokers and are lazy, the probability of freckles is 49%. For smokers and are hard-working, the probability of freckles is 21%. For nonsmokers, the probability of being hard-working is 24%. For smokers, the probability of being hard-working is 66%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.46
P(Y=1 | X=0, V2=1) = 0.25
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.24
P(V2=1 | X=1) = 0.66
0.66 * (0.25 - 0.46)+ 0.24 * (0.21 - 0.49)= -0.09
-0.09 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 46%. For nonsmokers and are hard-working, the probability of freckles is 25%. For smokers and are lazy, the probability of freckles is 49%. For smokers and are hard-working, the probability of freckles is 21%. For nonsmokers, the probability of being hard-working is 24%. For smokers, the probability of being hard-working is 66%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.46
P(Y=1 | X=0, V2=1) = 0.25
P(Y=1 | X=1, V2=0) = 0.49
P(Y=1 | X=1, V2=1) = 0.21
P(V2=1 | X=0) = 0.24
P(V2=1 | X=1) = 0.66
0.24 * (0.21 - 0.49) + 0.66 * (0.25 - 0.46) = 0.02
0.02 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 85%. The probability of nonsmoking and freckles is 6%. The probability of smoking and freckles is 26%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.26
0.26/0.85 - 0.06/0.15 = -0.10
-0.10 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 47%. For smokers, the probability of freckles is 45%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.45
0.45 - 0.47 = -0.03
-0.03 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 59%. For nonsmokers and are hard-working, the probability of freckles is 25%. For smokers and are lazy, the probability of freckles is 66%. For smokers and are hard-working, the probability of freckles is 29%. For nonsmokers, the probability of being hard-working is 34%. For smokers, the probability of being hard-working is 58%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.25
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.34
P(V2=1 | X=1) = 0.58
0.58 * (0.25 - 0.59)+ 0.34 * (0.29 - 0.66)= -0.08
-0.08 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20674,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 59%. For nonsmokers and are hard-working, the probability of freckles is 25%. For smokers and are lazy, the probability of freckles is 66%. For smokers and are hard-working, the probability of freckles is 29%. For nonsmokers, the probability of being hard-working is 34%. For smokers, the probability of being hard-working is 58%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.25
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.34
P(V2=1 | X=1) = 0.58
0.34 * (0.29 - 0.66) + 0.58 * (0.25 - 0.59) = 0.06
0.06 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 59%. For nonsmokers and are hard-working, the probability of freckles is 25%. For smokers and are lazy, the probability of freckles is 66%. For smokers and are hard-working, the probability of freckles is 29%. For nonsmokers, the probability of being hard-working is 34%. For smokers, the probability of being hard-working is 58%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.59
P(Y=1 | X=0, V2=1) = 0.25
P(Y=1 | X=1, V2=0) = 0.66
P(Y=1 | X=1, V2=1) = 0.29
P(V2=1 | X=0) = 0.34
P(V2=1 | X=1) = 0.58
0.34 * (0.29 - 0.66) + 0.58 * (0.25 - 0.59) = 0.06
0.06 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 92%. For nonsmokers, the probability of freckles is 47%. For smokers, the probability of freckles is 45%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.45
0.92*0.45 - 0.08*0.47 = 0.45
0.45 > 0",mediation,neg_mediation,1,marginal,P(Y)
20679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 92%. The probability of nonsmoking and freckles is 4%. The probability of smoking and freckles is 41%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.41
0.41/0.92 - 0.04/0.08 = -0.03
-0.03 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 55%. For nonsmokers and are hard-working, the probability of freckles is 24%. For smokers and are lazy, the probability of freckles is 81%. For smokers and are hard-working, the probability of freckles is 59%. For nonsmokers, the probability of being hard-working is 2%. For smokers, the probability of being hard-working is 59%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.55
P(Y=1 | X=0, V2=1) = 0.24
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.02
P(V2=1 | X=1) = 0.59
0.59 * (0.24 - 0.55)+ 0.02 * (0.59 - 0.81)= -0.18
-0.18 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 55%. For nonsmokers and are hard-working, the probability of freckles is 24%. For smokers and are lazy, the probability of freckles is 81%. For smokers and are hard-working, the probability of freckles is 59%. For nonsmokers, the probability of being hard-working is 2%. For smokers, the probability of being hard-working is 59%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.55
P(Y=1 | X=0, V2=1) = 0.24
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.02
P(V2=1 | X=1) = 0.59
0.02 * (0.59 - 0.81) + 0.59 * (0.24 - 0.55) = 0.27
0.27 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20693,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 91%. The probability of nonsmoking and freckles is 5%. The probability of smoking and freckles is 62%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.62
0.62/0.91 - 0.05/0.09 = 0.14
0.14 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
20696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 51%. For smokers, the probability of freckles is 37%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.37
0.37 - 0.51 = -0.14
-0.14 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 51%. For smokers, the probability of freckles is 37%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.37
0.37 - 0.51 = -0.14
-0.14 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 61%. For nonsmokers and are hard-working, the probability of freckles is 41%. For smokers and are lazy, the probability of freckles is 74%. For smokers and are hard-working, the probability of freckles is 31%. For nonsmokers, the probability of being hard-working is 50%. For smokers, the probability of being hard-working is 86%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.61
P(Y=1 | X=0, V2=1) = 0.41
P(Y=1 | X=1, V2=0) = 0.74
P(Y=1 | X=1, V2=1) = 0.31
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.86
0.86 * (0.41 - 0.61)+ 0.50 * (0.31 - 0.74)= -0.07
-0.07 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 61%. For nonsmokers and are hard-working, the probability of freckles is 41%. For smokers and are lazy, the probability of freckles is 74%. For smokers and are hard-working, the probability of freckles is 31%. For nonsmokers, the probability of being hard-working is 50%. For smokers, the probability of being hard-working is 86%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.61
P(Y=1 | X=0, V2=1) = 0.41
P(Y=1 | X=1, V2=0) = 0.74
P(Y=1 | X=1, V2=1) = 0.31
P(V2=1 | X=0) = 0.50
P(V2=1 | X=1) = 0.86
0.86 * (0.41 - 0.61)+ 0.50 * (0.31 - 0.74)= -0.07
-0.07 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 83%. For nonsmokers, the probability of freckles is 51%. For smokers, the probability of freckles is 37%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.37
0.83*0.37 - 0.17*0.51 = 0.40
0.40 > 0",mediation,neg_mediation,1,marginal,P(Y)
20708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 27%. For smokers, the probability of freckles is 17%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.17
0.17 - 0.27 = -0.10
-0.10 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20716,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 47%. For nonsmokers and are hard-working, the probability of freckles is 9%. For smokers and are lazy, the probability of freckles is 55%. For smokers and are hard-working, the probability of freckles is 14%. For nonsmokers, the probability of being hard-working is 54%. For smokers, the probability of being hard-working is 94%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.55
P(Y=1 | X=1, V2=1) = 0.14
P(V2=1 | X=0) = 0.54
P(V2=1 | X=1) = 0.94
0.54 * (0.14 - 0.55) + 0.94 * (0.09 - 0.47) = 0.06
0.06 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 82%. For nonsmokers, the probability of freckles is 27%. For smokers, the probability of freckles is 17%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.17
0.82*0.17 - 0.18*0.27 = 0.19
0.19 > 0",mediation,neg_mediation,1,marginal,P(Y)
20719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 82%. For nonsmokers, the probability of freckles is 27%. For smokers, the probability of freckles is 17%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.17
0.82*0.17 - 0.18*0.27 = 0.19
0.19 > 0",mediation,neg_mediation,1,marginal,P(Y)
20720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 82%. The probability of nonsmoking and freckles is 5%. The probability of smoking and freckles is 14%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.14
0.14/0.82 - 0.05/0.18 = -0.10
-0.10 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 51%. For smokers, the probability of freckles is 64%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.64
0.64 - 0.51 = 0.12
0.12 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 53%. For nonsmokers and are hard-working, the probability of freckles is 19%. For smokers and are lazy, the probability of freckles is 75%. For smokers and are hard-working, the probability of freckles is 47%. For nonsmokers, the probability of being hard-working is 4%. For smokers, the probability of being hard-working is 42%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.19
P(Y=1 | X=1, V2=0) = 0.75
P(Y=1 | X=1, V2=1) = 0.47
P(V2=1 | X=0) = 0.04
P(V2=1 | X=1) = 0.42
0.42 * (0.19 - 0.53)+ 0.04 * (0.47 - 0.75)= -0.13
-0.13 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20735,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 90%. The probability of nonsmoking and freckles is 5%. The probability of smoking and freckles is 57%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.57
0.57/0.90 - 0.05/0.10 = 0.12
0.12 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
20737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 63%. For smokers, the probability of freckles is 54%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.54
0.54 - 0.63 = -0.09
-0.09 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 63%. For smokers, the probability of freckles is 54%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.54
0.54 - 0.63 = -0.09
-0.09 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20742,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 68%. For nonsmokers and are hard-working, the probability of freckles is 45%. For smokers and are lazy, the probability of freckles is 84%. For smokers and are hard-working, the probability of freckles is 33%. For nonsmokers, the probability of being hard-working is 19%. For smokers, the probability of being hard-working is 58%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.68
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.84
P(Y=1 | X=1, V2=1) = 0.33
P(V2=1 | X=0) = 0.19
P(V2=1 | X=1) = 0.58
0.58 * (0.45 - 0.68)+ 0.19 * (0.33 - 0.84)= -0.09
-0.09 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 68%. For nonsmokers and are hard-working, the probability of freckles is 45%. For smokers and are lazy, the probability of freckles is 84%. For smokers and are hard-working, the probability of freckles is 33%. For nonsmokers, the probability of being hard-working is 19%. For smokers, the probability of being hard-working is 58%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.68
P(Y=1 | X=0, V2=1) = 0.45
P(Y=1 | X=1, V2=0) = 0.84
P(Y=1 | X=1, V2=1) = 0.33
P(V2=1 | X=0) = 0.19
P(V2=1 | X=1) = 0.58
0.19 * (0.33 - 0.84) + 0.58 * (0.45 - 0.68) = 0.11
0.11 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 86%. For nonsmokers, the probability of freckles is 63%. For smokers, the probability of freckles is 54%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.54
0.86*0.54 - 0.14*0.63 = 0.57
0.57 > 0",mediation,neg_mediation,1,marginal,P(Y)
20749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 86%. The probability of nonsmoking and freckles is 9%. The probability of smoking and freckles is 47%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.86
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.47
0.47/0.86 - 0.09/0.14 = -0.09
-0.09 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20752,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 85%. For smokers, the probability of freckles is 47%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.47
0.47 - 0.85 = -0.38
-0.38 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 85%. For smokers, the probability of freckles is 47%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.47
0.47 - 0.85 = -0.38
-0.38 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 92%. For nonsmokers and are hard-working, the probability of freckles is 50%. For smokers and are lazy, the probability of freckles is 80%. For smokers and are hard-working, the probability of freckles is 36%. For nonsmokers, the probability of being hard-working is 17%. For smokers, the probability of being hard-working is 74%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.92
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.80
P(Y=1 | X=1, V2=1) = 0.36
P(V2=1 | X=0) = 0.17
P(V2=1 | X=1) = 0.74
0.74 * (0.50 - 0.92)+ 0.17 * (0.36 - 0.80)= -0.25
-0.25 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 92%. For nonsmokers and are hard-working, the probability of freckles is 50%. For smokers and are lazy, the probability of freckles is 80%. For smokers and are hard-working, the probability of freckles is 36%. For nonsmokers, the probability of being hard-working is 17%. For smokers, the probability of being hard-working is 74%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.92
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.80
P(Y=1 | X=1, V2=1) = 0.36
P(V2=1 | X=0) = 0.17
P(V2=1 | X=1) = 0.74
0.17 * (0.36 - 0.80) + 0.74 * (0.50 - 0.92) = -0.12
-0.12 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 92%. For nonsmokers and are hard-working, the probability of freckles is 50%. For smokers and are lazy, the probability of freckles is 80%. For smokers and are hard-working, the probability of freckles is 36%. For nonsmokers, the probability of being hard-working is 17%. For smokers, the probability of being hard-working is 74%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.92
P(Y=1 | X=0, V2=1) = 0.50
P(Y=1 | X=1, V2=0) = 0.80
P(Y=1 | X=1, V2=1) = 0.36
P(V2=1 | X=0) = 0.17
P(V2=1 | X=1) = 0.74
0.17 * (0.36 - 0.80) + 0.74 * (0.50 - 0.92) = -0.12
-0.12 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 82%. For nonsmokers, the probability of freckles is 85%. For smokers, the probability of freckles is 47%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.47
0.82*0.47 - 0.18*0.85 = 0.54
0.54 > 0",mediation,neg_mediation,1,marginal,P(Y)
20762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 82%. The probability of nonsmoking and freckles is 16%. The probability of smoking and freckles is 39%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.39
0.39/0.82 - 0.16/0.18 = -0.38
-0.38 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 44%. For smokers, the probability of freckles is 66%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.66
0.66 - 0.44 = 0.23
0.23 > 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 44%. For smokers, the probability of freckles is 66%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.66
0.66 - 0.44 = 0.23
0.23 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 44%. For smokers, the probability of freckles is 66%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.66
0.66 - 0.44 = 0.23
0.23 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 93%. For nonsmokers, the probability of freckles is 44%. For smokers, the probability of freckles is 66%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.66
0.93*0.66 - 0.07*0.44 = 0.65
0.65 > 0",mediation,neg_mediation,1,marginal,P(Y)
20775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 93%. For nonsmokers, the probability of freckles is 44%. For smokers, the probability of freckles is 66%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.66
0.93*0.66 - 0.07*0.44 = 0.65
0.65 > 0",mediation,neg_mediation,1,marginal,P(Y)
20777,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 93%. The probability of nonsmoking and freckles is 3%. The probability of smoking and freckles is 62%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.62
0.62/0.93 - 0.03/0.07 = 0.23
0.23 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
20778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20782,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 56%. For smokers, the probability of freckles is 26%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.26
0.26 - 0.56 = -0.30
-0.30 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 84%. For nonsmokers, the probability of freckles is 56%. For smokers, the probability of freckles is 26%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.26
0.84*0.26 - 0.16*0.56 = 0.32
0.32 > 0",mediation,neg_mediation,1,marginal,P(Y)
20796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 53%. For smokers, the probability of freckles is 29%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.29
0.29 - 0.53 = -0.24
-0.24 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 53%. For smokers, the probability of freckles is 29%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.29
0.29 - 0.53 = -0.24
-0.24 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 55%. For nonsmokers and are hard-working, the probability of freckles is 29%. For smokers and are lazy, the probability of freckles is 63%. For smokers and are hard-working, the probability of freckles is 26%. For nonsmokers, the probability of being hard-working is 9%. For smokers, the probability of being hard-working is 92%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.55
P(Y=1 | X=0, V2=1) = 0.29
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.26
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.92
0.92 * (0.29 - 0.55)+ 0.09 * (0.26 - 0.63)= -0.22
-0.22 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 55%. For nonsmokers and are hard-working, the probability of freckles is 29%. For smokers and are lazy, the probability of freckles is 63%. For smokers and are hard-working, the probability of freckles is 26%. For nonsmokers, the probability of being hard-working is 9%. For smokers, the probability of being hard-working is 92%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.55
P(Y=1 | X=0, V2=1) = 0.29
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.26
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.92
0.92 * (0.29 - 0.55)+ 0.09 * (0.26 - 0.63)= -0.22
-0.22 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 55%. For nonsmokers and are hard-working, the probability of freckles is 29%. For smokers and are lazy, the probability of freckles is 63%. For smokers and are hard-working, the probability of freckles is 26%. For nonsmokers, the probability of being hard-working is 9%. For smokers, the probability of being hard-working is 92%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.55
P(Y=1 | X=0, V2=1) = 0.29
P(Y=1 | X=1, V2=0) = 0.63
P(Y=1 | X=1, V2=1) = 0.26
P(V2=1 | X=0) = 0.09
P(V2=1 | X=1) = 0.92
0.09 * (0.26 - 0.63) + 0.92 * (0.29 - 0.55) = 0.07
0.07 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 97%. For nonsmokers, the probability of freckles is 53%. For smokers, the probability of freckles is 29%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.29
0.97*0.29 - 0.03*0.53 = 0.30
0.30 > 0",mediation,neg_mediation,1,marginal,P(Y)
20804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 97%. The probability of nonsmoking and freckles is 2%. The probability of smoking and freckles is 28%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.28
0.28/0.97 - 0.02/0.03 = -0.24
-0.24 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 29%. For smokers, the probability of freckles is 62%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.62
0.62 - 0.29 = 0.32
0.32 > 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 29%. For smokers, the probability of freckles is 62%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.62
0.62 - 0.29 = 0.32
0.32 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20815,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 40%. For nonsmokers and are hard-working, the probability of freckles is 8%. For smokers and are lazy, the probability of freckles is 85%. For smokers and are hard-working, the probability of freckles is 52%. For nonsmokers, the probability of being hard-working is 33%. For smokers, the probability of being hard-working is 70%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.40
P(Y=1 | X=0, V2=1) = 0.08
P(Y=1 | X=1, V2=0) = 0.85
P(Y=1 | X=1, V2=1) = 0.52
P(V2=1 | X=0) = 0.33
P(V2=1 | X=1) = 0.70
0.33 * (0.52 - 0.85) + 0.70 * (0.08 - 0.40) = 0.45
0.45 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 89%. For nonsmokers, the probability of freckles is 29%. For smokers, the probability of freckles is 62%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.62
0.89*0.62 - 0.11*0.29 = 0.58
0.58 > 0",mediation,neg_mediation,1,marginal,P(Y)
20818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 89%. The probability of nonsmoking and freckles is 3%. The probability of smoking and freckles is 55%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.55
0.55/0.89 - 0.03/0.11 = 0.32
0.32 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
20819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 89%. The probability of nonsmoking and freckles is 3%. The probability of smoking and freckles is 55%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.55
0.55/0.89 - 0.03/0.11 = 0.32
0.32 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
20820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 72%. For nonsmokers and are hard-working, the probability of freckles is 48%. For smokers and are lazy, the probability of freckles is 85%. For smokers and are hard-working, the probability of freckles is 38%. For nonsmokers, the probability of being hard-working is 21%. For smokers, the probability of being hard-working is 92%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.72
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.85
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.21
P(V2=1 | X=1) = 0.92
0.92 * (0.48 - 0.72)+ 0.21 * (0.38 - 0.85)= -0.18
-0.18 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 72%. For nonsmokers and are hard-working, the probability of freckles is 48%. For smokers and are lazy, the probability of freckles is 85%. For smokers and are hard-working, the probability of freckles is 38%. For nonsmokers, the probability of being hard-working is 21%. For smokers, the probability of being hard-working is 92%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.72
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.85
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.21
P(V2=1 | X=1) = 0.92
0.21 * (0.38 - 0.85) + 0.92 * (0.48 - 0.72) = 0.08
0.08 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 81%. For nonsmokers, the probability of freckles is 67%. For smokers, the probability of freckles is 41%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.41
0.81*0.41 - 0.19*0.67 = 0.49
0.49 > 0",mediation,neg_mediation,1,marginal,P(Y)
20832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 81%. The probability of nonsmoking and freckles is 13%. The probability of smoking and freckles is 34%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.34
0.34/0.81 - 0.13/0.19 = -0.25
-0.25 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 71%. For smokers, the probability of freckles is 58%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.58
0.58 - 0.71 = -0.13
-0.13 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 78%. For nonsmokers and are hard-working, the probability of freckles is 28%. For smokers and are lazy, the probability of freckles is 75%. For smokers and are hard-working, the probability of freckles is 39%. For nonsmokers, the probability of being hard-working is 14%. For smokers, the probability of being hard-working is 47%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.78
P(Y=1 | X=0, V2=1) = 0.28
P(Y=1 | X=1, V2=0) = 0.75
P(Y=1 | X=1, V2=1) = 0.39
P(V2=1 | X=0) = 0.14
P(V2=1 | X=1) = 0.47
0.14 * (0.39 - 0.75) + 0.47 * (0.28 - 0.78) = -0.01
-0.01 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20844,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 94%. For nonsmokers, the probability of freckles is 71%. For smokers, the probability of freckles is 58%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.58
0.94*0.58 - 0.06*0.71 = 0.59
0.59 > 0",mediation,neg_mediation,1,marginal,P(Y)
20845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 94%. For nonsmokers, the probability of freckles is 71%. For smokers, the probability of freckles is 58%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.71
P(Y=1 | X=1) = 0.58
0.94*0.58 - 0.06*0.71 = 0.59
0.59 > 0",mediation,neg_mediation,1,marginal,P(Y)
20847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 94%. The probability of nonsmoking and freckles is 5%. The probability of smoking and freckles is 54%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.94
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.54
0.54/0.94 - 0.05/0.06 = -0.13
-0.13 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20853,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 32%. For smokers, the probability of freckles is 44%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.44
0.44 - 0.32 = 0.11
0.11 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 38%. For nonsmokers and are hard-working, the probability of freckles is 9%. For smokers and are lazy, the probability of freckles is 65%. For smokers and are hard-working, the probability of freckles is 38%. For nonsmokers, the probability of being hard-working is 20%. For smokers, the probability of being hard-working is 79%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.65
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.79
0.79 * (0.09 - 0.38)+ 0.20 * (0.38 - 0.65)= -0.17
-0.17 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 38%. For nonsmokers and are hard-working, the probability of freckles is 9%. For smokers and are lazy, the probability of freckles is 65%. For smokers and are hard-working, the probability of freckles is 38%. For nonsmokers, the probability of being hard-working is 20%. For smokers, the probability of being hard-working is 79%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.65
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.79
0.79 * (0.09 - 0.38)+ 0.20 * (0.38 - 0.65)= -0.17
-0.17 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 38%. For nonsmokers and are hard-working, the probability of freckles is 9%. For smokers and are lazy, the probability of freckles is 65%. For smokers and are hard-working, the probability of freckles is 38%. For nonsmokers, the probability of being hard-working is 20%. For smokers, the probability of being hard-working is 79%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.38
P(Y=1 | X=0, V2=1) = 0.09
P(Y=1 | X=1, V2=0) = 0.65
P(Y=1 | X=1, V2=1) = 0.38
P(V2=1 | X=0) = 0.20
P(V2=1 | X=1) = 0.79
0.20 * (0.38 - 0.65) + 0.79 * (0.09 - 0.38) = 0.27
0.27 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20859,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 82%. For nonsmokers, the probability of freckles is 32%. For smokers, the probability of freckles is 44%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.44
0.82*0.44 - 0.18*0.32 = 0.42
0.42 > 0",mediation,neg_mediation,1,marginal,P(Y)
20863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20864,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 88%. For smokers, the probability of freckles is 67%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.67
0.67 - 0.88 = -0.21
-0.21 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 88%. For smokers, the probability of freckles is 67%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.67
0.67 - 0.88 = -0.21
-0.21 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20866,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 88%. For smokers, the probability of freckles is 67%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.67
0.67 - 0.88 = -0.21
-0.21 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 98%. For nonsmokers and are hard-working, the probability of freckles is 62%. For smokers and are lazy, the probability of freckles is 85%. For smokers and are hard-working, the probability of freckles is 59%. For nonsmokers, the probability of being hard-working is 28%. For smokers, the probability of being hard-working is 69%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.85
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.28
P(V2=1 | X=1) = 0.69
0.69 * (0.62 - 0.98)+ 0.28 * (0.59 - 0.85)= -0.15
-0.15 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 98%. For nonsmokers and are hard-working, the probability of freckles is 62%. For smokers and are lazy, the probability of freckles is 85%. For smokers and are hard-working, the probability of freckles is 59%. For nonsmokers, the probability of being hard-working is 28%. For smokers, the probability of being hard-working is 69%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.85
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.28
P(V2=1 | X=1) = 0.69
0.28 * (0.59 - 0.85) + 0.69 * (0.62 - 0.98) = -0.10
-0.10 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20871,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 98%. For nonsmokers and are hard-working, the probability of freckles is 62%. For smokers and are lazy, the probability of freckles is 85%. For smokers and are hard-working, the probability of freckles is 59%. For nonsmokers, the probability of being hard-working is 28%. For smokers, the probability of being hard-working is 69%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.98
P(Y=1 | X=0, V2=1) = 0.62
P(Y=1 | X=1, V2=0) = 0.85
P(Y=1 | X=1, V2=1) = 0.59
P(V2=1 | X=0) = 0.28
P(V2=1 | X=1) = 0.69
0.28 * (0.59 - 0.85) + 0.69 * (0.62 - 0.98) = -0.10
-0.10 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 87%. For nonsmokers, the probability of freckles is 88%. For smokers, the probability of freckles is 67%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.67
0.87*0.67 - 0.13*0.88 = 0.69
0.69 > 0",mediation,neg_mediation,1,marginal,P(Y)
20873,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 87%. For nonsmokers, the probability of freckles is 88%. For smokers, the probability of freckles is 67%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.67
0.87*0.67 - 0.13*0.88 = 0.69
0.69 > 0",mediation,neg_mediation,1,marginal,P(Y)
20874,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 87%. The probability of nonsmoking and freckles is 11%. The probability of smoking and freckles is 59%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.87
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.59
0.59/0.87 - 0.11/0.13 = -0.21
-0.21 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20878,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 42%. For smokers, the probability of freckles is 32%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.32
0.32 - 0.42 = -0.10
-0.10 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20883,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 47%. For nonsmokers and are hard-working, the probability of freckles is 23%. For smokers and are lazy, the probability of freckles is 60%. For smokers and are hard-working, the probability of freckles is 18%. For nonsmokers, the probability of being hard-working is 22%. For smokers, the probability of being hard-working is 66%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.47
P(Y=1 | X=0, V2=1) = 0.23
P(Y=1 | X=1, V2=0) = 0.60
P(Y=1 | X=1, V2=1) = 0.18
P(V2=1 | X=0) = 0.22
P(V2=1 | X=1) = 0.66
0.66 * (0.23 - 0.47)+ 0.22 * (0.18 - 0.60)= -0.10
-0.10 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 49%. For smokers, the probability of freckles is 61%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.61
0.61 - 0.49 = 0.12
0.12 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 53%. For nonsmokers and are hard-working, the probability of freckles is 28%. For smokers and are lazy, the probability of freckles is 80%. For smokers and are hard-working, the probability of freckles is 58%. For nonsmokers, the probability of being hard-working is 17%. For smokers, the probability of being hard-working is 88%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.28
P(Y=1 | X=1, V2=0) = 0.80
P(Y=1 | X=1, V2=1) = 0.58
P(V2=1 | X=0) = 0.17
P(V2=1 | X=1) = 0.88
0.88 * (0.28 - 0.53)+ 0.17 * (0.58 - 0.80)= -0.18
-0.18 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 53%. For nonsmokers and are hard-working, the probability of freckles is 28%. For smokers and are lazy, the probability of freckles is 80%. For smokers and are hard-working, the probability of freckles is 58%. For nonsmokers, the probability of being hard-working is 17%. For smokers, the probability of being hard-working is 88%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.28
P(Y=1 | X=1, V2=0) = 0.80
P(Y=1 | X=1, V2=1) = 0.58
P(V2=1 | X=0) = 0.17
P(V2=1 | X=1) = 0.88
0.17 * (0.58 - 0.80) + 0.88 * (0.28 - 0.53) = 0.28
0.28 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 64%. For smokers, the probability of freckles is 37%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.37
0.37 - 0.64 = -0.28
-0.28 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 64%. For smokers, the probability of freckles is 37%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.37
0.37 - 0.64 = -0.28
-0.28 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 64%. For smokers, the probability of freckles is 37%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.37
0.37 - 0.64 = -0.28
-0.28 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 69%. For nonsmokers and are hard-working, the probability of freckles is 40%. For smokers and are lazy, the probability of freckles is 64%. For smokers and are hard-working, the probability of freckles is 26%. For nonsmokers, the probability of being hard-working is 16%. For smokers, the probability of being hard-working is 72%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.69
P(Y=1 | X=0, V2=1) = 0.40
P(Y=1 | X=1, V2=0) = 0.64
P(Y=1 | X=1, V2=1) = 0.26
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.72
0.72 * (0.40 - 0.69)+ 0.16 * (0.26 - 0.64)= -0.16
-0.16 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 69%. For nonsmokers and are hard-working, the probability of freckles is 40%. For smokers and are lazy, the probability of freckles is 64%. For smokers and are hard-working, the probability of freckles is 26%. For nonsmokers, the probability of being hard-working is 16%. For smokers, the probability of being hard-working is 72%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.69
P(Y=1 | X=0, V2=1) = 0.40
P(Y=1 | X=1, V2=0) = 0.64
P(Y=1 | X=1, V2=1) = 0.26
P(V2=1 | X=0) = 0.16
P(V2=1 | X=1) = 0.72
0.72 * (0.40 - 0.69)+ 0.16 * (0.26 - 0.64)= -0.16
-0.16 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 89%. The probability of nonsmoking and freckles is 7%. The probability of smoking and freckles is 33%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.33
0.33/0.89 - 0.07/0.11 = -0.28
-0.28 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 86%. For smokers, the probability of freckles is 58%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.58
0.58 - 0.86 = -0.28
-0.28 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 86%. For smokers, the probability of freckles is 58%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.58
0.58 - 0.86 = -0.28
-0.28 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20923,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 86%. For smokers, the probability of freckles is 58%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.86
P(Y=1 | X=1) = 0.58
0.58 - 0.86 = -0.28
-0.28 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 89%. For nonsmokers and are hard-working, the probability of freckles is 37%. For smokers and are lazy, the probability of freckles is 81%. For smokers and are hard-working, the probability of freckles is 46%. For nonsmokers, the probability of being hard-working is 5%. For smokers, the probability of being hard-working is 65%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.89
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.05
P(V2=1 | X=1) = 0.65
0.65 * (0.37 - 0.89)+ 0.05 * (0.46 - 0.81)= -0.31
-0.31 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 89%. For nonsmokers and are hard-working, the probability of freckles is 37%. For smokers and are lazy, the probability of freckles is 81%. For smokers and are hard-working, the probability of freckles is 46%. For nonsmokers, the probability of being hard-working is 5%. For smokers, the probability of being hard-working is 65%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.89
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.05
P(V2=1 | X=1) = 0.65
0.65 * (0.37 - 0.89)+ 0.05 * (0.46 - 0.81)= -0.31
-0.31 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 89%. For nonsmokers and are hard-working, the probability of freckles is 37%. For smokers and are lazy, the probability of freckles is 81%. For smokers and are hard-working, the probability of freckles is 46%. For nonsmokers, the probability of being hard-working is 5%. For smokers, the probability of being hard-working is 65%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.89
P(Y=1 | X=0, V2=1) = 0.37
P(Y=1 | X=1, V2=0) = 0.81
P(Y=1 | X=1, V2=1) = 0.46
P(V2=1 | X=0) = 0.05
P(V2=1 | X=1) = 0.65
0.05 * (0.46 - 0.81) + 0.65 * (0.37 - 0.89) = -0.07
-0.07 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 35%. For smokers, the probability of freckles is 46%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.46
0.46 - 0.35 = 0.11
0.11 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 51%. For nonsmokers and are hard-working, the probability of freckles is 12%. For smokers and are lazy, the probability of freckles is 86%. For smokers and are hard-working, the probability of freckles is 41%. For nonsmokers, the probability of being hard-working is 42%. For smokers, the probability of being hard-working is 89%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.51
P(Y=1 | X=0, V2=1) = 0.12
P(Y=1 | X=1, V2=0) = 0.86
P(Y=1 | X=1, V2=1) = 0.41
P(V2=1 | X=0) = 0.42
P(V2=1 | X=1) = 0.89
0.89 * (0.12 - 0.51)+ 0.42 * (0.41 - 0.86)= -0.18
-0.18 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 90%. For nonsmokers, the probability of freckles is 35%. For smokers, the probability of freckles is 46%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.46
0.90*0.46 - 0.10*0.35 = 0.45
0.45 > 0",mediation,neg_mediation,1,marginal,P(Y)
20946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 49%. For smokers, the probability of freckles is 39%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.39
0.39 - 0.49 = -0.11
-0.11 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 49%. For smokers, the probability of freckles is 39%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.39
0.39 - 0.49 = -0.11
-0.11 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 62%. For nonsmokers and are hard-working, the probability of freckles is 42%. For smokers and are lazy, the probability of freckles is 68%. For smokers and are hard-working, the probability of freckles is 33%. For nonsmokers, the probability of being hard-working is 63%. For smokers, the probability of being hard-working is 85%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.62
P(Y=1 | X=0, V2=1) = 0.42
P(Y=1 | X=1, V2=0) = 0.68
P(Y=1 | X=1, V2=1) = 0.33
P(V2=1 | X=0) = 0.63
P(V2=1 | X=1) = 0.85
0.63 * (0.33 - 0.68) + 0.85 * (0.42 - 0.62) = -0.03
-0.03 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 91%. The probability of nonsmoking and freckles is 5%. The probability of smoking and freckles is 35%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.35
0.35/0.91 - 0.05/0.09 = -0.11
-0.11 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 91%. For smokers, the probability of freckles is 65%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.65
0.65 - 0.91 = -0.27
-0.27 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 91%. For smokers, the probability of freckles is 65%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.65
0.65 - 0.91 = -0.27
-0.27 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
20964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 91%. For smokers, the probability of freckles is 65%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.65
0.65 - 0.91 = -0.27
-0.27 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20965,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 91%. For smokers, the probability of freckles is 65%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.65
0.65 - 0.91 = -0.27
-0.27 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 100%. For nonsmokers and are hard-working, the probability of freckles is 63%. For smokers and are lazy, the probability of freckles is 93%. For smokers and are hard-working, the probability of freckles is 45%. For nonsmokers, the probability of being hard-working is 23%. For smokers, the probability of being hard-working is 60%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 1.00
P(Y=1 | X=0, V2=1) = 0.63
P(Y=1 | X=1, V2=0) = 0.93
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.23
P(V2=1 | X=1) = 0.60
0.23 * (0.45 - 0.93) + 0.60 * (0.63 - 1.00) = -0.09
-0.09 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20970,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 98%. For nonsmokers, the probability of freckles is 91%. For smokers, the probability of freckles is 65%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.91
P(Y=1 | X=1) = 0.65
0.98*0.65 - 0.02*0.91 = 0.65
0.65 > 0",mediation,neg_mediation,1,marginal,P(Y)
20972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 98%. The probability of nonsmoking and freckles is 1%. The probability of smoking and freckles is 64%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.64
0.64/0.98 - 0.01/0.02 = -0.27
-0.27 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 98%. The probability of nonsmoking and freckles is 1%. The probability of smoking and freckles is 64%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.64
0.64/0.98 - 0.01/0.02 = -0.27
-0.27 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
20975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 35%. For smokers, the probability of freckles is 50%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.50
0.50 - 0.35 = 0.15
0.15 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 39%. For nonsmokers and are hard-working, the probability of freckles is 6%. For smokers and are lazy, the probability of freckles is 73%. For smokers and are hard-working, the probability of freckles is 35%. For nonsmokers, the probability of being hard-working is 12%. For smokers, the probability of being hard-working is 61%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.39
P(Y=1 | X=0, V2=1) = 0.06
P(Y=1 | X=1, V2=0) = 0.73
P(Y=1 | X=1, V2=1) = 0.35
P(V2=1 | X=0) = 0.12
P(V2=1 | X=1) = 0.61
0.61 * (0.06 - 0.39)+ 0.12 * (0.35 - 0.73)= -0.17
-0.17 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 98%. For nonsmokers, the probability of freckles is 35%. For smokers, the probability of freckles is 50%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.50
0.98*0.50 - 0.02*0.35 = 0.50
0.50 > 0",mediation,neg_mediation,1,marginal,P(Y)
20985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 98%. For nonsmokers, the probability of freckles is 35%. For smokers, the probability of freckles is 50%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.50
0.98*0.50 - 0.02*0.35 = 0.50
0.50 > 0",mediation,neg_mediation,1,marginal,P(Y)
20989,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
20993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 67%. For smokers, the probability of freckles is 55%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.55
0.55 - 0.67 = -0.12
-0.12 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
20995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 79%. For nonsmokers and are hard-working, the probability of freckles is 48%. For smokers and are lazy, the probability of freckles is 90%. For smokers and are hard-working, the probability of freckles is 45%. For nonsmokers, the probability of being hard-working is 40%. For smokers, the probability of being hard-working is 79%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.79
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.90
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.79
0.79 * (0.48 - 0.79)+ 0.40 * (0.45 - 0.90)= -0.12
-0.12 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
20996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 79%. For nonsmokers and are hard-working, the probability of freckles is 48%. For smokers and are lazy, the probability of freckles is 90%. For smokers and are hard-working, the probability of freckles is 45%. For nonsmokers, the probability of being hard-working is 40%. For smokers, the probability of being hard-working is 79%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.79
P(Y=1 | X=0, V2=1) = 0.48
P(Y=1 | X=1, V2=0) = 0.90
P(Y=1 | X=1, V2=1) = 0.45
P(V2=1 | X=0) = 0.40
P(V2=1 | X=1) = 0.79
0.40 * (0.45 - 0.90) + 0.79 * (0.48 - 0.79) = 0.05
0.05 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
20998,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 90%. For nonsmokers, the probability of freckles is 67%. For smokers, the probability of freckles is 55%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.55
0.90*0.55 - 0.10*0.67 = 0.56
0.56 > 0",mediation,neg_mediation,1,marginal,P(Y)
20999,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 90%. For nonsmokers, the probability of freckles is 67%. For smokers, the probability of freckles is 55%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.55
0.90*0.55 - 0.10*0.67 = 0.56
0.56 > 0",mediation,neg_mediation,1,marginal,P(Y)
21001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 90%. The probability of nonsmoking and freckles is 6%. The probability of smoking and freckles is 50%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.50
0.50/0.90 - 0.06/0.10 = -0.12
-0.12 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
21003,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
21004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 53%. For smokers, the probability of freckles is 39%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.39
0.39 - 0.53 = -0.14
-0.14 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 53%. For smokers, the probability of freckles is 39%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.39
0.39 - 0.53 = -0.14
-0.14 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 53%. For smokers, the probability of freckles is 39%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.39
0.39 - 0.53 = -0.14
-0.14 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 53%. For nonsmokers and are hard-working, the probability of freckles is 32%. For smokers and are lazy, the probability of freckles is 58%. For smokers and are hard-working, the probability of freckles is 23%. For nonsmokers, the probability of being hard-working is 2%. For smokers, the probability of being hard-working is 56%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.32
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.02
P(V2=1 | X=1) = 0.56
0.56 * (0.32 - 0.53)+ 0.02 * (0.23 - 0.58)= -0.11
-0.11 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 53%. For nonsmokers and are hard-working, the probability of freckles is 32%. For smokers and are lazy, the probability of freckles is 58%. For smokers and are hard-working, the probability of freckles is 23%. For nonsmokers, the probability of being hard-working is 2%. For smokers, the probability of being hard-working is 56%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
\sum_{V2 = v} P(Y=1|X =0,V2 = v)*[P(V2 = v | X = 1) − P(V2 = v | X = 0)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.32
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.02
P(V2=1 | X=1) = 0.56
0.56 * (0.32 - 0.53)+ 0.02 * (0.23 - 0.58)= -0.11
-0.11 < 0",mediation,neg_mediation,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 53%. For nonsmokers and are hard-working, the probability of freckles is 32%. For smokers and are lazy, the probability of freckles is 58%. For smokers and are hard-working, the probability of freckles is 23%. For nonsmokers, the probability of being hard-working is 2%. For smokers, the probability of being hard-working is 56%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.53
P(Y=1 | X=0, V2=1) = 0.32
P(Y=1 | X=1, V2=0) = 0.58
P(Y=1 | X=1, V2=1) = 0.23
P(V2=1 | X=0) = 0.02
P(V2=1 | X=1) = 0.56
0.02 * (0.23 - 0.58) + 0.56 * (0.32 - 0.53) = 0.05
0.05 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
21012,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 87%. For nonsmokers, the probability of freckles is 53%. For smokers, the probability of freckles is 39%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.39
0.87*0.39 - 0.13*0.53 = 0.42
0.42 > 0",mediation,neg_mediation,1,marginal,P(Y)
21015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 87%. The probability of nonsmoking and freckles is 7%. The probability of smoking and freckles is 34%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.87
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.34
0.34/0.87 - 0.07/0.13 = -0.14
-0.14 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
21017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
21018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 43%. For smokers, the probability of freckles is 22%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.22
0.22 - 0.43 = -0.21
-0.21 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 43%. For smokers, the probability of freckles is 22%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.22
0.22 - 0.43 = -0.21
-0.21 < 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 43%. For smokers, the probability of freckles is 22%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.22
0.22 - 0.43 = -0.21
-0.21 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21021,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 43%. For smokers, the probability of freckles is 22%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.22
0.22 - 0.43 = -0.21
-0.21 < 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 69%. For nonsmokers and are hard-working, the probability of freckles is 14%. For smokers and are lazy, the probability of freckles is 59%. For smokers and are hard-working, the probability of freckles is 17%. For nonsmokers, the probability of being hard-working is 47%. For smokers, the probability of being hard-working is 87%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.69
P(Y=1 | X=0, V2=1) = 0.14
P(Y=1 | X=1, V2=0) = 0.59
P(Y=1 | X=1, V2=1) = 0.17
P(V2=1 | X=0) = 0.47
P(V2=1 | X=1) = 0.87
0.47 * (0.17 - 0.59) + 0.87 * (0.14 - 0.69) = -0.04
-0.04 < 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
21026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 84%. For nonsmokers, the probability of freckles is 43%. For smokers, the probability of freckles is 22%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.22
0.84*0.22 - 0.16*0.43 = 0.25
0.25 > 0",mediation,neg_mediation,1,marginal,P(Y)
21027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 84%. For nonsmokers, the probability of freckles is 43%. For smokers, the probability of freckles is 22%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.22
0.84*0.22 - 0.16*0.43 = 0.25
0.25 > 0",mediation,neg_mediation,1,marginal,P(Y)
21028,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 84%. The probability of nonsmoking and freckles is 7%. The probability of smoking and freckles is 19%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.19
0.19/0.84 - 0.07/0.16 = -0.21
-0.21 < 0",mediation,neg_mediation,1,correlation,P(Y | X)
21031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to effort.",yes,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
21040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 84%. For nonsmokers, the probability of freckles is 63%. For smokers, the probability of freckles is 57%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.57
0.84*0.57 - 0.16*0.63 = 0.57
0.57 > 0",mediation,neg_mediation,1,marginal,P(Y)
21041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 84%. For nonsmokers, the probability of freckles is 63%. For smokers, the probability of freckles is 57%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.57
0.84*0.57 - 0.16*0.63 = 0.57
0.57 > 0",mediation,neg_mediation,1,marginal,P(Y)
21044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. Method 1: We look at how smoking correlates with freckles case by case according to effort. Method 2: We look directly at how smoking correlates with freckles in general.",no,"nan
nan
nan
nan
nan
nan
nan",mediation,neg_mediation,2,backadj,[backdoor adjustment set for Y given X]
21047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 48%. For smokers, the probability of freckles is 71%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.71
0.71 - 0.48 = 0.23
0.23 > 0",mediation,neg_mediation,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers, the probability of freckles is 48%. For smokers, the probability of freckles is 71%.",yes,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.71
0.71 - 0.48 = 0.23
0.23 > 0",mediation,neg_mediation,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. For nonsmokers and are lazy, the probability of freckles is 49%. For nonsmokers and are hard-working, the probability of freckles is 27%. For smokers and are lazy, the probability of freckles is 87%. For smokers and are hard-working, the probability of freckles is 56%. For nonsmokers, the probability of being hard-working is 4%. For smokers, the probability of being hard-working is 51%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]
\sum_{V2=v} P(V2=v|X=0)*[P(Y=1|X=1,V2=v) - P(Y=1|X=0, V2=v)]
P(Y=1 | X=0, V2=0) = 0.49
P(Y=1 | X=0, V2=1) = 0.27
P(Y=1 | X=1, V2=0) = 0.87
P(Y=1 | X=1, V2=1) = 0.56
P(V2=1 | X=0) = 0.04
P(V2=1 | X=1) = 0.51
0.04 * (0.56 - 0.87) + 0.51 * (0.27 - 0.49) = 0.37
0.37 > 0",mediation,neg_mediation,3,nde,"E[Y_{X=1, V2=0} - Y_{X=0, V2=0}]"
21057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and freckles. Effort has a direct effect on freckles. The overall probability of smoking is 87%. The probability of nonsmoking and freckles is 6%. The probability of smoking and freckles is 62%.",no,"Let X = smoking; V2 = effort; Y = freckles.
X->V2,X->Y,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.87
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.62
0.62/0.87 - 0.06/0.13 = 0.23
0.23 > 0",mediation,neg_mediation,1,correlation,P(Y | X)
21061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 59%. For people who play card games, the probability of long lifespan is 79%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.79
0.79 - 0.59 = 0.19
0.19 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 72%. For people who play card games and without diabetes, the probability of long lifespan is 74%. For people who play card games and with diabetes, the probability of long lifespan is 93%. For people who do not play card games and nonsmokers, the probability of having diabetes is 79%. For people who do not play card games and smokers, the probability of having diabetes is 50%. For people who play card games and nonsmokers, the probability of having diabetes is 52%. For people who play card games and smokers, the probability of having diabetes is 20%. The overall probability of smoker is 85%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.74
P(Y=1 | X=1, V3=1) = 0.93
P(V3=1 | X=0, V2=0) = 0.79
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.85
0.85 * (0.93 - 0.74) * 0.50 + 0.15 * (0.72 - 0.43) * 0.52 = 0.26
0.26 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 72%. For people who play card games and without diabetes, the probability of long lifespan is 74%. For people who play card games and with diabetes, the probability of long lifespan is 93%. For people who do not play card games and nonsmokers, the probability of having diabetes is 79%. For people who do not play card games and smokers, the probability of having diabetes is 50%. For people who play card games and nonsmokers, the probability of having diabetes is 52%. For people who play card games and smokers, the probability of having diabetes is 20%. The overall probability of smoker is 85%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.74
P(Y=1 | X=1, V3=1) = 0.93
P(V3=1 | X=0, V2=0) = 0.79
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.85
0.85 * (0.93 - 0.74) * 0.50 + 0.15 * (0.72 - 0.43) * 0.52 = 0.26
0.26 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 83%. For people who do not play card games, the probability of long lifespan is 59%. For people who play card games, the probability of long lifespan is 79%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.79
0.83*0.79 - 0.17*0.59 = 0.75
0.75 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 51%. For people who play card games, the probability of long lifespan is 66%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.66
0.66 - 0.51 = 0.15
0.15 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 51%. For people who play card games, the probability of long lifespan is 66%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.66
0.66 - 0.51 = 0.15
0.15 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 51%. For people who play card games, the probability of long lifespan is 66%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.66
0.66 - 0.51 = 0.15
0.15 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 32%. For people who do not play card games and with diabetes, the probability of long lifespan is 60%. For people who play card games and without diabetes, the probability of long lifespan is 62%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 57%. For people who do not play card games and smokers, the probability of having diabetes is 68%. For people who play card games and nonsmokers, the probability of having diabetes is 31%. For people who play card games and smokers, the probability of having diabetes is 19%. The overall probability of smoker is 88%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.57
P(V3=1 | X=0, V2=1) = 0.68
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.19
P(V2=1) = 0.88
0.88 * 0.60 * (0.19 - 0.31)+ 0.12 * 0.60 * (0.68 - 0.57)= -0.12
-0.12 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 32%. For people who do not play card games and with diabetes, the probability of long lifespan is 60%. For people who play card games and without diabetes, the probability of long lifespan is 62%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 57%. For people who do not play card games and smokers, the probability of having diabetes is 68%. For people who play card games and nonsmokers, the probability of having diabetes is 31%. For people who play card games and smokers, the probability of having diabetes is 19%. The overall probability of smoker is 88%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.57
P(V3=1 | X=0, V2=1) = 0.68
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.19
P(V2=1) = 0.88
0.88 * (0.81 - 0.62) * 0.68 + 0.12 * (0.60 - 0.32) * 0.31 = 0.25
0.25 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 84%. The probability of not playing card games and long lifespan is 8%. The probability of playing card games and long lifespan is 55%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.55
0.55/0.84 - 0.08/0.16 = 0.15
0.15 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 84%. The probability of not playing card games and long lifespan is 8%. The probability of playing card games and long lifespan is 55%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.55
0.55/0.84 - 0.08/0.16 = 0.15
0.15 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 81%. For people who play card games, the probability of long lifespan is 70%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.70
0.70 - 0.81 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 50%. For people who do not play card games and with diabetes, the probability of long lifespan is 83%. For people who play card games and without diabetes, the probability of long lifespan is 56%. For people who play card games and with diabetes, the probability of long lifespan is 82%. For people who do not play card games and nonsmokers, the probability of having diabetes is 88%. For people who do not play card games and smokers, the probability of having diabetes is 97%. For people who play card games and nonsmokers, the probability of having diabetes is 51%. For people who play card games and smokers, the probability of having diabetes is 52%. The overall probability of smoker is 90%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.50
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.82
P(V3=1 | X=0, V2=0) = 0.88
P(V3=1 | X=0, V2=1) = 0.97
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.52
P(V2=1) = 0.90
0.90 * (0.82 - 0.56) * 0.97 + 0.10 * (0.83 - 0.50) * 0.51 = -0.01
-0.01 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 90%. For people who do not play card games, the probability of long lifespan is 81%. For people who play card games, the probability of long lifespan is 70%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.81
P(Y=1 | X=1) = 0.70
0.90*0.70 - 0.10*0.81 = 0.71
0.71 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 90%. The probability of not playing card games and long lifespan is 8%. The probability of playing card games and long lifespan is 62%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.62
0.62/0.90 - 0.08/0.10 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21100,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21103,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 58%. For people who play card games, the probability of long lifespan is 76%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.76
0.76 - 0.58 = 0.18
0.18 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 58%. For people who play card games, the probability of long lifespan is 76%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.76
0.76 - 0.58 = 0.18
0.18 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 81%. The probability of not playing card games and long lifespan is 11%. The probability of playing card games and long lifespan is 62%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.62
0.62/0.81 - 0.11/0.19 = 0.18
0.18 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 44%. For people who play card games, the probability of long lifespan is 60%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.60
0.60 - 0.44 = 0.16
0.16 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 44%. For people who play card games, the probability of long lifespan is 60%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.60
0.60 - 0.44 = 0.16
0.16 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 91%. For people who do not play card games, the probability of long lifespan is 44%. For people who play card games, the probability of long lifespan is 60%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.60
0.91*0.60 - 0.09*0.44 = 0.59
0.59 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 74%. For people who play card games, the probability of long lifespan is 62%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.62
0.62 - 0.74 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 56%. For people who do not play card games and with diabetes, the probability of long lifespan is 82%. For people who play card games and without diabetes, the probability of long lifespan is 56%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 58%. For people who do not play card games and smokers, the probability of having diabetes is 72%. For people who play card games and nonsmokers, the probability of having diabetes is 29%. For people who play card games and smokers, the probability of having diabetes is 20%. The overall probability of smoker is 86%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.58
P(V3=1 | X=0, V2=1) = 0.72
P(V3=1 | X=1, V2=0) = 0.29
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.86
0.86 * 0.82 * (0.20 - 0.29)+ 0.14 * 0.82 * (0.72 - 0.58)= -0.11
-0.11 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 56%. For people who do not play card games and with diabetes, the probability of long lifespan is 82%. For people who play card games and without diabetes, the probability of long lifespan is 56%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 58%. For people who do not play card games and smokers, the probability of having diabetes is 72%. For people who play card games and nonsmokers, the probability of having diabetes is 29%. For people who play card games and smokers, the probability of having diabetes is 20%. The overall probability of smoker is 86%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.82
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.58
P(V3=1 | X=0, V2=1) = 0.72
P(V3=1 | X=1, V2=0) = 0.29
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.86
0.86 * (0.81 - 0.56) * 0.72 + 0.14 * (0.82 - 0.56) * 0.29 = 0.01
0.01 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 82%. For people who do not play card games, the probability of long lifespan is 74%. For people who play card games, the probability of long lifespan is 62%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.62
0.82*0.62 - 0.18*0.74 = 0.64
0.64 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 82%. The probability of not playing card games and long lifespan is 13%. The probability of playing card games and long lifespan is 51%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.51
0.51/0.82 - 0.13/0.18 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 82%. The probability of not playing card games and long lifespan is 13%. The probability of playing card games and long lifespan is 51%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.51
0.51/0.82 - 0.13/0.18 = -0.12
-0.12 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 40%. For people who play card games, the probability of long lifespan is 58%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.58
0.58 - 0.40 = 0.17
0.17 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 23%. For people who do not play card games and with diabetes, the probability of long lifespan is 51%. For people who play card games and without diabetes, the probability of long lifespan is 52%. For people who play card games and with diabetes, the probability of long lifespan is 75%. For people who do not play card games and nonsmokers, the probability of having diabetes is 80%. For people who do not play card games and smokers, the probability of having diabetes is 58%. For people who play card games and nonsmokers, the probability of having diabetes is 51%. For people who play card games and smokers, the probability of having diabetes is 22%. The overall probability of smoker is 88%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.75
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.88
0.88 * 0.51 * (0.22 - 0.51)+ 0.12 * 0.51 * (0.58 - 0.80)= -0.11
-0.11 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 23%. For people who do not play card games and with diabetes, the probability of long lifespan is 51%. For people who play card games and without diabetes, the probability of long lifespan is 52%. For people who play card games and with diabetes, the probability of long lifespan is 75%. For people who do not play card games and nonsmokers, the probability of having diabetes is 80%. For people who do not play card games and smokers, the probability of having diabetes is 58%. For people who play card games and nonsmokers, the probability of having diabetes is 51%. For people who play card games and smokers, the probability of having diabetes is 22%. The overall probability of smoker is 88%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.75
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.88
0.88 * 0.51 * (0.22 - 0.51)+ 0.12 * 0.51 * (0.58 - 0.80)= -0.11
-0.11 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21150,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 23%. For people who do not play card games and with diabetes, the probability of long lifespan is 51%. For people who play card games and without diabetes, the probability of long lifespan is 52%. For people who play card games and with diabetes, the probability of long lifespan is 75%. For people who do not play card games and nonsmokers, the probability of having diabetes is 80%. For people who do not play card games and smokers, the probability of having diabetes is 58%. For people who play card games and nonsmokers, the probability of having diabetes is 51%. For people who play card games and smokers, the probability of having diabetes is 22%. The overall probability of smoker is 88%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.51
P(Y=1 | X=1, V3=0) = 0.52
P(Y=1 | X=1, V3=1) = 0.75
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.88
0.88 * (0.75 - 0.52) * 0.58 + 0.12 * (0.51 - 0.23) * 0.51 = 0.27
0.27 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 98%. The probability of not playing card games and long lifespan is 1%. The probability of playing card games and long lifespan is 57%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.57
0.57/0.98 - 0.01/0.02 = 0.18
0.18 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 50%. For people who play card games, the probability of long lifespan is 64%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.64
0.64 - 0.50 = 0.14
0.14 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21166,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 82%. For people who do not play card games, the probability of long lifespan is 50%. For people who play card games, the probability of long lifespan is 64%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.64
0.82*0.64 - 0.18*0.50 = 0.61
0.61 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 82%. The probability of not playing card games and long lifespan is 9%. The probability of playing card games and long lifespan is 52%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.52
0.52/0.82 - 0.09/0.18 = 0.14
0.14 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 66%. For people who play card games, the probability of long lifespan is 56%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.56
0.56 - 0.66 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21173,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 66%. For people who play card games, the probability of long lifespan is 56%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.56
0.56 - 0.66 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 66%. For people who play card games, the probability of long lifespan is 56%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.56
0.56 - 0.66 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 74%. For people who play card games and without diabetes, the probability of long lifespan is 48%. For people who play card games and with diabetes, the probability of long lifespan is 72%. For people who do not play card games and nonsmokers, the probability of having diabetes is 76%. For people who do not play card games and smokers, the probability of having diabetes is 74%. For people who play card games and nonsmokers, the probability of having diabetes is 39%. For people who play card games and smokers, the probability of having diabetes is 31%. The overall probability of smoker is 92%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.72
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.74
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.92
0.92 * 0.74 * (0.31 - 0.39)+ 0.08 * 0.74 * (0.74 - 0.76)= -0.13
-0.13 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21177,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 74%. For people who play card games and without diabetes, the probability of long lifespan is 48%. For people who play card games and with diabetes, the probability of long lifespan is 72%. For people who do not play card games and nonsmokers, the probability of having diabetes is 76%. For people who do not play card games and smokers, the probability of having diabetes is 74%. For people who play card games and nonsmokers, the probability of having diabetes is 39%. For people who play card games and smokers, the probability of having diabetes is 31%. The overall probability of smoker is 92%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.72
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.74
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.92
0.92 * 0.74 * (0.31 - 0.39)+ 0.08 * 0.74 * (0.74 - 0.76)= -0.13
-0.13 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 74%. For people who play card games and without diabetes, the probability of long lifespan is 48%. For people who play card games and with diabetes, the probability of long lifespan is 72%. For people who do not play card games and nonsmokers, the probability of having diabetes is 76%. For people who do not play card games and smokers, the probability of having diabetes is 74%. For people who play card games and nonsmokers, the probability of having diabetes is 39%. For people who play card games and smokers, the probability of having diabetes is 31%. The overall probability of smoker is 92%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.72
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.74
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.92
0.92 * (0.72 - 0.48) * 0.74 + 0.08 * (0.74 - 0.43) * 0.39 = 0.00
0.00 = 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 96%. For people who do not play card games, the probability of long lifespan is 66%. For people who play card games, the probability of long lifespan is 56%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.56
0.96*0.56 - 0.04*0.66 = 0.56
0.56 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 96%. The probability of not playing card games and long lifespan is 3%. The probability of playing card games and long lifespan is 54%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.54
0.54/0.96 - 0.03/0.04 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 96%. The probability of not playing card games and long lifespan is 3%. The probability of playing card games and long lifespan is 54%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.54
0.54/0.96 - 0.03/0.04 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 36%. For people who play card games, the probability of long lifespan is 58%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.58
0.58 - 0.36 = 0.22
0.22 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 36%. For people who play card games, the probability of long lifespan is 58%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.58
0.58 - 0.36 = 0.22
0.22 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 23%. For people who do not play card games and with diabetes, the probability of long lifespan is 45%. For people who play card games and without diabetes, the probability of long lifespan is 53%. For people who play card games and with diabetes, the probability of long lifespan is 71%. For people who do not play card games and nonsmokers, the probability of having diabetes is 97%. For people who do not play card games and smokers, the probability of having diabetes is 53%. For people who play card games and nonsmokers, the probability of having diabetes is 61%. For people who play card games and smokers, the probability of having diabetes is 26%. The overall probability of smoker is 92%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0, V2=0) = 0.97
P(V3=1 | X=0, V2=1) = 0.53
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.92
0.92 * 0.45 * (0.26 - 0.61)+ 0.08 * 0.45 * (0.53 - 0.97)= -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 23%. For people who do not play card games and with diabetes, the probability of long lifespan is 45%. For people who play card games and without diabetes, the probability of long lifespan is 53%. For people who play card games and with diabetes, the probability of long lifespan is 71%. For people who do not play card games and nonsmokers, the probability of having diabetes is 97%. For people who do not play card games and smokers, the probability of having diabetes is 53%. For people who play card games and nonsmokers, the probability of having diabetes is 61%. For people who play card games and smokers, the probability of having diabetes is 26%. The overall probability of smoker is 92%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0, V2=0) = 0.97
P(V3=1 | X=0, V2=1) = 0.53
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.92
0.92 * 0.45 * (0.26 - 0.61)+ 0.08 * 0.45 * (0.53 - 0.97)= -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21192,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 23%. For people who do not play card games and with diabetes, the probability of long lifespan is 45%. For people who play card games and without diabetes, the probability of long lifespan is 53%. For people who play card games and with diabetes, the probability of long lifespan is 71%. For people who do not play card games and nonsmokers, the probability of having diabetes is 97%. For people who do not play card games and smokers, the probability of having diabetes is 53%. For people who play card games and nonsmokers, the probability of having diabetes is 61%. For people who play card games and smokers, the probability of having diabetes is 26%. The overall probability of smoker is 92%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.23
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0, V2=0) = 0.97
P(V3=1 | X=0, V2=1) = 0.53
P(V3=1 | X=1, V2=0) = 0.61
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.92
0.92 * (0.71 - 0.53) * 0.53 + 0.08 * (0.45 - 0.23) * 0.61 = 0.28
0.28 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 96%. For people who do not play card games, the probability of long lifespan is 36%. For people who play card games, the probability of long lifespan is 58%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.58
0.96*0.58 - 0.04*0.36 = 0.57
0.57 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 32%. For people who do not play card games and with diabetes, the probability of long lifespan is 60%. For people who play card games and without diabetes, the probability of long lifespan is 58%. For people who play card games and with diabetes, the probability of long lifespan is 83%. For people who do not play card games and nonsmokers, the probability of having diabetes is 61%. For people who do not play card games and smokers, the probability of having diabetes is 61%. For people who play card games and nonsmokers, the probability of having diabetes is 26%. For people who play card games and smokers, the probability of having diabetes is 23%. The overall probability of smoker is 91%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.61
P(V3=1 | X=0, V2=1) = 0.61
P(V3=1 | X=1, V2=0) = 0.26
P(V3=1 | X=1, V2=1) = 0.23
P(V2=1) = 0.91
0.91 * (0.83 - 0.58) * 0.61 + 0.09 * (0.60 - 0.32) * 0.26 = 0.24
0.24 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21212,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 87%. For people who play card games, the probability of long lifespan is 64%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.64
0.64 - 0.87 = -0.23
-0.23 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21219,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 56%. For people who do not play card games and with diabetes, the probability of long lifespan is 91%. For people who play card games and without diabetes, the probability of long lifespan is 55%. For people who play card games and with diabetes, the probability of long lifespan is 84%. For people who do not play card games and nonsmokers, the probability of having diabetes is 77%. For people who do not play card games and smokers, the probability of having diabetes is 88%. For people who play card games and nonsmokers, the probability of having diabetes is 45%. For people who play card games and smokers, the probability of having diabetes is 28%. The overall probability of smoker is 91%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0, V2=0) = 0.77
P(V3=1 | X=0, V2=1) = 0.88
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.91
0.91 * 0.91 * (0.28 - 0.45)+ 0.09 * 0.91 * (0.88 - 0.77)= -0.19
-0.19 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 56%. For people who do not play card games and with diabetes, the probability of long lifespan is 91%. For people who play card games and without diabetes, the probability of long lifespan is 55%. For people who play card games and with diabetes, the probability of long lifespan is 84%. For people who do not play card games and nonsmokers, the probability of having diabetes is 77%. For people who do not play card games and smokers, the probability of having diabetes is 88%. For people who play card games and nonsmokers, the probability of having diabetes is 45%. For people who play card games and smokers, the probability of having diabetes is 28%. The overall probability of smoker is 91%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.55
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0, V2=0) = 0.77
P(V3=1 | X=0, V2=1) = 0.88
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.91
0.91 * (0.84 - 0.55) * 0.88 + 0.09 * (0.91 - 0.56) * 0.45 = -0.05
-0.05 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 86%. For people who do not play card games, the probability of long lifespan is 87%. For people who play card games, the probability of long lifespan is 64%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.64
0.86*0.64 - 0.14*0.87 = 0.67
0.67 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 56%. For people who play card games, the probability of long lifespan is 70%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.70
0.70 - 0.56 = 0.15
0.15 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 56%. For people who play card games, the probability of long lifespan is 70%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.70
0.70 - 0.56 = 0.15
0.15 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 42%. For people who do not play card games and with diabetes, the probability of long lifespan is 63%. For people who play card games and without diabetes, the probability of long lifespan is 63%. For people who play card games and with diabetes, the probability of long lifespan is 86%. For people who do not play card games and nonsmokers, the probability of having diabetes is 87%. For people who do not play card games and smokers, the probability of having diabetes is 59%. For people who play card games and nonsmokers, the probability of having diabetes is 57%. For people who play card games and smokers, the probability of having diabetes is 28%. The overall probability of smoker is 81%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.86
P(V3=1 | X=0, V2=0) = 0.87
P(V3=1 | X=0, V2=1) = 0.59
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.81
0.81 * (0.86 - 0.63) * 0.59 + 0.19 * (0.63 - 0.42) * 0.57 = 0.23
0.23 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 85%. For people who do not play card games, the probability of long lifespan is 56%. For people who play card games, the probability of long lifespan is 70%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.70
0.85*0.70 - 0.15*0.56 = 0.68
0.68 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 85%. For people who do not play card games, the probability of long lifespan is 56%. For people who play card games, the probability of long lifespan is 70%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.70
0.85*0.70 - 0.15*0.56 = 0.68
0.68 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 85%. The probability of not playing card games and long lifespan is 8%. The probability of playing card games and long lifespan is 60%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.60
0.60/0.85 - 0.08/0.15 = 0.15
0.15 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 65%. For people who play card games, the probability of long lifespan is 83%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.83
0.83 - 0.65 = 0.18
0.18 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 65%. For people who play card games, the probability of long lifespan is 83%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.83
0.83 - 0.65 = 0.18
0.18 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 73%. For people who play card games, the probability of long lifespan is 63%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.63
0.63 - 0.73 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 73%. For people who play card games, the probability of long lifespan is 63%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.63
0.63 - 0.73 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 73%. For people who play card games, the probability of long lifespan is 63%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.63
0.63 - 0.73 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 78%. For people who play card games and without diabetes, the probability of long lifespan is 56%. For people who play card games and with diabetes, the probability of long lifespan is 76%. For people who do not play card games and nonsmokers, the probability of having diabetes is 73%. For people who do not play card games and smokers, the probability of having diabetes is 88%. For people who play card games and nonsmokers, the probability of having diabetes is 51%. For people who play card games and smokers, the probability of having diabetes is 33%. The overall probability of smoker is 88%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.76
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.88
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.88
0.88 * 0.78 * (0.33 - 0.51)+ 0.12 * 0.78 * (0.88 - 0.73)= -0.16
-0.16 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 78%. For people who play card games and without diabetes, the probability of long lifespan is 56%. For people who play card games and with diabetes, the probability of long lifespan is 76%. For people who do not play card games and nonsmokers, the probability of having diabetes is 73%. For people who do not play card games and smokers, the probability of having diabetes is 88%. For people who play card games and nonsmokers, the probability of having diabetes is 51%. For people who play card games and smokers, the probability of having diabetes is 33%. The overall probability of smoker is 88%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.76
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.88
P(V3=1 | X=1, V2=0) = 0.51
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.88
0.88 * 0.78 * (0.33 - 0.51)+ 0.12 * 0.78 * (0.88 - 0.73)= -0.16
-0.16 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 86%. For people who do not play card games, the probability of long lifespan is 73%. For people who play card games, the probability of long lifespan is 63%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.63
0.86*0.63 - 0.14*0.73 = 0.64
0.64 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 86%. The probability of not playing card games and long lifespan is 10%. The probability of playing card games and long lifespan is 54%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.86
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.54
0.54/0.86 - 0.10/0.14 = -0.10
-0.10 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 50%. For people who play card games, the probability of long lifespan is 68%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.68
0.68 - 0.50 = 0.18
0.18 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 50%. For people who play card games, the probability of long lifespan is 68%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.68
0.68 - 0.50 = 0.18
0.18 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 36%. For people who do not play card games and with diabetes, the probability of long lifespan is 58%. For people who play card games and without diabetes, the probability of long lifespan is 59%. For people who play card games and with diabetes, the probability of long lifespan is 82%. For people who do not play card games and nonsmokers, the probability of having diabetes is 79%. For people who do not play card games and smokers, the probability of having diabetes is 58%. For people who play card games and nonsmokers, the probability of having diabetes is 58%. For people who play card games and smokers, the probability of having diabetes is 36%. The overall probability of smoker is 82%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.36
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.82
P(V3=1 | X=0, V2=0) = 0.79
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.82
0.82 * (0.82 - 0.59) * 0.58 + 0.18 * (0.58 - 0.36) * 0.58 = 0.24
0.24 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21280,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 94%. The probability of not playing card games and long lifespan is 3%. The probability of playing card games and long lifespan is 64%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.94
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.64
0.64/0.94 - 0.03/0.06 = 0.18
0.18 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 48%. For people who play card games, the probability of long lifespan is 67%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.67
0.67 - 0.48 = 0.19
0.19 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 48%. For people who play card games, the probability of long lifespan is 67%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.67
0.67 - 0.48 = 0.19
0.19 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 48%. For people who play card games, the probability of long lifespan is 67%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.67
0.67 - 0.48 = 0.19
0.19 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 48%. For people who play card games, the probability of long lifespan is 67%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.67
0.67 - 0.48 = 0.19
0.19 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 32%. For people who do not play card games and with diabetes, the probability of long lifespan is 60%. For people who play card games and without diabetes, the probability of long lifespan is 57%. For people who play card games and with diabetes, the probability of long lifespan is 86%. For people who do not play card games and nonsmokers, the probability of having diabetes is 61%. For people who do not play card games and smokers, the probability of having diabetes is 57%. For people who play card games and nonsmokers, the probability of having diabetes is 26%. For people who play card games and smokers, the probability of having diabetes is 33%. The overall probability of smoker is 91%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.86
P(V3=1 | X=0, V2=0) = 0.61
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.26
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.91
0.91 * 0.60 * (0.33 - 0.26)+ 0.09 * 0.60 * (0.57 - 0.61)= -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21289,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 32%. For people who do not play card games and with diabetes, the probability of long lifespan is 60%. For people who play card games and without diabetes, the probability of long lifespan is 57%. For people who play card games and with diabetes, the probability of long lifespan is 86%. For people who do not play card games and nonsmokers, the probability of having diabetes is 61%. For people who do not play card games and smokers, the probability of having diabetes is 57%. For people who play card games and nonsmokers, the probability of having diabetes is 26%. For people who play card games and smokers, the probability of having diabetes is 33%. The overall probability of smoker is 91%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.86
P(V3=1 | X=0, V2=0) = 0.61
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.26
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.91
0.91 * 0.60 * (0.33 - 0.26)+ 0.09 * 0.60 * (0.57 - 0.61)= -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 32%. For people who do not play card games and with diabetes, the probability of long lifespan is 60%. For people who play card games and without diabetes, the probability of long lifespan is 57%. For people who play card games and with diabetes, the probability of long lifespan is 86%. For people who do not play card games and nonsmokers, the probability of having diabetes is 61%. For people who do not play card games and smokers, the probability of having diabetes is 57%. For people who play card games and nonsmokers, the probability of having diabetes is 26%. For people who play card games and smokers, the probability of having diabetes is 33%. The overall probability of smoker is 91%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.57
P(Y=1 | X=1, V3=1) = 0.86
P(V3=1 | X=0, V2=0) = 0.61
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.26
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.91
0.91 * (0.86 - 0.57) * 0.57 + 0.09 * (0.60 - 0.32) * 0.26 = 0.26
0.26 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21298,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 64%. For people who play card games, the probability of long lifespan is 50%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.50
0.50 - 0.64 = -0.15
-0.15 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 64%. For people who play card games, the probability of long lifespan is 50%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.50
0.50 - 0.64 = -0.15
-0.15 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 38%. For people who do not play card games and with diabetes, the probability of long lifespan is 74%. For people who play card games and without diabetes, the probability of long lifespan is 39%. For people who play card games and with diabetes, the probability of long lifespan is 74%. For people who do not play card games and nonsmokers, the probability of having diabetes is 69%. For people who do not play card games and smokers, the probability of having diabetes is 73%. For people who play card games and nonsmokers, the probability of having diabetes is 19%. For people who play card games and smokers, the probability of having diabetes is 33%. The overall probability of smoker is 81%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.38
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.69
P(V3=1 | X=0, V2=1) = 0.73
P(V3=1 | X=1, V2=0) = 0.19
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.81
0.81 * (0.74 - 0.39) * 0.73 + 0.19 * (0.74 - 0.38) * 0.19 = -0.01
-0.01 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 38%. For people who do not play card games and with diabetes, the probability of long lifespan is 74%. For people who play card games and without diabetes, the probability of long lifespan is 39%. For people who play card games and with diabetes, the probability of long lifespan is 74%. For people who do not play card games and nonsmokers, the probability of having diabetes is 69%. For people who do not play card games and smokers, the probability of having diabetes is 73%. For people who play card games and nonsmokers, the probability of having diabetes is 19%. For people who play card games and smokers, the probability of having diabetes is 33%. The overall probability of smoker is 81%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.38
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.74
P(V3=1 | X=0, V2=0) = 0.69
P(V3=1 | X=0, V2=1) = 0.73
P(V3=1 | X=1, V2=0) = 0.19
P(V3=1 | X=1, V2=1) = 0.33
P(V2=1) = 0.81
0.81 * (0.74 - 0.39) * 0.73 + 0.19 * (0.74 - 0.38) * 0.19 = -0.01
-0.01 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 85%. The probability of not playing card games and long lifespan is 10%. The probability of playing card games and long lifespan is 42%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.42
0.42/0.85 - 0.10/0.15 = -0.15
-0.15 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 50%. For people who play card games, the probability of long lifespan is 64%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.64
0.64 - 0.50 = 0.15
0.15 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 50%. For people who play card games, the probability of long lifespan is 64%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.64
0.64 - 0.50 = 0.15
0.15 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21315,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 50%. For people who play card games, the probability of long lifespan is 64%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.64
0.64 - 0.50 = 0.15
0.15 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21317,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 33%. For people who do not play card games and with diabetes, the probability of long lifespan is 61%. For people who play card games and without diabetes, the probability of long lifespan is 60%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 87%. For people who do not play card games and smokers, the probability of having diabetes is 58%. For people who play card games and nonsmokers, the probability of having diabetes is 47%. For people who play card games and smokers, the probability of having diabetes is 18%. The overall probability of smoker is 93%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.87
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.47
P(V3=1 | X=1, V2=1) = 0.18
P(V2=1) = 0.93
0.93 * 0.61 * (0.18 - 0.47)+ 0.07 * 0.61 * (0.58 - 0.87)= -0.12
-0.12 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 33%. For people who do not play card games and with diabetes, the probability of long lifespan is 61%. For people who play card games and without diabetes, the probability of long lifespan is 60%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 87%. For people who do not play card games and smokers, the probability of having diabetes is 58%. For people who play card games and nonsmokers, the probability of having diabetes is 47%. For people who play card games and smokers, the probability of having diabetes is 18%. The overall probability of smoker is 93%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.33
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.87
P(V3=1 | X=0, V2=1) = 0.58
P(V3=1 | X=1, V2=0) = 0.47
P(V3=1 | X=1, V2=1) = 0.18
P(V2=1) = 0.93
0.93 * (0.81 - 0.60) * 0.58 + 0.07 * (0.61 - 0.33) * 0.47 = 0.24
0.24 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 96%. For people who do not play card games, the probability of long lifespan is 50%. For people who play card games, the probability of long lifespan is 64%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.64
0.96*0.64 - 0.04*0.50 = 0.64
0.64 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 49%. For people who play card games, the probability of long lifespan is 60%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.60
0.60 - 0.49 = 0.12
0.12 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 49%. For people who play card games, the probability of long lifespan is 60%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.60
0.60 - 0.49 = 0.12
0.12 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 28%. For people who do not play card games and with diabetes, the probability of long lifespan is 59%. For people who play card games and without diabetes, the probability of long lifespan is 51%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 71%. For people who do not play card games and smokers, the probability of having diabetes is 65%. For people who play card games and nonsmokers, the probability of having diabetes is 37%. For people who play card games and smokers, the probability of having diabetes is 31%. The overall probability of smoker is 93%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.28
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.71
P(V3=1 | X=0, V2=1) = 0.65
P(V3=1 | X=1, V2=0) = 0.37
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.93
0.93 * (0.81 - 0.51) * 0.65 + 0.07 * (0.59 - 0.28) * 0.37 = 0.22
0.22 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 99%. For people who do not play card games, the probability of long lifespan is 49%. For people who play card games, the probability of long lifespan is 60%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.60
0.99*0.60 - 0.01*0.49 = 0.60
0.60 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21335,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 99%. For people who do not play card games, the probability of long lifespan is 49%. For people who play card games, the probability of long lifespan is 60%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.60
0.99*0.60 - 0.01*0.49 = 0.60
0.60 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 65%. For people who play card games, the probability of long lifespan is 56%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.56
0.56 - 0.65 = -0.09
-0.09 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 65%. For people who play card games, the probability of long lifespan is 56%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.56
0.56 - 0.65 = -0.09
-0.09 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 53%. For people who play card games, the probability of long lifespan is 69%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.69 - 0.53 = 0.16
0.16 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 53%. For people who play card games, the probability of long lifespan is 69%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.69 - 0.53 = 0.16
0.16 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 53%. For people who play card games, the probability of long lifespan is 69%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.69 - 0.53 = 0.16
0.16 > 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 41%. For people who do not play card games and with diabetes, the probability of long lifespan is 61%. For people who play card games and without diabetes, the probability of long lifespan is 63%. For people who play card games and with diabetes, the probability of long lifespan is 86%. For people who do not play card games and nonsmokers, the probability of having diabetes is 84%. For people who do not play card games and smokers, the probability of having diabetes is 60%. For people who play card games and nonsmokers, the probability of having diabetes is 56%. For people who play card games and smokers, the probability of having diabetes is 25%. The overall probability of smoker is 95%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.41
P(Y=1 | X=0, V3=1) = 0.61
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.86
P(V3=1 | X=0, V2=0) = 0.84
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.95
0.95 * (0.86 - 0.63) * 0.60 + 0.05 * (0.61 - 0.41) * 0.56 = 0.24
0.24 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 97%. For people who do not play card games, the probability of long lifespan is 53%. For people who play card games, the probability of long lifespan is 69%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.97*0.69 - 0.03*0.53 = 0.68
0.68 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 97%. For people who do not play card games, the probability of long lifespan is 53%. For people who play card games, the probability of long lifespan is 69%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.69
0.97*0.69 - 0.03*0.53 = 0.68
0.68 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21364,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 97%. The probability of not playing card games and long lifespan is 2%. The probability of playing card games and long lifespan is 67%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.67
0.67/0.97 - 0.02/0.03 = 0.16
0.16 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 55%. For people who play card games, the probability of long lifespan is 70%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.70
0.70 - 0.55 = 0.15
0.15 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 85%. For people who play card games, the probability of long lifespan is 64%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.64
0.64 - 0.85 = -0.21
-0.21 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 85%. For people who play card games, the probability of long lifespan is 64%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.64
0.64 - 0.85 = -0.21
-0.21 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 65%. For people who do not play card games and with diabetes, the probability of long lifespan is 95%. For people who play card games and without diabetes, the probability of long lifespan is 56%. For people who play card games and with diabetes, the probability of long lifespan is 88%. For people who do not play card games and nonsmokers, the probability of having diabetes is 79%. For people who do not play card games and smokers, the probability of having diabetes is 67%. For people who play card games and nonsmokers, the probability of having diabetes is 40%. For people who play card games and smokers, the probability of having diabetes is 25%. The overall probability of smoker is 95%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.95
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0, V2=0) = 0.79
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.40
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.95
0.95 * 0.95 * (0.25 - 0.40)+ 0.05 * 0.95 * (0.67 - 0.79)= -0.13
-0.13 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 65%. For people who do not play card games and with diabetes, the probability of long lifespan is 95%. For people who play card games and without diabetes, the probability of long lifespan is 56%. For people who play card games and with diabetes, the probability of long lifespan is 88%. For people who do not play card games and nonsmokers, the probability of having diabetes is 79%. For people who do not play card games and smokers, the probability of having diabetes is 67%. For people who play card games and nonsmokers, the probability of having diabetes is 40%. For people who play card games and smokers, the probability of having diabetes is 25%. The overall probability of smoker is 95%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.95
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.88
P(V3=1 | X=0, V2=0) = 0.79
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.40
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.95
0.95 * (0.88 - 0.56) * 0.67 + 0.05 * (0.95 - 0.65) * 0.40 = -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 91%. For people who do not play card games, the probability of long lifespan is 85%. For people who play card games, the probability of long lifespan is 64%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.64
0.91*0.64 - 0.09*0.85 = 0.66
0.66 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 91%. The probability of not playing card games and long lifespan is 7%. The probability of playing card games and long lifespan is 58%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.58
0.58/0.91 - 0.07/0.09 = -0.22
-0.22 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 47%. For people who play card games, the probability of long lifespan is 63%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.63
0.63 - 0.47 = 0.16
0.16 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21400,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 35%. For people who do not play card games and with diabetes, the probability of long lifespan is 58%. For people who play card games and without diabetes, the probability of long lifespan is 58%. For people who play card games and with diabetes, the probability of long lifespan is 83%. For people who do not play card games and nonsmokers, the probability of having diabetes is 80%. For people who do not play card games and smokers, the probability of having diabetes is 50%. For people who play card games and nonsmokers, the probability of having diabetes is 53%. For people who play card games and smokers, the probability of having diabetes is 17%. The overall probability of smoker is 96%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.96
0.96 * 0.58 * (0.17 - 0.53)+ 0.04 * 0.58 * (0.50 - 0.80)= -0.08
-0.08 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 35%. For people who do not play card games and with diabetes, the probability of long lifespan is 58%. For people who play card games and without diabetes, the probability of long lifespan is 58%. For people who play card games and with diabetes, the probability of long lifespan is 83%. For people who do not play card games and nonsmokers, the probability of having diabetes is 80%. For people who do not play card games and smokers, the probability of having diabetes is 50%. For people who play card games and nonsmokers, the probability of having diabetes is 53%. For people who play card games and smokers, the probability of having diabetes is 17%. The overall probability of smoker is 96%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.96
0.96 * 0.58 * (0.17 - 0.53)+ 0.04 * 0.58 * (0.50 - 0.80)= -0.08
-0.08 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 35%. For people who do not play card games and with diabetes, the probability of long lifespan is 58%. For people who play card games and without diabetes, the probability of long lifespan is 58%. For people who play card games and with diabetes, the probability of long lifespan is 83%. For people who do not play card games and nonsmokers, the probability of having diabetes is 80%. For people who do not play card games and smokers, the probability of having diabetes is 50%. For people who play card games and nonsmokers, the probability of having diabetes is 53%. For people who play card games and smokers, the probability of having diabetes is 17%. The overall probability of smoker is 96%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.83
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.50
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.96
0.96 * (0.83 - 0.58) * 0.50 + 0.04 * (0.58 - 0.35) * 0.53 = 0.25
0.25 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 84%. The probability of not playing card games and long lifespan is 8%. The probability of playing card games and long lifespan is 53%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.53
0.53/0.84 - 0.08/0.16 = 0.16
0.16 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 59%. For people who play card games, the probability of long lifespan is 74%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.74
0.74 - 0.59 = 0.15
0.15 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21416,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 35%. For people who do not play card games and with diabetes, the probability of long lifespan is 62%. For people who play card games and without diabetes, the probability of long lifespan is 61%. For people who play card games and with diabetes, the probability of long lifespan is 84%. For people who do not play card games and nonsmokers, the probability of having diabetes is 87%. For people who do not play card games and smokers, the probability of having diabetes is 89%. For people who play card games and nonsmokers, the probability of having diabetes is 53%. For people who play card games and smokers, the probability of having diabetes is 59%. The overall probability of smoker is 95%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.35
P(Y=1 | X=0, V3=1) = 0.62
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.84
P(V3=1 | X=0, V2=0) = 0.87
P(V3=1 | X=0, V2=1) = 0.89
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.59
P(V2=1) = 0.95
0.95 * (0.84 - 0.61) * 0.89 + 0.05 * (0.62 - 0.35) * 0.53 = 0.23
0.23 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21419,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 91%. For people who do not play card games, the probability of long lifespan is 59%. For people who play card games, the probability of long lifespan is 74%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.74
0.91*0.74 - 0.09*0.59 = 0.73
0.73 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 91%. The probability of not playing card games and long lifespan is 6%. The probability of playing card games and long lifespan is 67%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.67
0.67/0.91 - 0.06/0.09 = 0.15
0.15 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 91%. The probability of not playing card games and long lifespan is 6%. The probability of playing card games and long lifespan is 67%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.91
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.67
0.67/0.91 - 0.06/0.09 = 0.15
0.15 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 63%. For people who play card games, the probability of long lifespan is 53%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.53
0.53 - 0.63 = -0.09
-0.09 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 63%. For people who play card games, the probability of long lifespan is 53%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.53
0.53 - 0.63 = -0.09
-0.09 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 52%. For people who do not play card games and with diabetes, the probability of long lifespan is 74%. For people who play card games and without diabetes, the probability of long lifespan is 49%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 54%. For people who do not play card games and smokers, the probability of having diabetes is 46%. For people who play card games and nonsmokers, the probability of having diabetes is 4%. For people who play card games and smokers, the probability of having diabetes is 16%. The overall probability of smoker is 87%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.54
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.04
P(V3=1 | X=1, V2=1) = 0.16
P(V2=1) = 0.87
0.87 * 0.74 * (0.16 - 0.04)+ 0.13 * 0.74 * (0.46 - 0.54)= -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 52%. For people who do not play card games and with diabetes, the probability of long lifespan is 74%. For people who play card games and without diabetes, the probability of long lifespan is 49%. For people who play card games and with diabetes, the probability of long lifespan is 81%. For people who do not play card games and nonsmokers, the probability of having diabetes is 54%. For people who do not play card games and smokers, the probability of having diabetes is 46%. For people who play card games and nonsmokers, the probability of having diabetes is 4%. For people who play card games and smokers, the probability of having diabetes is 16%. The overall probability of smoker is 87%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.81
P(V3=1 | X=0, V2=0) = 0.54
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.04
P(V3=1 | X=1, V2=1) = 0.16
P(V2=1) = 0.87
0.87 * 0.74 * (0.16 - 0.04)+ 0.13 * 0.74 * (0.46 - 0.54)= -0.07
-0.07 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 95%. For people who do not play card games, the probability of long lifespan is 63%. For people who play card games, the probability of long lifespan is 53%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.53
0.95*0.53 - 0.05*0.63 = 0.54
0.54 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21435,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 95%. The probability of not playing card games and long lifespan is 3%. The probability of playing card games and long lifespan is 50%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.50
0.50/0.95 - 0.03/0.05 = -0.09
-0.09 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 62%. For people who play card games, the probability of long lifespan is 55%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.55
0.55 - 0.62 = -0.06
-0.06 < 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 62%. For people who play card games, the probability of long lifespan is 55%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.55
0.55 - 0.62 = -0.06
-0.06 < 0",arrowhead,obesity_mortality,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 78%. For people who play card games and without diabetes, the probability of long lifespan is 48%. For people who play card games and with diabetes, the probability of long lifespan is 77%. For people who do not play card games and nonsmokers, the probability of having diabetes is 66%. For people who do not play card games and smokers, the probability of having diabetes is 52%. For people who play card games and nonsmokers, the probability of having diabetes is 10%. For people who play card games and smokers, the probability of having diabetes is 26%. The overall probability of smoker is 95%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.66
P(V3=1 | X=0, V2=1) = 0.52
P(V3=1 | X=1, V2=0) = 0.10
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.95
0.95 * 0.78 * (0.26 - 0.10)+ 0.05 * 0.78 * (0.52 - 0.66)= -0.10
-0.10 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21445,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 43%. For people who do not play card games and with diabetes, the probability of long lifespan is 78%. For people who play card games and without diabetes, the probability of long lifespan is 48%. For people who play card games and with diabetes, the probability of long lifespan is 77%. For people who do not play card games and nonsmokers, the probability of having diabetes is 66%. For people who do not play card games and smokers, the probability of having diabetes is 52%. For people who play card games and nonsmokers, the probability of having diabetes is 10%. For people who play card games and smokers, the probability of having diabetes is 26%. The overall probability of smoker is 95%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.48
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.66
P(V3=1 | X=0, V2=1) = 0.52
P(V3=1 | X=1, V2=0) = 0.10
P(V3=1 | X=1, V2=1) = 0.26
P(V2=1) = 0.95
0.95 * (0.77 - 0.48) * 0.52 + 0.05 * (0.78 - 0.43) * 0.10 = 0.01
0.01 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 81%. For people who do not play card games, the probability of long lifespan is 62%. For people who play card games, the probability of long lifespan is 55%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.55
0.81*0.55 - 0.19*0.62 = 0.56
0.56 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 81%. The probability of not playing card games and long lifespan is 12%. The probability of playing card games and long lifespan is 45%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.45
0.45/0.81 - 0.12/0.19 = -0.06
-0.06 < 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games, the probability of long lifespan is 53%. For people who play card games, the probability of long lifespan is 74%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.74
0.74 - 0.53 = 0.21
0.21 > 0",arrowhead,obesity_mortality,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 89%. For people who do not play card games, the probability of long lifespan is 53%. For people who play card games, the probability of long lifespan is 74%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.74
0.89*0.74 - 0.11*0.53 = 0.72
0.72 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 89%. The probability of not playing card games and long lifespan is 6%. The probability of playing card games and long lifespan is 66%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.66
0.66/0.89 - 0.06/0.11 = 0.21
0.21 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 34%. For people who do not play card games and with diabetes, the probability of long lifespan is 64%. For people who play card games and without diabetes, the probability of long lifespan is 68%. For people who play card games and with diabetes, the probability of long lifespan is 92%. For people who do not play card games and nonsmokers, the probability of having diabetes is 95%. For people who do not play card games and smokers, the probability of having diabetes is 99%. For people who play card games and nonsmokers, the probability of having diabetes is 58%. For people who play card games and smokers, the probability of having diabetes is 46%. The overall probability of smoker is 95%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.68
P(Y=1 | X=1, V3=1) = 0.92
P(V3=1 | X=0, V2=0) = 0.95
P(V3=1 | X=0, V2=1) = 0.99
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.95
0.95 * 0.64 * (0.46 - 0.58)+ 0.05 * 0.64 * (0.99 - 0.95)= -0.13
-0.13 < 0",arrowhead,obesity_mortality,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
21472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. For people who do not play card games and without diabetes, the probability of long lifespan is 34%. For people who do not play card games and with diabetes, the probability of long lifespan is 64%. For people who play card games and without diabetes, the probability of long lifespan is 68%. For people who play card games and with diabetes, the probability of long lifespan is 92%. For people who do not play card games and nonsmokers, the probability of having diabetes is 95%. For people who do not play card games and smokers, the probability of having diabetes is 99%. For people who play card games and nonsmokers, the probability of having diabetes is 58%. For people who play card games and smokers, the probability of having diabetes is 46%. The overall probability of smoker is 95%.",yes,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.34
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.68
P(Y=1 | X=1, V3=1) = 0.92
P(V3=1 | X=0, V2=0) = 0.95
P(V3=1 | X=0, V2=1) = 0.99
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.95
0.95 * (0.92 - 0.68) * 0.99 + 0.05 * (0.64 - 0.34) * 0.58 = 0.29
0.29 > 0",arrowhead,obesity_mortality,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
21475,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 93%. For people who do not play card games, the probability of long lifespan is 63%. For people who play card games, the probability of long lifespan is 80%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.80
0.93*0.80 - 0.07*0.63 = 0.78
0.78 > 0",arrowhead,obesity_mortality,1,marginal,P(Y)
21477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. The overall probability of playing card games is 93%. The probability of not playing card games and long lifespan is 5%. The probability of playing card games and long lifespan is 74%.",no,"Let V2 = smoking; X = playing card games; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.74
0.74/0.93 - 0.05/0.07 = 0.16
0.16 > 0",arrowhead,obesity_mortality,1,correlation,P(Y | X)
21478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look at how playing card games correlates with lifespan case by case according to diabetes. Method 2: We look directly at how playing card games correlates with lifespan in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Playing card games has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. Method 1: We look directly at how playing card games correlates with lifespan in general. Method 2: We look at this correlation case by case according to diabetes.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,obesity_mortality,2,backadj,[backdoor adjustment set for Y given X]
21495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 46%. For patients consuming citrus, the probability of curly hair is 57%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.57
0.57 - 0.46 = 0.11
0.11 > 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 19%. For patients not consuming citrus, the probability of curly hair is 46%. For patients consuming citrus, the probability of curly hair is 57%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.57
0.19*0.57 - 0.81*0.46 = 0.48
0.48 > 0",chain,orange_scurvy,1,marginal,P(Y)
21501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 19%. The probability of absence of citrus and curly hair is 37%. The probability of citrus intake and curly hair is 11%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.11
0.11/0.19 - 0.37/0.81 = 0.11
0.11 > 0",chain,orange_scurvy,1,correlation,P(Y | X)
21503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 73%. For patients consuming citrus, the probability of curly hair is 54%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.54
0.54 - 0.73 = -0.19
-0.19 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 73%. For patients consuming citrus, the probability of curly hair is 54%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.54
0.54 - 0.73 = -0.19
-0.19 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21512,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 20%. The probability of absence of citrus and curly hair is 58%. The probability of citrus intake and curly hair is 11%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.11
0.11/0.20 - 0.58/0.80 = -0.19
-0.19 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 20%. The probability of absence of citrus and curly hair is 58%. The probability of citrus intake and curly hair is 11%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.58
P(Y=1, X=1=1) = 0.11
0.11/0.20 - 0.58/0.80 = -0.19
-0.19 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21514,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 57%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.57
0.57 - 0.47 = 0.10
0.10 > 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 57%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.57
0.57 - 0.47 = 0.10
0.10 > 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 17%. For patients not consuming citrus, the probability of curly hair is 47%. For patients consuming citrus, the probability of curly hair is 57%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.17
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.57
0.17*0.57 - 0.83*0.47 = 0.49
0.49 > 0",chain,orange_scurvy,1,marginal,P(Y)
21525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 17%. The probability of absence of citrus and curly hair is 39%. The probability of citrus intake and curly hair is 9%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.09
0.09/0.17 - 0.39/0.83 = 0.10
0.10 > 0",chain,orange_scurvy,1,correlation,P(Y | X)
21528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 56%. For patients consuming citrus, the probability of curly hair is 39%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.39
0.39 - 0.56 = -0.17
-0.17 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 56%. For patients consuming citrus, the probability of curly hair is 39%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.39
0.39 - 0.56 = -0.17
-0.17 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 56%. For patients consuming citrus, the probability of curly hair is 39%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.39
0.39 - 0.56 = -0.17
-0.17 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21533,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 56%. For patients consuming citrus, the probability of curly hair is 39%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.39
0.39 - 0.56 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 78%. For patients consuming citrus, the probability of curly hair is 52%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.52
0.52 - 0.78 = -0.27
-0.27 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 78%. For patients consuming citrus, the probability of curly hair is 52%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.52
0.52 - 0.78 = -0.27
-0.27 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 58%. For patients consuming citrus, the probability of curly hair is 32%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.32
0.32 - 0.58 = -0.26
-0.26 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 58%. For patients consuming citrus, the probability of curly hair is 32%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.32
0.32 - 0.58 = -0.26
-0.26 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21559,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 9%. For patients not consuming citrus, the probability of curly hair is 58%. For patients consuming citrus, the probability of curly hair is 32%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.32
0.09*0.32 - 0.91*0.58 = 0.55
0.55 > 0",chain,orange_scurvy,1,marginal,P(Y)
21562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 46%. For patients consuming citrus, the probability of curly hair is 61%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.61
0.61 - 0.46 = 0.15
0.15 > 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 46%. For patients consuming citrus, the probability of curly hair is 61%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.61
0.61 - 0.46 = 0.15
0.15 > 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 46%. For patients consuming citrus, the probability of curly hair is 61%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.61
0.61 - 0.46 = 0.15
0.15 > 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 8%. The probability of absence of citrus and curly hair is 43%. The probability of citrus intake and curly hair is 5%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.05
0.05/0.08 - 0.43/0.92 = 0.15
0.15 > 0",chain,orange_scurvy,1,correlation,P(Y | X)
21573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 8%. The probability of absence of citrus and curly hair is 43%. The probability of citrus intake and curly hair is 5%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.43
P(Y=1, X=1=1) = 0.05
0.05/0.08 - 0.43/0.92 = 0.15
0.15 > 0",chain,orange_scurvy,1,correlation,P(Y | X)
21582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 5%. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 32%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.32
0.05*0.32 - 0.95*0.49 = 0.48
0.48 > 0",chain,orange_scurvy,1,marginal,P(Y)
21583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 5%. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 32%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.05
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.32
0.05*0.32 - 0.95*0.49 = 0.48
0.48 > 0",chain,orange_scurvy,1,marginal,P(Y)
21584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 5%. The probability of absence of citrus and curly hair is 46%. The probability of citrus intake and curly hair is 2%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.02
0.02/0.05 - 0.46/0.95 = -0.17
-0.17 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 5%. The probability of absence of citrus and curly hair is 46%. The probability of citrus intake and curly hair is 2%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.05
P(Y=1, X=0=1) = 0.46
P(Y=1, X=1=1) = 0.02
0.02/0.05 - 0.46/0.95 = -0.17
-0.17 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 75%. For patients consuming citrus, the probability of curly hair is 46%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.46
0.46 - 0.75 = -0.29
-0.29 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21597,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 11%. The probability of absence of citrus and curly hair is 67%. The probability of citrus intake and curly hair is 5%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.11
P(Y=1, X=0=1) = 0.67
P(Y=1, X=1=1) = 0.05
0.05/0.11 - 0.67/0.89 = -0.29
-0.29 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21600,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 49%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.49
0.49 - 0.68 = -0.19
-0.19 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 49%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.49
0.49 - 0.68 = -0.19
-0.19 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21602,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 49%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.49
0.49 - 0.68 = -0.19
-0.19 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21607,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 18%. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 49%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.18
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.49
0.18*0.49 - 0.82*0.68 = 0.65
0.65 > 0",chain,orange_scurvy,1,marginal,P(Y)
21613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 44%. For patients consuming citrus, the probability of curly hair is 29%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.29
0.29 - 0.44 = -0.16
-0.16 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 44%. For patients consuming citrus, the probability of curly hair is 29%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.29
0.29 - 0.44 = -0.16
-0.16 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21619,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 10%. For patients not consuming citrus, the probability of curly hair is 44%. For patients consuming citrus, the probability of curly hair is 29%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.29
0.10*0.29 - 0.90*0.44 = 0.43
0.43 > 0",chain,orange_scurvy,1,marginal,P(Y)
21620,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 10%. The probability of absence of citrus and curly hair is 40%. The probability of citrus intake and curly hair is 3%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.03
0.03/0.10 - 0.40/0.90 = -0.16
-0.16 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 38%. For patients consuming citrus, the probability of curly hair is 13%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.13
0.13 - 0.38 = -0.25
-0.25 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 12%. The probability of absence of citrus and curly hair is 34%. The probability of citrus intake and curly hair is 2%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.12
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.02
0.02/0.12 - 0.34/0.88 = -0.25
-0.25 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21636,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 17%. For patients consuming citrus, the probability of curly hair is 30%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.30
0.30 - 0.17 = 0.14
0.14 > 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 17%. For patients consuming citrus, the probability of curly hair is 30%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.30
0.30 - 0.17 = 0.14
0.14 > 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21638,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 17%. For patients consuming citrus, the probability of curly hair is 30%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.30
0.30 - 0.17 = 0.14
0.14 > 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21646,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 17%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.17
0.17 - 0.33 = -0.16
-0.16 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 17%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.17
0.17 - 0.33 = -0.16
-0.16 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 33%. For patients consuming citrus, the probability of curly hair is 17%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.17
0.17 - 0.33 = -0.16
-0.16 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 64%. For patients consuming citrus, the probability of curly hair is 72%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.72
0.72 - 0.64 = 0.08
0.08 > 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21672,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 75%. For patients consuming citrus, the probability of curly hair is 42%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.42
0.42 - 0.75 = -0.32
-0.32 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 75%. For patients consuming citrus, the probability of curly hair is 42%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.42
0.42 - 0.75 = -0.32
-0.32 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 75%. For patients consuming citrus, the probability of curly hair is 42%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.42
0.42 - 0.75 = -0.32
-0.32 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 2%. For patients not consuming citrus, the probability of curly hair is 75%. For patients consuming citrus, the probability of curly hair is 42%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.02
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.42
0.02*0.42 - 0.98*0.75 = 0.74
0.74 > 0",chain,orange_scurvy,1,marginal,P(Y)
21680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 2%. The probability of absence of citrus and curly hair is 73%. The probability of citrus intake and curly hair is 1%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.02
P(Y=1, X=0=1) = 0.73
P(Y=1, X=1=1) = 0.01
0.01/0.02 - 0.73/0.98 = -0.32
-0.32 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 60%. For patients consuming citrus, the probability of curly hair is 74%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.74
0.74 - 0.60 = 0.13
0.13 > 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 60%. For patients consuming citrus, the probability of curly hair is 74%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.74
0.74 - 0.60 = 0.13
0.13 > 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 3%. For patients not consuming citrus, the probability of curly hair is 60%. For patients consuming citrus, the probability of curly hair is 74%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.74
0.03*0.74 - 0.97*0.60 = 0.61
0.61 > 0",chain,orange_scurvy,1,marginal,P(Y)
21691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 3%. For patients not consuming citrus, the probability of curly hair is 60%. For patients consuming citrus, the probability of curly hair is 74%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.74
0.03*0.74 - 0.97*0.60 = 0.61
0.61 > 0",chain,orange_scurvy,1,marginal,P(Y)
21700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 65%. For patients consuming citrus, the probability of curly hair is 34%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.34
0.34 - 0.65 = -0.31
-0.31 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 19%. For patients not consuming citrus, the probability of curly hair is 65%. For patients consuming citrus, the probability of curly hair is 34%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.34
0.19*0.34 - 0.81*0.65 = 0.59
0.59 > 0",chain,orange_scurvy,1,marginal,P(Y)
21705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 19%. The probability of absence of citrus and curly hair is 53%. The probability of citrus intake and curly hair is 6%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.06
0.06/0.19 - 0.53/0.81 = -0.31
-0.31 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 56%. For patients consuming citrus, the probability of curly hair is 74%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.74
0.74 - 0.56 = 0.18
0.18 > 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 56%. For patients consuming citrus, the probability of curly hair is 74%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.74
0.74 - 0.56 = 0.18
0.18 > 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 56%. For patients consuming citrus, the probability of curly hair is 74%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.74
0.74 - 0.56 = 0.18
0.18 > 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 56%. For patients consuming citrus, the probability of curly hair is 74%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.74
0.74 - 0.56 = 0.18
0.18 > 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21721,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 38%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.38
0.38 - 0.49 = -0.10
-0.10 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 38%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.38
0.38 - 0.49 = -0.10
-0.10 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 38%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.38
0.38 - 0.49 = -0.10
-0.10 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 16%. For patients not consuming citrus, the probability of curly hair is 49%. For patients consuming citrus, the probability of curly hair is 38%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.16
P(Y=1 | X=0) = 0.49
P(Y=1 | X=1) = 0.38
0.16*0.38 - 0.84*0.49 = 0.47
0.47 > 0",chain,orange_scurvy,1,marginal,P(Y)
21728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 16%. The probability of absence of citrus and curly hair is 41%. The probability of citrus intake and curly hair is 6%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.06
0.06/0.16 - 0.41/0.84 = -0.10
-0.10 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 45%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.45
0.45 - 0.61 = -0.16
-0.16 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21735,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 45%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.45
0.45 - 0.61 = -0.16
-0.16 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21736,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 45%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.45
0.45 - 0.61 = -0.16
-0.16 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 45%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.45
0.45 - 0.61 = -0.16
-0.16 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 13%. For patients not consuming citrus, the probability of curly hair is 61%. For patients consuming citrus, the probability of curly hair is 45%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.45
0.13*0.45 - 0.87*0.61 = 0.59
0.59 > 0",chain,orange_scurvy,1,marginal,P(Y)
21745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 76%. For patients consuming citrus, the probability of curly hair is 60%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.60
0.60 - 0.76 = -0.17
-0.17 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 76%. For patients consuming citrus, the probability of curly hair is 60%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.60
0.60 - 0.76 = -0.17
-0.17 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 76%. For patients consuming citrus, the probability of curly hair is 60%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.60
0.60 - 0.76 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 76%. For patients consuming citrus, the probability of curly hair is 60%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.60
0.60 - 0.76 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 20%. For patients not consuming citrus, the probability of curly hair is 76%. For patients consuming citrus, the probability of curly hair is 60%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.20
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.60
0.20*0.60 - 0.80*0.76 = 0.73
0.73 > 0",chain,orange_scurvy,1,marginal,P(Y)
21753,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 20%. The probability of absence of citrus and curly hair is 61%. The probability of citrus intake and curly hair is 12%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.20
P(Y=1, X=0=1) = 0.61
P(Y=1, X=1=1) = 0.12
0.12/0.20 - 0.61/0.80 = -0.17
-0.17 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 55%. For patients consuming citrus, the probability of curly hair is 41%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.41
0.41 - 0.55 = -0.14
-0.14 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 55%. For patients consuming citrus, the probability of curly hair is 41%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.41
0.41 - 0.55 = -0.14
-0.14 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 55%. For patients consuming citrus, the probability of curly hair is 41%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.41
0.41 - 0.55 = -0.14
-0.14 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 10%. For patients not consuming citrus, the probability of curly hair is 55%. For patients consuming citrus, the probability of curly hair is 41%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.41
0.10*0.41 - 0.90*0.55 = 0.54
0.54 > 0",chain,orange_scurvy,1,marginal,P(Y)
21764,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 10%. The probability of absence of citrus and curly hair is 50%. The probability of citrus intake and curly hair is 4%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.04
0.04/0.10 - 0.50/0.90 = -0.14
-0.14 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 54%. For patients consuming citrus, the probability of curly hair is 36%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.36
0.36 - 0.54 = -0.17
-0.17 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 6%. For patients not consuming citrus, the probability of curly hair is 54%. For patients consuming citrus, the probability of curly hair is 36%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.06
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.36
0.06*0.36 - 0.94*0.54 = 0.53
0.53 > 0",chain,orange_scurvy,1,marginal,P(Y)
21776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 6%. The probability of absence of citrus and curly hair is 50%. The probability of citrus intake and curly hair is 2%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.06
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.02
0.02/0.06 - 0.50/0.94 = -0.17
-0.17 < 0",chain,orange_scurvy,1,correlation,P(Y | X)
21783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 74%. For patients consuming citrus, the probability of curly hair is 63%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.63
0.63 - 0.74 = -0.12
-0.12 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 74%. For patients consuming citrus, the probability of curly hair is 63%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.63
0.63 - 0.74 = -0.12
-0.12 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 74%. For patients consuming citrus, the probability of curly hair is 63%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.63
0.63 - 0.74 = -0.12
-0.12 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 3%. For patients not consuming citrus, the probability of curly hair is 74%. For patients consuming citrus, the probability of curly hair is 63%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.03
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.63
0.03*0.63 - 0.97*0.74 = 0.74
0.74 > 0",chain,orange_scurvy,1,marginal,P(Y)
21791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21794,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 56%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.56
0.56 - 0.68 = -0.12
-0.12 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 56%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.56
0.56 - 0.68 = -0.12
-0.12 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 8%. For patients not consuming citrus, the probability of curly hair is 68%. For patients consuming citrus, the probability of curly hair is 56%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.56
0.08*0.56 - 0.92*0.68 = 0.67
0.67 > 0",chain,orange_scurvy,1,marginal,P(Y)
21802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look at how eating citrus correlates with curly hair case by case according to vitmain C. Method 2: We look directly at how eating citrus correlates with curly hair in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 19%. For patients consuming citrus, the probability of curly hair is 16%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.16
0.16 - 0.19 = -0.03
-0.03 < 0",chain,orange_scurvy,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
21811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. The overall probability of citrus intake is 4%. For patients not consuming citrus, the probability of curly hair is 19%. For patients consuming citrus, the probability of curly hair is 16%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.04
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.16
0.04*0.16 - 0.96*0.19 = 0.19
0.19 > 0",chain,orange_scurvy,1,marginal,P(Y)
21821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 45%. For patients consuming citrus, the probability of curly hair is 91%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.91
0.91 - 0.45 = 0.46
0.46 > 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 72%. For patients consuming citrus, the probability of curly hair is 28%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.28
0.28 - 0.72 = -0.44
-0.44 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 72%. For patients consuming citrus, the probability of curly hair is 28%.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.28
0.28 - 0.72 = -0.44
-0.44 < 0",chain,orange_scurvy,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. For patients not consuming citrus, the probability of curly hair is 72%. For patients consuming citrus, the probability of curly hair is 28%.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.28
0.28 - 0.72 = -0.44
-0.44 < 0",chain,orange_scurvy,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
21839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. Method 1: We look directly at how eating citrus correlates with curly hair in general. Method 2: We look at this correlation case by case according to vitmain C.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,orange_scurvy,2,backadj,[backdoor adjustment set for Y given X]
21840,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 69%. For farms with increased crop yield per acre, the probability of increased price is 60%. For farms with reduced crop yield per acre, the probability of full moon is 85%. For farms with increased crop yield per acre, the probability of full moon is 54%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.69
P(Y=1 | V2=1) = 0.60
P(X=1 | V2=0) = 0.85
P(X=1 | V2=1) = 0.54
(0.60 - 0.69) / (0.54 - 0.85) = 0.29
0.29 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 82%. For situations where there is no full moon, the probability of increased price is 38%. For situations where there is a full moon, the probability of increased price is 74%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.74
0.82*0.74 - 0.18*0.38 = 0.68
0.68 > 0",IV,price,1,marginal,P(Y)
21846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21848,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 81%. For farms with increased crop yield per acre, the probability of increased price is 76%. For farms with reduced crop yield per acre, the probability of full moon is 67%. For farms with increased crop yield per acre, the probability of full moon is 46%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.81
P(Y=1 | V2=1) = 0.76
P(X=1 | V2=0) = 0.67
P(X=1 | V2=1) = 0.46
(0.76 - 0.81) / (0.46 - 0.67) = 0.26
0.26 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 59%. For farms with increased crop yield per acre, the probability of increased price is 59%. For farms with reduced crop yield per acre, the probability of full moon is 82%. For farms with increased crop yield per acre, the probability of full moon is 83%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.82
P(X=1 | V2=1) = 0.83
(0.59 - 0.59) / (0.83 - 0.82) = 0.06
0.06 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 83%. The probability of no full moon and increased price is 9%. The probability of full moon and increased price is 50%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.50
0.50/0.83 - 0.09/0.17 = 0.05
0.05 > 0",IV,price,1,correlation,P(Y | X)
21864,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 85%. For farms with increased crop yield per acre, the probability of increased price is 79%. For farms with reduced crop yield per acre, the probability of full moon is 67%. For farms with increased crop yield per acre, the probability of full moon is 45%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.85
P(Y=1 | V2=1) = 0.79
P(X=1 | V2=0) = 0.67
P(X=1 | V2=1) = 0.45
(0.79 - 0.85) / (0.45 - 0.67) = 0.27
0.27 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 66%. For situations where there is no full moon, the probability of increased price is 65%. For situations where there is a full moon, the probability of increased price is 94%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.94
0.66*0.94 - 0.34*0.65 = 0.85
0.85 > 0",IV,price,1,marginal,P(Y)
21871,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 75%. For situations where there is no full moon, the probability of increased price is 48%. For situations where there is a full moon, the probability of increased price is 77%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.75
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.77
0.75*0.77 - 0.25*0.48 = 0.70
0.70 > 0",IV,price,1,marginal,P(Y)
21877,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 75%. The probability of no full moon and increased price is 12%. The probability of full moon and increased price is 57%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.75
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.57
0.57/0.75 - 0.12/0.25 = 0.29
0.29 > 0",IV,price,1,correlation,P(Y | X)
21880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 36%. For farms with increased crop yield per acre, the probability of increased price is 37%. For farms with reduced crop yield per acre, the probability of full moon is 62%. For farms with increased crop yield per acre, the probability of full moon is 67%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.36
P(Y=1 | V2=1) = 0.37
P(X=1 | V2=0) = 0.62
P(X=1 | V2=1) = 0.67
(0.37 - 0.36) / (0.67 - 0.62) = 0.23
0.23 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 67%. The probability of no full moon and increased price is 8%. The probability of full moon and increased price is 30%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.67
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.30
0.30/0.67 - 0.08/0.33 = 0.21
0.21 > 0",IV,price,1,correlation,P(Y | X)
21886,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 61%. For farms with increased crop yield per acre, the probability of increased price is 52%. For farms with reduced crop yield per acre, the probability of full moon is 68%. For farms with increased crop yield per acre, the probability of full moon is 30%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.61
P(Y=1 | V2=1) = 0.52
P(X=1 | V2=0) = 0.68
P(X=1 | V2=1) = 0.30
(0.52 - 0.61) / (0.30 - 0.68) = 0.25
0.25 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 66%. The probability of no full moon and increased price is 14%. The probability of full moon and increased price is 47%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.47
0.47/0.66 - 0.14/0.34 = 0.29
0.29 > 0",IV,price,1,correlation,P(Y | X)
21894,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 59%. For farms with increased crop yield per acre, the probability of increased price is 40%. For farms with reduced crop yield per acre, the probability of full moon is 60%. For farms with increased crop yield per acre, the probability of full moon is 8%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.59
P(Y=1 | V2=1) = 0.40
P(X=1 | V2=0) = 0.60
P(X=1 | V2=1) = 0.08
(0.40 - 0.59) / (0.08 - 0.60) = 0.36
0.36 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21898,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 59%. For situations where there is no full moon, the probability of increased price is 38%. For situations where there is a full moon, the probability of increased price is 72%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.72
0.59*0.72 - 0.41*0.38 = 0.58
0.58 > 0",IV,price,1,marginal,P(Y)
21899,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 59%. For situations where there is no full moon, the probability of increased price is 38%. For situations where there is a full moon, the probability of increased price is 72%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.72
0.59*0.72 - 0.41*0.38 = 0.58
0.58 > 0",IV,price,1,marginal,P(Y)
21901,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 59%. The probability of no full moon and increased price is 15%. The probability of full moon and increased price is 43%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.43
0.43/0.59 - 0.15/0.41 = 0.35
0.35 > 0",IV,price,1,correlation,P(Y | X)
21905,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 63%. For farms with increased crop yield per acre, the probability of increased price is 65%. For farms with reduced crop yield per acre, the probability of full moon is 85%. For farms with increased crop yield per acre, the probability of full moon is 73%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.63
P(Y=1 | V2=1) = 0.65
P(X=1 | V2=0) = 0.85
P(X=1 | V2=1) = 0.73
(0.65 - 0.63) / (0.73 - 0.85) = -0.16
-0.16 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 75%. For situations where there is no full moon, the probability of increased price is 79%. For situations where there is a full moon, the probability of increased price is 61%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.75
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.61
0.75*0.61 - 0.25*0.79 = 0.64
0.64 > 0",IV,price,1,marginal,P(Y)
21908,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 75%. The probability of no full moon and increased price is 20%. The probability of full moon and increased price is 45%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.75
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.45
0.45/0.75 - 0.20/0.25 = -0.18
-0.18 < 0",IV,price,1,correlation,P(Y | X)
21921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 75%. For farms with increased crop yield per acre, the probability of increased price is 65%. For farms with reduced crop yield per acre, the probability of full moon is 96%. For farms with increased crop yield per acre, the probability of full moon is 52%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.75
P(Y=1 | V2=1) = 0.65
P(X=1 | V2=0) = 0.96
P(X=1 | V2=1) = 0.52
(0.65 - 0.75) / (0.52 - 0.96) = 0.24
0.24 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21932,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 93%. The probability of no full moon and increased price is 6%. The probability of full moon and increased price is 87%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.87
0.87/0.93 - 0.06/0.07 = 0.06
0.06 > 0",IV,price,1,correlation,P(Y | X)
21938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 87%. For situations where there is no full moon, the probability of increased price is 40%. For situations where there is a full moon, the probability of increased price is 82%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.82
0.87*0.82 - 0.13*0.40 = 0.76
0.76 > 0",IV,price,1,marginal,P(Y)
21939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 87%. For situations where there is no full moon, the probability of increased price is 40%. For situations where there is a full moon, the probability of increased price is 82%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.82
0.87*0.82 - 0.13*0.40 = 0.76
0.76 > 0",IV,price,1,marginal,P(Y)
21941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 87%. The probability of no full moon and increased price is 5%. The probability of full moon and increased price is 71%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.87
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.71
0.71/0.87 - 0.05/0.13 = 0.42
0.42 > 0",IV,price,1,correlation,P(Y | X)
21942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 78%. For farms with increased crop yield per acre, the probability of increased price is 65%. For farms with reduced crop yield per acre, the probability of full moon is 74%. For farms with increased crop yield per acre, the probability of full moon is 26%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.78
P(Y=1 | V2=1) = 0.65
P(X=1 | V2=0) = 0.74
P(X=1 | V2=1) = 0.26
(0.65 - 0.78) / (0.26 - 0.74) = 0.28
0.28 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 68%. The probability of no full moon and increased price is 19%. The probability of full moon and increased price is 57%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.68
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.57
0.57/0.68 - 0.19/0.32 = 0.24
0.24 > 0",IV,price,1,correlation,P(Y | X)
21951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 32%. For situations where there is no full moon, the probability of increased price is 44%. For situations where there is a full moon, the probability of increased price is 58%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.32
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.58
0.32*0.58 - 0.68*0.44 = 0.47
0.47 > 0",IV,price,1,marginal,P(Y)
21956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 32%. The probability of no full moon and increased price is 30%. The probability of full moon and increased price is 18%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.32
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.18
0.18/0.32 - 0.30/0.68 = 0.14
0.14 > 0",IV,price,1,correlation,P(Y | X)
21958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 70%. For situations where there is no full moon, the probability of increased price is 33%. For situations where there is a full moon, the probability of increased price is 84%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.70
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.84
0.70*0.84 - 0.30*0.33 = 0.69
0.69 > 0",IV,price,1,marginal,P(Y)
21963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 70%. For situations where there is no full moon, the probability of increased price is 33%. For situations where there is a full moon, the probability of increased price is 84%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.70
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.84
0.70*0.84 - 0.30*0.33 = 0.69
0.69 > 0",IV,price,1,marginal,P(Y)
21966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 67%. For farms with increased crop yield per acre, the probability of increased price is 58%. For farms with reduced crop yield per acre, the probability of full moon is 77%. For farms with increased crop yield per acre, the probability of full moon is 39%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.67
P(Y=1 | V2=1) = 0.58
P(X=1 | V2=0) = 0.77
P(X=1 | V2=1) = 0.39
(0.58 - 0.67) / (0.39 - 0.77) = 0.25
0.25 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 67%. For farms with increased crop yield per acre, the probability of increased price is 58%. For farms with reduced crop yield per acre, the probability of full moon is 77%. For farms with increased crop yield per acre, the probability of full moon is 39%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.67
P(Y=1 | V2=1) = 0.58
P(X=1 | V2=0) = 0.77
P(X=1 | V2=1) = 0.39
(0.58 - 0.67) / (0.39 - 0.77) = 0.25
0.25 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21970,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 74%. For situations where there is no full moon, the probability of increased price is 47%. For situations where there is a full moon, the probability of increased price is 74%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.74
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.74
0.74*0.74 - 0.26*0.47 = 0.67
0.67 > 0",IV,price,1,marginal,P(Y)
21976,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 67%. For farms with increased crop yield per acre, the probability of increased price is 69%. For farms with reduced crop yield per acre, the probability of full moon is 72%. For farms with increased crop yield per acre, the probability of full moon is 66%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.67
P(Y=1 | V2=1) = 0.69
P(X=1 | V2=0) = 0.72
P(X=1 | V2=1) = 0.66
(0.69 - 0.67) / (0.66 - 0.72) = -0.24
-0.24 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 66%. For situations where there is no full moon, the probability of increased price is 84%. For situations where there is a full moon, the probability of increased price is 60%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.60
0.66*0.60 - 0.34*0.84 = 0.68
0.68 > 0",IV,price,1,marginal,P(Y)
21979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 66%. For situations where there is no full moon, the probability of increased price is 84%. For situations where there is a full moon, the probability of increased price is 60%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.84
P(Y=1 | X=1) = 0.60
0.66*0.60 - 0.34*0.84 = 0.68
0.68 > 0",IV,price,1,marginal,P(Y)
21980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 66%. The probability of no full moon and increased price is 29%. The probability of full moon and increased price is 40%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.66
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.40
0.40/0.66 - 0.29/0.34 = -0.24
-0.24 < 0",IV,price,1,correlation,P(Y | X)
21982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 73%. For farms with increased crop yield per acre, the probability of increased price is 64%. For farms with reduced crop yield per acre, the probability of full moon is 80%. For farms with increased crop yield per acre, the probability of full moon is 50%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.73
P(Y=1 | V2=1) = 0.64
P(X=1 | V2=0) = 0.80
P(X=1 | V2=1) = 0.50
(0.64 - 0.73) / (0.50 - 0.80) = 0.32
0.32 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21987,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 78%. For situations where there is no full moon, the probability of increased price is 44%. For situations where there is a full moon, the probability of increased price is 81%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.78
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.81
0.78*0.81 - 0.22*0.44 = 0.73
0.73 > 0",IV,price,1,marginal,P(Y)
21989,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 78%. The probability of no full moon and increased price is 10%. The probability of full moon and increased price is 63%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.78
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.63
0.63/0.78 - 0.10/0.22 = 0.37
0.37 > 0",IV,price,1,correlation,P(Y | X)
21991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
21993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 66%. For farms with increased crop yield per acre, the probability of increased price is 54%. For farms with reduced crop yield per acre, the probability of full moon is 63%. For farms with increased crop yield per acre, the probability of full moon is 25%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.66
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.63
P(X=1 | V2=1) = 0.25
(0.54 - 0.66) / (0.25 - 0.63) = 0.30
0.30 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
21994,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 57%. For situations where there is no full moon, the probability of increased price is 47%. For situations where there is a full moon, the probability of increased price is 76%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.76
0.57*0.76 - 0.43*0.47 = 0.64
0.64 > 0",IV,price,1,marginal,P(Y)
21996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 57%. The probability of no full moon and increased price is 20%. The probability of full moon and increased price is 43%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.43
0.43/0.57 - 0.20/0.43 = 0.29
0.29 > 0",IV,price,1,correlation,P(Y | X)
22000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 48%. For farms with increased crop yield per acre, the probability of increased price is 50%. For farms with reduced crop yield per acre, the probability of full moon is 49%. For farms with increased crop yield per acre, the probability of full moon is 60%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.48
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.49
P(X=1 | V2=1) = 0.60
(0.50 - 0.48) / (0.60 - 0.49) = 0.12
0.12 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 48%. For farms with increased crop yield per acre, the probability of increased price is 50%. For farms with reduced crop yield per acre, the probability of full moon is 49%. For farms with increased crop yield per acre, the probability of full moon is 60%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.48
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.49
P(X=1 | V2=1) = 0.60
(0.50 - 0.48) / (0.60 - 0.49) = 0.12
0.12 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22002,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 60%. For situations where there is no full moon, the probability of increased price is 41%. For situations where there is a full moon, the probability of increased price is 56%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.56
0.60*0.56 - 0.40*0.41 = 0.50
0.50 > 0",IV,price,1,marginal,P(Y)
22005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 60%. The probability of no full moon and increased price is 16%. The probability of full moon and increased price is 34%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.34
0.34/0.60 - 0.16/0.40 = 0.15
0.15 > 0",IV,price,1,correlation,P(Y | X)
22007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
22009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 66%. For farms with increased crop yield per acre, the probability of increased price is 58%. For farms with reduced crop yield per acre, the probability of full moon is 69%. For farms with increased crop yield per acre, the probability of full moon is 42%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.66
P(Y=1 | V2=1) = 0.58
P(X=1 | V2=0) = 0.69
P(X=1 | V2=1) = 0.42
(0.58 - 0.66) / (0.42 - 0.69) = 0.26
0.26 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 69%. For situations where there is no full moon, the probability of increased price is 45%. For situations where there is a full moon, the probability of increased price is 74%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.69
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.74
0.69*0.74 - 0.31*0.45 = 0.65
0.65 > 0",IV,price,1,marginal,P(Y)
22013,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 69%. The probability of no full moon and increased price is 14%. The probability of full moon and increased price is 51%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.69
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.51
0.51/0.69 - 0.14/0.31 = 0.29
0.29 > 0",IV,price,1,correlation,P(Y | X)
22017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 62%. For farms with increased crop yield per acre, the probability of increased price is 54%. For farms with reduced crop yield per acre, the probability of full moon is 77%. For farms with increased crop yield per acre, the probability of full moon is 41%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.62
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.77
P(X=1 | V2=1) = 0.41
(0.54 - 0.62) / (0.41 - 0.77) = 0.21
0.21 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 76%. The probability of no full moon and increased price is 11%. The probability of full moon and increased price is 51%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.76
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.51
0.51/0.76 - 0.11/0.24 = 0.24
0.24 > 0",IV,price,1,correlation,P(Y | X)
22023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
22025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 80%. For farms with increased crop yield per acre, the probability of increased price is 74%. For farms with reduced crop yield per acre, the probability of full moon is 29%. For farms with increased crop yield per acre, the probability of full moon is 46%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.80
P(Y=1 | V2=1) = 0.74
P(X=1 | V2=0) = 0.29
P(X=1 | V2=1) = 0.46
(0.74 - 0.80) / (0.46 - 0.29) = -0.37
-0.37 < 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 44%. The probability of no full moon and increased price is 50%. The probability of full moon and increased price is 25%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.25
0.25/0.44 - 0.50/0.56 = -0.34
-0.34 < 0",IV,price,1,correlation,P(Y | X)
22031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
22032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 51%. For farms with increased crop yield per acre, the probability of increased price is 42%. For farms with reduced crop yield per acre, the probability of full moon is 73%. For farms with increased crop yield per acre, the probability of full moon is 45%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.51
P(Y=1 | V2=1) = 0.42
P(X=1 | V2=0) = 0.73
P(X=1 | V2=1) = 0.45
(0.42 - 0.51) / (0.45 - 0.73) = 0.32
0.32 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 71%. For situations where there is no full moon, the probability of increased price is 25%. For situations where there is a full moon, the probability of increased price is 61%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.61
0.71*0.61 - 0.29*0.25 = 0.50
0.50 > 0",IV,price,1,marginal,P(Y)
22035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 71%. For situations where there is no full moon, the probability of increased price is 25%. For situations where there is a full moon, the probability of increased price is 61%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.71
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.61
0.71*0.61 - 0.29*0.25 = 0.50
0.50 > 0",IV,price,1,marginal,P(Y)
22037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 71%. The probability of no full moon and increased price is 7%. The probability of full moon and increased price is 43%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.71
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.43
0.43/0.71 - 0.07/0.29 = 0.35
0.35 > 0",IV,price,1,correlation,P(Y | X)
22039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
22040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 62%. For farms with increased crop yield per acre, the probability of increased price is 49%. For farms with reduced crop yield per acre, the probability of full moon is 69%. For farms with increased crop yield per acre, the probability of full moon is 24%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.62
P(Y=1 | V2=1) = 0.49
P(X=1 | V2=0) = 0.69
P(X=1 | V2=1) = 0.24
(0.49 - 0.62) / (0.24 - 0.69) = 0.30
0.30 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 63%. For situations where there is no full moon, the probability of increased price is 41%. For situations where there is a full moon, the probability of increased price is 72%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.72
0.63*0.72 - 0.37*0.41 = 0.60
0.60 > 0",IV,price,1,marginal,P(Y)
22045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 63%. The probability of no full moon and increased price is 15%. The probability of full moon and increased price is 45%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.45
0.45/0.63 - 0.15/0.37 = 0.31
0.31 > 0",IV,price,1,correlation,P(Y | X)
22046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look directly at how full moon correlates with price in general. Method 2: We look at this correlation case by case according to demand.",no,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
22047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
22049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 30%. For farms with increased crop yield per acre, the probability of increased price is 36%. For farms with reduced crop yield per acre, the probability of full moon is 13%. For farms with increased crop yield per acre, the probability of full moon is 48%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.30
P(Y=1 | V2=1) = 0.36
P(X=1 | V2=0) = 0.13
P(X=1 | V2=1) = 0.48
(0.36 - 0.30) / (0.48 - 0.13) = 0.19
0.19 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 82%. For farms with increased crop yield per acre, the probability of increased price is 68%. For farms with reduced crop yield per acre, the probability of full moon is 95%. For farms with increased crop yield per acre, the probability of full moon is 48%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.82
P(Y=1 | V2=1) = 0.68
P(X=1 | V2=0) = 0.95
P(X=1 | V2=1) = 0.48
(0.68 - 0.82) / (0.48 - 0.95) = 0.30
0.30 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22058,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 93%. For situations where there is no full moon, the probability of increased price is 50%. For situations where there is a full moon, the probability of increased price is 84%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.84
0.93*0.84 - 0.07*0.50 = 0.82
0.82 > 0",IV,price,1,marginal,P(Y)
22061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 93%. The probability of no full moon and increased price is 3%. The probability of full moon and increased price is 78%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.78
0.78/0.93 - 0.03/0.07 = 0.34
0.34 > 0",IV,price,1,correlation,P(Y | X)
22063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. Method 1: We look at how full moon correlates with price case by case according to demand. Method 2: We look directly at how full moon correlates with price in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,price,2,backadj,[backdoor adjustment set for Y given X]
22068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. The overall probability of full moon is 62%. The probability of no full moon and increased price is 21%. The probability of full moon and increased price is 50%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.62
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.50
0.50/0.62 - 0.21/0.38 = 0.24
0.24 > 0",IV,price,1,correlation,P(Y | X)
22072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 74%. For farms with increased crop yield per acre, the probability of increased price is 61%. For farms with reduced crop yield per acre, the probability of full moon is 88%. For farms with increased crop yield per acre, the probability of full moon is 39%.",yes,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.74
P(Y=1 | V2=1) = 0.61
P(X=1 | V2=0) = 0.88
P(X=1 | V2=1) = 0.39
(0.61 - 0.74) / (0.39 - 0.88) = 0.27
0.27 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on full moon and price. Yield per acre has a direct effect on full moon. Full moon has a direct effect on price. Demand is unobserved. For farms with reduced crop yield per acre, the probability of increased price is 74%. For farms with increased crop yield per acre, the probability of increased price is 61%. For farms with reduced crop yield per acre, the probability of full moon is 88%. For farms with increased crop yield per acre, the probability of full moon is 39%.",no,"Let V2 = yield per acre; V1 = demand; X = full moon; Y = price.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.74
P(Y=1 | V2=1) = 0.61
P(X=1 | V2=0) = 0.88
P(X=1 | V2=1) = 0.39
(0.61 - 0.74) / (0.39 - 0.88) = 0.27
0.27 > 0",IV,price,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22092,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 92%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 61%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 36%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 6%. The overall probability of male gender is 55%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.92
P(Y=1 | V1=0, X=1) = 0.61
P(Y=1 | V1=1, X=0) = 0.36
P(Y=1 | V1=1, X=1) = 0.06
P(V1=1) = 0.55
0.45 * (0.61 - 0.92) + 0.55 * (0.06 - 0.36) = -0.31
-0.31 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22093,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 92%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 61%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 36%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 6%. The overall probability of male gender is 55%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.92
P(Y=1 | V1=0, X=1) = 0.61
P(Y=1 | V1=1, X=0) = 0.36
P(Y=1 | V1=1, X=1) = 0.06
P(V1=1) = 0.55
0.45 * (0.61 - 0.92) + 0.55 * (0.06 - 0.36) = -0.31
-0.31 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22094,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 40%. For patients not receiving treatment, the probability of being allergic to peanuts is 43%. For patients receiving treatment, the probability of being allergic to peanuts is 59%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.59
0.40*0.59 - 0.60*0.43 = 0.50
0.50 > 0",confounding,simpson_drug,1,marginal,P(Y)
22095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 40%. For patients not receiving treatment, the probability of being allergic to peanuts is 43%. For patients receiving treatment, the probability of being allergic to peanuts is 59%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.59
0.40*0.59 - 0.60*0.43 = 0.50
0.50 > 0",confounding,simpson_drug,1,marginal,P(Y)
22096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 40%. The probability of receives no treatment and being allergic to peanuts is 26%. The probability of receives treatment and being allergic to peanuts is 24%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.24
0.24/0.40 - 0.26/0.60 = 0.16
0.16 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 40%. The probability of receives no treatment and being allergic to peanuts is 26%. The probability of receives treatment and being allergic to peanuts is 24%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.26
P(Y=1, X=1=1) = 0.24
0.24/0.40 - 0.26/0.60 = 0.16
0.16 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 96%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 84%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 33%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 20%. The overall probability of male gender is 52%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.84
P(Y=1 | V1=1, X=0) = 0.33
P(Y=1 | V1=1, X=1) = 0.20
P(V1=1) = 0.52
0.48 * (0.84 - 0.96) + 0.52 * (0.20 - 0.33) = -0.12
-0.12 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 46%. The probability of receives no treatment and being allergic to peanuts is 21%. The probability of receives treatment and being allergic to peanuts is 37%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.37
0.37/0.46 - 0.21/0.54 = 0.42
0.42 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 96%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 64%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 38%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 8%. The overall probability of male gender is 49%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.64
P(Y=1 | V1=1, X=0) = 0.38
P(Y=1 | V1=1, X=1) = 0.08
P(V1=1) = 0.49
0.51 * (0.64 - 0.96) + 0.49 * (0.08 - 0.38) = -0.32
-0.32 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 90%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 80%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 30%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 20%. The overall probability of male gender is 50%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.90
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.30
P(Y=1 | V1=1, X=1) = 0.20
P(V1=1) = 0.50
0.50 * (0.80 - 0.90) + 0.50 * (0.20 - 0.30) = -0.10
-0.10 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 55%. The probability of receives no treatment and being allergic to peanuts is 14%. The probability of receives treatment and being allergic to peanuts is 41%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.41
0.41/0.55 - 0.14/0.45 = 0.43
0.43 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22129,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 94%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 61%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 34%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 0%. The overall probability of male gender is 48%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.61
P(Y=1 | V1=1, X=0) = 0.34
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.48
0.52 * (0.61 - 0.94) + 0.48 * (0.00 - 0.34) = -0.33
-0.33 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 94%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 61%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 34%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 0%. The overall probability of male gender is 48%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.61
P(Y=1 | V1=1, X=0) = 0.34
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.48
0.52 * (0.61 - 0.94) + 0.48 * (0.00 - 0.34) = -0.33
-0.33 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 51%. For patients not receiving treatment, the probability of being allergic to peanuts is 38%. For patients receiving treatment, the probability of being allergic to peanuts is 59%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.59
0.51*0.59 - 0.49*0.38 = 0.48
0.48 > 0",confounding,simpson_drug,1,marginal,P(Y)
22136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 51%. The probability of receives no treatment and being allergic to peanuts is 18%. The probability of receives treatment and being allergic to peanuts is 30%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.30
0.30/0.51 - 0.18/0.49 = 0.22
0.22 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 55%. The probability of receives no treatment and being allergic to peanuts is 14%. The probability of receives treatment and being allergic to peanuts is 39%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.39
0.39/0.55 - 0.14/0.45 = 0.41
0.41 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 55%. The probability of receives no treatment and being allergic to peanuts is 14%. The probability of receives treatment and being allergic to peanuts is 39%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.39
0.39/0.55 - 0.14/0.45 = 0.41
0.41 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 97%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 66%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 39%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 7%. The overall probability of male gender is 48%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.66
P(Y=1 | V1=1, X=0) = 0.39
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.48
0.52 * (0.66 - 0.97) + 0.48 * (0.07 - 0.39) = -0.32
-0.32 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 97%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 66%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 39%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 7%. The overall probability of male gender is 48%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.66
P(Y=1 | V1=1, X=0) = 0.39
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.48
0.52 * (0.66 - 0.97) + 0.48 * (0.07 - 0.39) = -0.32
-0.32 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 80%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 67%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 19%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 4%. The overall probability of male gender is 41%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.80
P(Y=1 | V1=0, X=1) = 0.67
P(Y=1 | V1=1, X=0) = 0.19
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.41
0.59 * (0.67 - 0.80) + 0.41 * (0.04 - 0.19) = -0.14
-0.14 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 59%. For patients not receiving treatment, the probability of being allergic to peanuts is 24%. For patients receiving treatment, the probability of being allergic to peanuts is 64%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.64
0.59*0.64 - 0.41*0.24 = 0.47
0.47 > 0",confounding,simpson_drug,1,marginal,P(Y)
22165,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 59%. For patients not receiving treatment, the probability of being allergic to peanuts is 24%. For patients receiving treatment, the probability of being allergic to peanuts is 64%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.64
0.59*0.64 - 0.41*0.24 = 0.47
0.47 > 0",confounding,simpson_drug,1,marginal,P(Y)
22167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 59%. The probability of receives no treatment and being allergic to peanuts is 10%. The probability of receives treatment and being allergic to peanuts is 38%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.59
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.38
0.38/0.59 - 0.10/0.41 = 0.39
0.39 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 47%. For patients not receiving treatment, the probability of being allergic to peanuts is 37%. For patients receiving treatment, the probability of being allergic to peanuts is 52%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.52
0.47*0.52 - 0.53*0.37 = 0.45
0.45 > 0",confounding,simpson_drug,1,marginal,P(Y)
22179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 97%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 75%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 25%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 7%. The overall probability of male gender is 51%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.51
0.49 * (0.75 - 0.97) + 0.51 * (0.07 - 0.25) = -0.22
-0.22 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 55%. For patients not receiving treatment, the probability of being allergic to peanuts is 27%. For patients receiving treatment, the probability of being allergic to peanuts is 66%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.66
0.55*0.66 - 0.45*0.27 = 0.50
0.50 > 0",confounding,simpson_drug,1,marginal,P(Y)
22193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 93%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 62%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 35%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 4%. The overall probability of male gender is 58%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.93
P(Y=1 | V1=0, X=1) = 0.62
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.58
0.42 * (0.62 - 0.93) + 0.58 * (0.04 - 0.35) = -0.31
-0.31 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22195,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 44%. For patients not receiving treatment, the probability of being allergic to peanuts is 38%. For patients receiving treatment, the probability of being allergic to peanuts is 56%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.56
0.44*0.56 - 0.56*0.38 = 0.46
0.46 > 0",confounding,simpson_drug,1,marginal,P(Y)
22201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 86%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 74%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 28%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 13%. The overall probability of male gender is 50%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.86
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.28
P(Y=1 | V1=1, X=1) = 0.13
P(V1=1) = 0.50
0.50 * (0.74 - 0.86) + 0.50 * (0.13 - 0.28) = -0.13
-0.13 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 49%. For patients not receiving treatment, the probability of being allergic to peanuts is 32%. For patients receiving treatment, the probability of being allergic to peanuts is 71%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.71
0.49*0.71 - 0.51*0.32 = 0.50
0.50 > 0",confounding,simpson_drug,1,marginal,P(Y)
22206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 49%. The probability of receives no treatment and being allergic to peanuts is 16%. The probability of receives treatment and being allergic to peanuts is 35%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.35
0.35/0.49 - 0.16/0.51 = 0.39
0.39 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22211,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 93%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 61%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 35%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 2%. The overall probability of male gender is 41%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.93
P(Y=1 | V1=0, X=1) = 0.61
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.41
0.59 * (0.61 - 0.93) + 0.41 * (0.02 - 0.35) = -0.32
-0.32 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22219,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 99%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 77%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 26%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 9%. The overall probability of male gender is 47%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.26
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.47
0.53 * (0.77 - 0.99) + 0.47 * (0.09 - 0.26) = -0.20
-0.20 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 99%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 77%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 26%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 9%. The overall probability of male gender is 47%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.26
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.47
0.53 * (0.77 - 0.99) + 0.47 * (0.09 - 0.26) = -0.22
-0.22 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 99%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 77%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 26%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 9%. The overall probability of male gender is 47%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.26
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.47
0.53 * (0.77 - 0.99) + 0.47 * (0.09 - 0.26) = -0.22
-0.22 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 55%. For patients not receiving treatment, the probability of being allergic to peanuts is 30%. For patients receiving treatment, the probability of being allergic to peanuts is 72%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.72
0.55*0.72 - 0.45*0.30 = 0.54
0.54 > 0",confounding,simpson_drug,1,marginal,P(Y)
22226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 55%. The probability of receives no treatment and being allergic to peanuts is 14%. The probability of receives treatment and being allergic to peanuts is 39%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.39
0.39/0.55 - 0.14/0.45 = 0.42
0.42 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 97%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 67%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 41%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 9%. The overall probability of male gender is 58%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.67
P(Y=1 | V1=1, X=0) = 0.41
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.58
0.42 * (0.67 - 0.97) + 0.58 * (0.09 - 0.41) = -0.31
-0.31 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 41%. For patients not receiving treatment, the probability of being allergic to peanuts is 45%. For patients receiving treatment, the probability of being allergic to peanuts is 63%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.63
0.41*0.63 - 0.59*0.45 = 0.52
0.52 > 0",confounding,simpson_drug,1,marginal,P(Y)
22238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22242,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 91%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 81%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 30%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 15%. The overall probability of male gender is 44%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.30
P(Y=1 | V1=1, X=1) = 0.15
P(V1=1) = 0.44
0.56 * (0.81 - 0.91) + 0.44 * (0.15 - 0.30) = -0.10
-0.10 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 56%. For patients not receiving treatment, the probability of being allergic to peanuts is 35%. For patients receiving treatment, the probability of being allergic to peanuts is 77%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.77
0.56*0.77 - 0.44*0.35 = 0.57
0.57 > 0",confounding,simpson_drug,1,marginal,P(Y)
22248,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 67%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 41%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 10%. The overall probability of male gender is 43%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.67
P(Y=1 | V1=1, X=0) = 0.41
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.43
0.57 * (0.67 - 0.98) + 0.43 * (0.10 - 0.41) = -0.32
-0.32 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 67%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 41%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 10%. The overall probability of male gender is 43%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.67
P(Y=1 | V1=1, X=0) = 0.41
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.43
0.57 * (0.67 - 0.98) + 0.43 * (0.10 - 0.41) = -0.32
-0.32 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 82%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 65%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 18%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 1%. The overall probability of male gender is 44%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.82
P(Y=1 | V1=0, X=1) = 0.65
P(Y=1 | V1=1, X=0) = 0.18
P(Y=1 | V1=1, X=1) = 0.01
P(V1=1) = 0.44
0.56 * (0.65 - 0.82) + 0.44 * (0.01 - 0.18) = -0.17
-0.17 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 82%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 65%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 18%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 1%. The overall probability of male gender is 44%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.82
P(Y=1 | V1=0, X=1) = 0.65
P(Y=1 | V1=1, X=0) = 0.18
P(Y=1 | V1=1, X=1) = 0.01
P(V1=1) = 0.44
0.56 * (0.65 - 0.82) + 0.44 * (0.01 - 0.18) = -0.17
-0.17 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 56%. For patients not receiving treatment, the probability of being allergic to peanuts is 18%. For patients receiving treatment, the probability of being allergic to peanuts is 64%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.64
0.56*0.64 - 0.44*0.18 = 0.44
0.44 > 0",confounding,simpson_drug,1,marginal,P(Y)
22266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 56%. The probability of receives no treatment and being allergic to peanuts is 8%. The probability of receives treatment and being allergic to peanuts is 36%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.36
0.36/0.56 - 0.08/0.44 = 0.46
0.46 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 56%. The probability of receives no treatment and being allergic to peanuts is 8%. The probability of receives treatment and being allergic to peanuts is 36%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.36
0.36/0.56 - 0.08/0.44 = 0.46
0.46 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 95%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 65%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 40%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 7%. The overall probability of male gender is 43%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.65
P(Y=1 | V1=1, X=0) = 0.40
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.43
0.57 * (0.65 - 0.95) + 0.43 * (0.07 - 0.40) = -0.31
-0.31 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 95%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 65%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 40%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 7%. The overall probability of male gender is 43%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.65
P(Y=1 | V1=1, X=0) = 0.40
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.43
0.57 * (0.65 - 0.95) + 0.43 * (0.07 - 0.40) = -0.30
-0.30 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 52%. For patients not receiving treatment, the probability of being allergic to peanuts is 46%. For patients receiving treatment, the probability of being allergic to peanuts is 64%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.64
0.52*0.64 - 0.48*0.46 = 0.55
0.55 > 0",confounding,simpson_drug,1,marginal,P(Y)
22275,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 52%. For patients not receiving treatment, the probability of being allergic to peanuts is 46%. For patients receiving treatment, the probability of being allergic to peanuts is 64%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.64
0.52*0.64 - 0.48*0.46 = 0.55
0.55 > 0",confounding,simpson_drug,1,marginal,P(Y)
22278,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22282,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 87%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 34%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 14%. The overall probability of male gender is 43%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.87
P(Y=1 | V1=1, X=0) = 0.34
P(Y=1 | V1=1, X=1) = 0.14
P(V1=1) = 0.43
0.57 * (0.87 - 0.98) + 0.43 * (0.14 - 0.34) = -0.11
-0.11 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 87%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 34%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 14%. The overall probability of male gender is 43%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.87
P(Y=1 | V1=1, X=0) = 0.34
P(Y=1 | V1=1, X=1) = 0.14
P(V1=1) = 0.43
0.57 * (0.87 - 0.98) + 0.43 * (0.14 - 0.34) = -0.11
-0.11 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22284,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 57%. For patients not receiving treatment, the probability of being allergic to peanuts is 38%. For patients receiving treatment, the probability of being allergic to peanuts is 84%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.84
0.57*0.84 - 0.43*0.38 = 0.62
0.62 > 0",confounding,simpson_drug,1,marginal,P(Y)
22285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 57%. For patients not receiving treatment, the probability of being allergic to peanuts is 38%. For patients receiving treatment, the probability of being allergic to peanuts is 84%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.84
0.57*0.84 - 0.43*0.38 = 0.62
0.62 > 0",confounding,simpson_drug,1,marginal,P(Y)
22292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 64%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 39%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 9%. The overall probability of male gender is 40%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.64
P(Y=1 | V1=1, X=0) = 0.39
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.40
0.60 * (0.64 - 0.98) + 0.40 * (0.09 - 0.39) = -0.34
-0.34 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22293,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 64%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 39%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 9%. The overall probability of male gender is 40%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.64
P(Y=1 | V1=1, X=0) = 0.39
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.40
0.60 * (0.64 - 0.98) + 0.40 * (0.09 - 0.39) = -0.34
-0.34 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 57%. For patients not receiving treatment, the probability of being allergic to peanuts is 46%. For patients receiving treatment, the probability of being allergic to peanuts is 61%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.61
0.57*0.61 - 0.43*0.46 = 0.56
0.56 > 0",confounding,simpson_drug,1,marginal,P(Y)
22299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 87%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 77%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 27%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 13%. The overall probability of male gender is 54%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.87
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.13
P(V1=1) = 0.54
0.46 * (0.77 - 0.87) + 0.54 * (0.13 - 0.27) = -0.13
-0.13 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22303,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 87%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 77%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 27%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 13%. The overall probability of male gender is 54%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.87
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.13
P(V1=1) = 0.54
0.46 * (0.77 - 0.87) + 0.54 * (0.13 - 0.27) = -0.11
-0.11 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 45%. For patients not receiving treatment, the probability of being allergic to peanuts is 31%. For patients receiving treatment, the probability of being allergic to peanuts is 73%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.73
0.45*0.73 - 0.55*0.31 = 0.49
0.49 > 0",confounding,simpson_drug,1,marginal,P(Y)
22308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 42%. For patients not receiving treatment, the probability of being allergic to peanuts is 36%. For patients receiving treatment, the probability of being allergic to peanuts is 52%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.42
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.52
0.42*0.52 - 0.58*0.36 = 0.43
0.43 > 0",confounding,simpson_drug,1,marginal,P(Y)
22316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 42%. The probability of receives no treatment and being allergic to peanuts is 21%. The probability of receives treatment and being allergic to peanuts is 22%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.22
0.22/0.42 - 0.21/0.58 = 0.16
0.16 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22317,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 42%. The probability of receives no treatment and being allergic to peanuts is 21%. The probability of receives treatment and being allergic to peanuts is 22%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.22
0.22/0.42 - 0.21/0.58 = 0.16
0.16 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 83%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 73%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 27%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 16%. The overall probability of male gender is 58%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.83
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.16
P(V1=1) = 0.58
0.42 * (0.73 - 0.83) + 0.58 * (0.16 - 0.27) = -0.10
-0.10 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 45%. For patients not receiving treatment, the probability of being allergic to peanuts is 27%. For patients receiving treatment, the probability of being allergic to peanuts is 69%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.69
0.45*0.69 - 0.55*0.27 = 0.46
0.46 > 0",confounding,simpson_drug,1,marginal,P(Y)
22326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 45%. The probability of receives no treatment and being allergic to peanuts is 15%. The probability of receives treatment and being allergic to peanuts is 31%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.31
0.31/0.45 - 0.15/0.55 = 0.42
0.42 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 45%. The probability of receives no treatment and being allergic to peanuts is 15%. The probability of receives treatment and being allergic to peanuts is 31%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.31
0.31/0.45 - 0.15/0.55 = 0.42
0.42 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 94%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 61%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 35%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 5%. The overall probability of male gender is 40%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.61
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.40
0.60 * (0.61 - 0.94) + 0.40 * (0.05 - 0.35) = -0.32
-0.32 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 94%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 61%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 35%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 5%. The overall probability of male gender is 40%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.61
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.40
0.60 * (0.61 - 0.94) + 0.40 * (0.05 - 0.35) = -0.33
-0.33 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look directly at how treatment correlates with peanut allergy in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 84%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 71%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 21%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 3%. The overall probability of male gender is 54%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.84
P(Y=1 | V1=0, X=1) = 0.71
P(Y=1 | V1=1, X=0) = 0.21
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.54
0.46 * (0.71 - 0.84) + 0.54 * (0.03 - 0.21) = -0.13
-0.13 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 47%. The probability of receives no treatment and being allergic to peanuts is 13%. The probability of receives treatment and being allergic to peanuts is 31%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.31
0.31/0.47 - 0.13/0.53 = 0.41
0.41 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 64%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 36%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 2%. The overall probability of male gender is 48%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.64
P(Y=1 | V1=1, X=0) = 0.36
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.48
0.52 * (0.64 - 0.98) + 0.48 * (0.02 - 0.36) = -0.34
-0.34 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 64%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 36%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 2%. The overall probability of male gender is 48%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.64
P(Y=1 | V1=1, X=0) = 0.36
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.48
0.52 * (0.64 - 0.98) + 0.48 * (0.02 - 0.36) = -0.34
-0.34 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 98%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 64%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 36%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 2%. The overall probability of male gender is 48%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.64
P(Y=1 | V1=1, X=0) = 0.36
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.48
0.52 * (0.64 - 0.98) + 0.48 * (0.02 - 0.36) = -0.34
-0.34 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 52%. The probability of receives no treatment and being allergic to peanuts is 20%. The probability of receives treatment and being allergic to peanuts is 31%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.31
0.31/0.52 - 0.20/0.48 = 0.19
0.19 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 52%. The probability of receives no treatment and being allergic to peanuts is 20%. The probability of receives treatment and being allergic to peanuts is 31%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.31
0.31/0.52 - 0.20/0.48 = 0.19
0.19 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22360,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 78%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 62%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 13%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 2%. The overall probability of male gender is 57%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.78
P(Y=1 | V1=0, X=1) = 0.62
P(Y=1 | V1=1, X=0) = 0.13
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.57
0.43 * (0.62 - 0.78) + 0.57 * (0.02 - 0.13) = -0.13
-0.13 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 78%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 62%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 13%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 2%. The overall probability of male gender is 57%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.78
P(Y=1 | V1=0, X=1) = 0.62
P(Y=1 | V1=1, X=0) = 0.13
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.57
0.43 * (0.62 - 0.78) + 0.57 * (0.02 - 0.13) = -0.15
-0.15 < 0",confounding,simpson_drug,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 44%. The probability of receives no treatment and being allergic to peanuts is 9%. The probability of receives treatment and being allergic to peanuts is 25%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.25
0.25/0.44 - 0.09/0.56 = 0.42
0.42 > 0",confounding,simpson_drug,1,correlation,P(Y | X)
22369,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. Method 1: We look at how treatment correlates with peanut allergy case by case according to gender. Method 2: We look directly at how treatment correlates with peanut allergy in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_drug,2,backadj,[backdoor adjustment set for Y given X]
22370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. For patients who are not male and not receiving treatment, the probability of being allergic to peanuts is 99%. For patients who are not male and receiving treatment, the probability of being allergic to peanuts is 66%. For patients who are male and not receiving treatment, the probability of being allergic to peanuts is 35%. For patients who are male and receiving treatment, the probability of being allergic to peanuts is 2%. The overall probability of male gender is 52%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.66
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.52
0.48 * (0.66 - 0.99) + 0.52 * (0.02 - 0.35) = -0.33
-0.33 < 0",confounding,simpson_drug,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 50%. For patients not receiving treatment, the probability of being allergic to peanuts is 39%. For patients receiving treatment, the probability of being allergic to peanuts is 60%.",no,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.60
0.50*0.60 - 0.50*0.39 = 0.49
0.49 > 0",confounding,simpson_drug,1,marginal,P(Y)
22375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on treatment and peanut allergy. Treatment has a direct effect on peanut allergy. The overall probability of receives treatment is 50%. For patients not receiving treatment, the probability of being allergic to peanuts is 39%. For patients receiving treatment, the probability of being allergic to peanuts is 60%.",yes,"Let V1 = gender; X = treatment; Y = peanut allergy.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.60
0.50*0.60 - 0.50*0.39 = 0.49
0.49 > 0",confounding,simpson_drug,1,marginal,P(Y)
22380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 97%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 57%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.57
0.43 * (0.75 - 0.97) + 0.57 * (0.02 - 0.24) = -0.22
-0.22 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 97%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 57%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.57
0.43 * (0.75 - 0.97) + 0.57 * (0.02 - 0.24) = -0.22
-0.22 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 97%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 57%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.57
0.43 * (0.75 - 0.97) + 0.57 * (0.02 - 0.24) = -0.22
-0.22 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 97%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 57%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.57
0.43 * (0.75 - 0.97) + 0.57 * (0.02 - 0.24) = -0.22
-0.22 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 37%. For patients who pay a low hospital bill, the probability of thick lips is 36%. For people who pay a high hospital bill, the probability of thick lips is 69%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.69
0.37*0.69 - 0.63*0.36 = 0.48
0.48 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 37%. The probability of low hospital bill and thick lips is 23%. The probability of high hospital bill and thick lips is 25%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.25
0.25/0.37 - 0.23/0.63 = 0.33
0.33 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 89%. For patients who are young and pay a high hospital bill, the probability of thick lips is 76%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 10%. The overall probability of old age is 42%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.89
P(Y=1 | V1=0, X=1) = 0.76
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.42
0.58 * (0.76 - 0.89) + 0.42 * (0.10 - 0.24) = -0.13
-0.13 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 97%. For patients who are young and pay a high hospital bill, the probability of thick lips is 76%. For patients who are old and pay a low hospital bill, the probability of thick lips is 25%. For patients who are old and pay a high hospital bill, the probability of thick lips is 3%. The overall probability of old age is 48%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.76
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.48
0.52 * (0.76 - 0.97) + 0.48 * (0.03 - 0.25) = -0.21
-0.21 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 51%. For patients who pay a low hospital bill, the probability of thick lips is 32%. For people who pay a high hospital bill, the probability of thick lips is 70%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.70
0.51*0.70 - 0.49*0.32 = 0.52
0.52 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 51%. The probability of low hospital bill and thick lips is 16%. The probability of high hospital bill and thick lips is 36%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.36
0.36/0.51 - 0.16/0.49 = 0.38
0.38 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 91%. For patients who are young and pay a high hospital bill, the probability of thick lips is 77%. For patients who are old and pay a low hospital bill, the probability of thick lips is 31%. For patients who are old and pay a high hospital bill, the probability of thick lips is 20%. The overall probability of old age is 50%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.31
P(Y=1 | V1=1, X=1) = 0.20
P(V1=1) = 0.50
0.50 * (0.77 - 0.91) + 0.50 * (0.20 - 0.31) = -0.13
-0.13 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 91%. For patients who are young and pay a high hospital bill, the probability of thick lips is 77%. For patients who are old and pay a low hospital bill, the probability of thick lips is 31%. For patients who are old and pay a high hospital bill, the probability of thick lips is 20%. The overall probability of old age is 50%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.31
P(Y=1 | V1=1, X=1) = 0.20
P(V1=1) = 0.50
0.50 * (0.77 - 0.91) + 0.50 * (0.20 - 0.31) = -0.13
-0.13 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 91%. For patients who are young and pay a high hospital bill, the probability of thick lips is 77%. For patients who are old and pay a low hospital bill, the probability of thick lips is 31%. For patients who are old and pay a high hospital bill, the probability of thick lips is 20%. The overall probability of old age is 50%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.31
P(Y=1 | V1=1, X=1) = 0.20
P(V1=1) = 0.50
0.50 * (0.77 - 0.91) + 0.50 * (0.20 - 0.31) = -0.13
-0.13 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 53%. For patients who pay a low hospital bill, the probability of thick lips is 34%. For people who pay a high hospital bill, the probability of thick lips is 72%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.72
0.53*0.72 - 0.47*0.34 = 0.54
0.54 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22424,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 40%. For patients who pay a low hospital bill, the probability of thick lips is 33%. For people who pay a high hospital bill, the probability of thick lips is 69%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.69
0.40*0.69 - 0.60*0.33 = 0.47
0.47 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 40%. For patients who pay a low hospital bill, the probability of thick lips is 33%. For people who pay a high hospital bill, the probability of thick lips is 69%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.69
0.40*0.69 - 0.60*0.33 = 0.47
0.47 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 82%. For patients who are young and pay a high hospital bill, the probability of thick lips is 71%. For patients who are old and pay a low hospital bill, the probability of thick lips is 25%. For patients who are old and pay a high hospital bill, the probability of thick lips is 11%. The overall probability of old age is 46%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.82
P(Y=1 | V1=0, X=1) = 0.71
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.11
P(V1=1) = 0.46
0.54 * (0.71 - 0.82) + 0.46 * (0.11 - 0.25) = -0.12
-0.12 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 82%. For patients who are young and pay a high hospital bill, the probability of thick lips is 71%. For patients who are old and pay a low hospital bill, the probability of thick lips is 25%. For patients who are old and pay a high hospital bill, the probability of thick lips is 11%. The overall probability of old age is 46%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.82
P(Y=1 | V1=0, X=1) = 0.71
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.11
P(V1=1) = 0.46
0.54 * (0.71 - 0.82) + 0.46 * (0.11 - 0.25) = -0.12
-0.12 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22435,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 53%. For patients who pay a low hospital bill, the probability of thick lips is 29%. For people who pay a high hospital bill, the probability of thick lips is 68%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.68
0.53*0.68 - 0.47*0.29 = 0.49
0.49 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 53%. The probability of low hospital bill and thick lips is 14%. The probability of high hospital bill and thick lips is 36%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.36
0.36/0.53 - 0.14/0.47 = 0.39
0.39 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 55%. For patients who pay a low hospital bill, the probability of thick lips is 25%. For people who pay a high hospital bill, the probability of thick lips is 59%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.59
0.55*0.59 - 0.45*0.25 = 0.44
0.44 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22445,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 55%. For patients who pay a low hospital bill, the probability of thick lips is 25%. For people who pay a high hospital bill, the probability of thick lips is 59%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.59
0.55*0.59 - 0.45*0.25 = 0.44
0.44 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 55%. The probability of low hospital bill and thick lips is 11%. The probability of high hospital bill and thick lips is 32%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.32
0.32/0.55 - 0.11/0.45 = 0.34
0.34 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 84%. For patients who are young and pay a high hospital bill, the probability of thick lips is 69%. For patients who are old and pay a low hospital bill, the probability of thick lips is 23%. For patients who are old and pay a high hospital bill, the probability of thick lips is 10%. The overall probability of old age is 54%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.84
P(Y=1 | V1=0, X=1) = 0.69
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.54
0.46 * (0.69 - 0.84) + 0.54 * (0.10 - 0.23) = -0.14
-0.14 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 84%. For patients who are young and pay a high hospital bill, the probability of thick lips is 69%. For patients who are old and pay a low hospital bill, the probability of thick lips is 23%. For patients who are old and pay a high hospital bill, the probability of thick lips is 10%. The overall probability of old age is 54%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.84
P(Y=1 | V1=0, X=1) = 0.69
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.54
0.46 * (0.69 - 0.84) + 0.54 * (0.10 - 0.23) = -0.14
-0.14 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 47%. For patients who pay a low hospital bill, the probability of thick lips is 24%. For people who pay a high hospital bill, the probability of thick lips is 67%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.67
0.47*0.67 - 0.53*0.24 = 0.45
0.45 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22457,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 47%. The probability of low hospital bill and thick lips is 13%. The probability of high hospital bill and thick lips is 32%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.47
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.32
0.32/0.47 - 0.13/0.53 = 0.43
0.43 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 25%. For patients who are old and pay a high hospital bill, the probability of thick lips is 5%. The overall probability of old age is 52%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.52
0.48 * (0.75 - 0.96) + 0.52 * (0.05 - 0.25) = -0.20
-0.20 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 25%. For patients who are old and pay a high hospital bill, the probability of thick lips is 5%. The overall probability of old age is 52%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.52
0.48 * (0.75 - 0.96) + 0.52 * (0.05 - 0.25) = -0.21
-0.21 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 25%. For patients who are old and pay a high hospital bill, the probability of thick lips is 5%. The overall probability of old age is 52%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.52
0.48 * (0.75 - 0.96) + 0.52 * (0.05 - 0.25) = -0.21
-0.21 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22466,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 62%. The probability of low hospital bill and thick lips is 14%. The probability of high hospital bill and thick lips is 33%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.62
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.33
0.33/0.62 - 0.14/0.38 = 0.18
0.18 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 62%. The probability of low hospital bill and thick lips is 14%. The probability of high hospital bill and thick lips is 33%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.62
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.33
0.33/0.62 - 0.14/0.38 = 0.18
0.18 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 87%. For patients who are young and pay a high hospital bill, the probability of thick lips is 72%. For patients who are old and pay a low hospital bill, the probability of thick lips is 21%. For patients who are old and pay a high hospital bill, the probability of thick lips is 8%. The overall probability of old age is 41%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.87
P(Y=1 | V1=0, X=1) = 0.72
P(Y=1 | V1=1, X=0) = 0.21
P(Y=1 | V1=1, X=1) = 0.08
P(V1=1) = 0.41
0.59 * (0.72 - 0.87) + 0.41 * (0.08 - 0.21) = -0.14
-0.14 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 58%. For patients who pay a low hospital bill, the probability of thick lips is 26%. For people who pay a high hospital bill, the probability of thick lips is 69%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.69
0.58*0.69 - 0.42*0.26 = 0.52
0.52 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22485,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 63%. For patients who pay a low hospital bill, the probability of thick lips is 27%. For people who pay a high hospital bill, the probability of thick lips is 58%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.58
0.63*0.58 - 0.37*0.27 = 0.46
0.46 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22486,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 63%. The probability of low hospital bill and thick lips is 10%. The probability of high hospital bill and thick lips is 36%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.36
0.36/0.63 - 0.10/0.37 = 0.31
0.31 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 99%. For patients who are young and pay a high hospital bill, the probability of thick lips is 78%. For patients who are old and pay a low hospital bill, the probability of thick lips is 27%. For patients who are old and pay a high hospital bill, the probability of thick lips is 5%. The overall probability of old age is 52%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.78
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.52
0.48 * (0.78 - 0.99) + 0.52 * (0.05 - 0.27) = -0.21
-0.21 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 49%. For patients who pay a low hospital bill, the probability of thick lips is 39%. For people who pay a high hospital bill, the probability of thick lips is 63%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.63
0.49*0.63 - 0.51*0.39 = 0.51
0.51 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 49%. The probability of low hospital bill and thick lips is 20%. The probability of high hospital bill and thick lips is 31%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.31
0.31/0.49 - 0.20/0.51 = 0.24
0.24 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 80%. For patients who are young and pay a high hospital bill, the probability of thick lips is 65%. For patients who are old and pay a low hospital bill, the probability of thick lips is 18%. For patients who are old and pay a high hospital bill, the probability of thick lips is 1%. The overall probability of old age is 54%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.80
P(Y=1 | V1=0, X=1) = 0.65
P(Y=1 | V1=1, X=0) = 0.18
P(Y=1 | V1=1, X=1) = 0.01
P(V1=1) = 0.54
0.46 * (0.65 - 0.80) + 0.54 * (0.01 - 0.18) = -0.16
-0.16 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22512,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 80%. For patients who are young and pay a high hospital bill, the probability of thick lips is 65%. For patients who are old and pay a low hospital bill, the probability of thick lips is 18%. For patients who are old and pay a high hospital bill, the probability of thick lips is 1%. The overall probability of old age is 54%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.80
P(Y=1 | V1=0, X=1) = 0.65
P(Y=1 | V1=1, X=0) = 0.18
P(Y=1 | V1=1, X=1) = 0.01
P(V1=1) = 0.54
0.46 * (0.65 - 0.80) + 0.54 * (0.01 - 0.18) = -0.15
-0.15 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 45%. For patients who pay a low hospital bill, the probability of thick lips is 24%. For people who pay a high hospital bill, the probability of thick lips is 60%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.60
0.45*0.60 - 0.55*0.24 = 0.39
0.39 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 45%. The probability of low hospital bill and thick lips is 13%. The probability of high hospital bill and thick lips is 27%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.27
0.27/0.45 - 0.13/0.55 = 0.36
0.36 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 45%. The probability of low hospital bill and thick lips is 13%. The probability of high hospital bill and thick lips is 27%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.27
0.27/0.45 - 0.13/0.55 = 0.36
0.36 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 95%. For patients who are young and pay a high hospital bill, the probability of thick lips is 73%. For patients who are old and pay a low hospital bill, the probability of thick lips is 22%. For patients who are old and pay a high hospital bill, the probability of thick lips is 0%. The overall probability of old age is 40%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.40
0.60 * (0.73 - 0.95) + 0.40 * (0.00 - 0.22) = -0.22
-0.22 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 95%. For patients who are young and pay a high hospital bill, the probability of thick lips is 73%. For patients who are old and pay a low hospital bill, the probability of thick lips is 22%. For patients who are old and pay a high hospital bill, the probability of thick lips is 0%. The overall probability of old age is 40%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.40
0.60 * (0.73 - 0.95) + 0.40 * (0.00 - 0.22) = -0.22
-0.22 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 60%. For patients who pay a low hospital bill, the probability of thick lips is 39%. For people who pay a high hospital bill, the probability of thick lips is 62%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.60
P(Y=1 | X=0) = 0.39
P(Y=1 | X=1) = 0.62
0.60*0.62 - 0.40*0.39 = 0.53
0.53 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 60%. The probability of low hospital bill and thick lips is 15%. The probability of high hospital bill and thick lips is 37%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.60
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.37
0.37/0.60 - 0.15/0.40 = 0.24
0.24 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 86%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 27%. For patients who are old and pay a high hospital bill, the probability of thick lips is 11%. The overall probability of old age is 54%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.86
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.11
P(V1=1) = 0.54
0.46 * (0.75 - 0.86) + 0.54 * (0.11 - 0.27) = -0.13
-0.13 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 86%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 27%. For patients who are old and pay a high hospital bill, the probability of thick lips is 11%. The overall probability of old age is 54%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.86
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.11
P(V1=1) = 0.54
0.46 * (0.75 - 0.86) + 0.54 * (0.11 - 0.27) = -0.11
-0.11 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22533,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 86%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 27%. For patients who are old and pay a high hospital bill, the probability of thick lips is 11%. The overall probability of old age is 54%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.86
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.11
P(V1=1) = 0.54
0.46 * (0.75 - 0.86) + 0.54 * (0.11 - 0.27) = -0.11
-0.11 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22536,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 44%. The probability of low hospital bill and thick lips is 17%. The probability of high hospital bill and thick lips is 32%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.32
0.32/0.44 - 0.17/0.56 = 0.44
0.44 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 23%. For patients who are old and pay a high hospital bill, the probability of thick lips is 3%. The overall probability of old age is 52%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.52
0.48 * (0.75 - 0.96) + 0.52 * (0.03 - 0.23) = -0.21
-0.21 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 52%. The probability of low hospital bill and thick lips is 17%. The probability of high hospital bill and thick lips is 30%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.30
0.30/0.52 - 0.17/0.48 = 0.24
0.24 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 84%. For patients who are young and pay a high hospital bill, the probability of thick lips is 74%. For patients who are old and pay a low hospital bill, the probability of thick lips is 22%. For patients who are old and pay a high hospital bill, the probability of thick lips is 6%. The overall probability of old age is 42%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.84
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.06
P(V1=1) = 0.42
0.58 * (0.74 - 0.84) + 0.42 * (0.06 - 0.22) = -0.13
-0.13 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 58%. The probability of low hospital bill and thick lips is 11%. The probability of high hospital bill and thick lips is 41%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.58
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.41
0.41/0.58 - 0.11/0.42 = 0.44
0.44 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 74%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 40%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.40
0.60 * (0.74 - 0.96) + 0.40 * (0.02 - 0.24) = -0.22
-0.22 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 74%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 40%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.40
0.60 * (0.74 - 0.96) + 0.40 * (0.02 - 0.24) = -0.22
-0.22 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 59%. For patients who pay a low hospital bill, the probability of thick lips is 32%. For people who pay a high hospital bill, the probability of thick lips is 69%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.59
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.69
0.59*0.69 - 0.41*0.32 = 0.54
0.54 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 91%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 29%. For patients who are old and pay a high hospital bill, the probability of thick lips is 16%. The overall probability of old age is 41%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.29
P(Y=1 | V1=1, X=1) = 0.16
P(V1=1) = 0.41
0.59 * (0.75 - 0.91) + 0.41 * (0.16 - 0.29) = -0.15
-0.15 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 91%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 29%. For patients who are old and pay a high hospital bill, the probability of thick lips is 16%. The overall probability of old age is 41%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.29
P(Y=1 | V1=1, X=1) = 0.16
P(V1=1) = 0.41
0.59 * (0.75 - 0.91) + 0.41 * (0.16 - 0.29) = -0.16
-0.16 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 91%. For patients who are young and pay a high hospital bill, the probability of thick lips is 75%. For patients who are old and pay a low hospital bill, the probability of thick lips is 29%. For patients who are old and pay a high hospital bill, the probability of thick lips is 16%. The overall probability of old age is 41%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.29
P(Y=1 | V1=1, X=1) = 0.16
P(V1=1) = 0.41
0.59 * (0.75 - 0.91) + 0.41 * (0.16 - 0.29) = -0.16
-0.16 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 55%. The probability of low hospital bill and thick lips is 17%. The probability of high hospital bill and thick lips is 40%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.40
0.40/0.55 - 0.17/0.45 = 0.37
0.37 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 74%. For patients who are old and pay a low hospital bill, the probability of thick lips is 23%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 46%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.46
0.54 * (0.74 - 0.96) + 0.46 * (0.02 - 0.23) = -0.21
-0.21 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 74%. For patients who are old and pay a low hospital bill, the probability of thick lips is 23%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 46%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.46
0.54 * (0.74 - 0.96) + 0.46 * (0.02 - 0.23) = -0.21
-0.21 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 57%. For patients who pay a low hospital bill, the probability of thick lips is 32%. For people who pay a high hospital bill, the probability of thick lips is 64%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.64
0.57*0.64 - 0.43*0.32 = 0.50
0.50 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 57%. The probability of low hospital bill and thick lips is 14%. The probability of high hospital bill and thick lips is 37%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.37
0.37/0.57 - 0.14/0.43 = 0.33
0.33 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 57%. The probability of low hospital bill and thick lips is 14%. The probability of high hospital bill and thick lips is 37%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.37
0.37/0.57 - 0.14/0.43 = 0.33
0.33 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 99%. For patients who are young and pay a high hospital bill, the probability of thick lips is 87%. For patients who are old and pay a low hospital bill, the probability of thick lips is 30%. For patients who are old and pay a high hospital bill, the probability of thick lips is 19%. The overall probability of old age is 47%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.87
P(Y=1 | V1=1, X=0) = 0.30
P(Y=1 | V1=1, X=1) = 0.19
P(V1=1) = 0.47
0.53 * (0.87 - 0.99) + 0.47 * (0.19 - 0.30) = -0.13
-0.13 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 100%. For patients who are young and pay a high hospital bill, the probability of thick lips is 79%. For patients who are old and pay a low hospital bill, the probability of thick lips is 27%. For patients who are old and pay a high hospital bill, the probability of thick lips is 7%. The overall probability of old age is 47%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 1.00
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.47
0.53 * (0.79 - 1.00) + 0.47 * (0.07 - 0.27) = -0.21
-0.21 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22602,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 100%. For patients who are young and pay a high hospital bill, the probability of thick lips is 79%. For patients who are old and pay a low hospital bill, the probability of thick lips is 27%. For patients who are old and pay a high hospital bill, the probability of thick lips is 7%. The overall probability of old age is 47%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 1.00
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.47
0.53 * (0.79 - 1.00) + 0.47 * (0.07 - 0.27) = -0.21
-0.21 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22604,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 69%. For patients who pay a low hospital bill, the probability of thick lips is 32%. For people who pay a high hospital bill, the probability of thick lips is 61%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.69
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.61
0.69*0.61 - 0.31*0.32 = 0.52
0.52 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 91%. For patients who are young and pay a high hospital bill, the probability of thick lips is 76%. For patients who are old and pay a low hospital bill, the probability of thick lips is 28%. For patients who are old and pay a high hospital bill, the probability of thick lips is 12%. The overall probability of old age is 57%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.76
P(Y=1 | V1=1, X=0) = 0.28
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.57
0.43 * (0.76 - 0.91) + 0.57 * (0.12 - 0.28) = -0.16
-0.16 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 91%. For patients who are young and pay a high hospital bill, the probability of thick lips is 76%. For patients who are old and pay a low hospital bill, the probability of thick lips is 28%. For patients who are old and pay a high hospital bill, the probability of thick lips is 12%. The overall probability of old age is 57%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.76
P(Y=1 | V1=1, X=0) = 0.28
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.57
0.43 * (0.76 - 0.91) + 0.57 * (0.12 - 0.28) = -0.15
-0.15 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22617,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 42%. The probability of low hospital bill and thick lips is 18%. The probability of high hospital bill and thick lips is 30%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.42
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.30
0.30/0.42 - 0.18/0.58 = 0.39
0.39 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22619,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 95%. For patients who are young and pay a high hospital bill, the probability of thick lips is 74%. For patients who are old and pay a low hospital bill, the probability of thick lips is 23%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 48%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.48
0.52 * (0.74 - 0.95) + 0.48 * (0.02 - 0.23) = -0.21
-0.21 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 95%. For patients who are young and pay a high hospital bill, the probability of thick lips is 74%. For patients who are old and pay a low hospital bill, the probability of thick lips is 23%. For patients who are old and pay a high hospital bill, the probability of thick lips is 2%. The overall probability of old age is 48%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.48
0.52 * (0.74 - 0.95) + 0.48 * (0.02 - 0.23) = -0.21
-0.21 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 51%. The probability of low hospital bill and thick lips is 19%. The probability of high hospital bill and thick lips is 30%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.30
0.30/0.51 - 0.19/0.49 = 0.19
0.19 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22630,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 89%. For patients who are young and pay a high hospital bill, the probability of thick lips is 73%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 9%. The overall probability of old age is 59%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.89
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.59
0.41 * (0.73 - 0.89) + 0.59 * (0.09 - 0.24) = -0.16
-0.16 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 89%. For patients who are young and pay a high hospital bill, the probability of thick lips is 73%. For patients who are old and pay a low hospital bill, the probability of thick lips is 24%. For patients who are old and pay a high hospital bill, the probability of thick lips is 9%. The overall probability of old age is 59%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.89
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.59
0.41 * (0.73 - 0.89) + 0.59 * (0.09 - 0.24) = -0.16
-0.16 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 44%. For patients who pay a low hospital bill, the probability of thick lips is 28%. For people who pay a high hospital bill, the probability of thick lips is 64%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.64
0.44*0.64 - 0.56*0.28 = 0.44
0.44 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 44%. For patients who pay a low hospital bill, the probability of thick lips is 28%. For people who pay a high hospital bill, the probability of thick lips is 64%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.64
0.44*0.64 - 0.56*0.28 = 0.44
0.44 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22644,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 38%. For patients who pay a low hospital bill, the probability of thick lips is 37%. For people who pay a high hospital bill, the probability of thick lips is 61%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.38
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.61
0.38*0.61 - 0.62*0.37 = 0.47
0.47 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22646,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 38%. The probability of low hospital bill and thick lips is 23%. The probability of high hospital bill and thick lips is 23%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.23
0.23/0.38 - 0.23/0.62 = 0.24
0.24 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22647,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 38%. The probability of low hospital bill and thick lips is 23%. The probability of high hospital bill and thick lips is 23%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.23
0.23/0.38 - 0.23/0.62 = 0.24
0.24 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 96%. For patients who are young and pay a high hospital bill, the probability of thick lips is 79%. For patients who are old and pay a low hospital bill, the probability of thick lips is 34%. For patients who are old and pay a high hospital bill, the probability of thick lips is 20%. The overall probability of old age is 49%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.34
P(Y=1 | V1=1, X=1) = 0.20
P(V1=1) = 0.49
0.51 * (0.79 - 0.96) + 0.49 * (0.20 - 0.34) = -0.17
-0.17 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22654,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 55%. For patients who pay a low hospital bill, the probability of thick lips is 35%. For people who pay a high hospital bill, the probability of thick lips is 74%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.74
0.55*0.74 - 0.45*0.35 = 0.57
0.57 > 0",confounding,simpson_hospital,1,marginal,P(Y)
22657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. The overall probability of high hospital bill is 55%. The probability of low hospital bill and thick lips is 16%. The probability of high hospital bill and thick lips is 40%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.40
0.40/0.55 - 0.16/0.45 = 0.39
0.39 > 0",confounding,simpson_hospital,1,correlation,P(Y | X)
22658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 83%. For patients who are young and pay a high hospital bill, the probability of thick lips is 68%. For patients who are old and pay a low hospital bill, the probability of thick lips is 21%. For patients who are old and pay a high hospital bill, the probability of thick lips is 10%. The overall probability of old age is 47%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.83
P(Y=1 | V1=0, X=1) = 0.68
P(Y=1 | V1=1, X=0) = 0.21
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.47
0.53 * (0.68 - 0.83) + 0.47 * (0.10 - 0.21) = -0.14
-0.14 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look at how hospital costs correlates with lip thickness case by case according to age. Method 2: We look directly at how hospital costs correlates with lip thickness in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22670,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 95%. For patients who are young and pay a high hospital bill, the probability of thick lips is 73%. For patients who are old and pay a low hospital bill, the probability of thick lips is 22%. For patients who are old and pay a high hospital bill, the probability of thick lips is 0%. The overall probability of old age is 52%.",no,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.52
0.48 * (0.73 - 0.95) + 0.52 * (0.00 - 0.22) = -0.22
-0.22 < 0",confounding,simpson_hospital,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22672,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. For patients who are young and pay a low hospital bill, the probability of thick lips is 95%. For patients who are young and pay a high hospital bill, the probability of thick lips is 73%. For patients who are old and pay a low hospital bill, the probability of thick lips is 22%. For patients who are old and pay a high hospital bill, the probability of thick lips is 0%. The overall probability of old age is 52%.",yes,"Let V1 = age; X = hospital costs; Y = lip thickness.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.52
0.48 * (0.73 - 0.95) + 0.52 * (0.00 - 0.22) = -0.22
-0.22 < 0",confounding,simpson_hospital,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and lip thickness. Hospital costs has a direct effect on lip thickness. Method 1: We look directly at how hospital costs correlates with lip thickness in general. Method 2: We look at this correlation case by case according to age.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_hospital,2,backadj,[backdoor adjustment set for Y given X]
22683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 96%. For patients who have small kidney stones and speak english, the probability of recovery is 83%. For patients who have large kidney stones and do not speak english, the probability of recovery is 18%. For patients who have large kidney stones and speak english, the probability of recovery is 6%. The overall probability of large kidney stone is 43%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.83
P(Y=1 | V1=1, X=0) = 0.18
P(Y=1 | V1=1, X=1) = 0.06
P(V1=1) = 0.43
0.57 * (0.83 - 0.96) + 0.43 * (0.06 - 0.18) = -0.13
-0.13 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 65%. For patients who do not speak english, the probability of recovery is 37%. For patients who speak english, the probability of recovery is 63%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.65
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.63
0.65*0.63 - 0.35*0.37 = 0.54
0.54 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 65%. For patients who do not speak english, the probability of recovery is 37%. For patients who speak english, the probability of recovery is 63%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.65
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.63
0.65*0.63 - 0.35*0.37 = 0.54
0.54 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 65%. The probability of not speaking english and recovery is 13%. The probability of speaking english and recovery is 41%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.41
0.41/0.65 - 0.13/0.35 = 0.26
0.26 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 96%. For patients who have small kidney stones and speak english, the probability of recovery is 90%. For patients who have large kidney stones and do not speak english, the probability of recovery is 32%. For patients who have large kidney stones and speak english, the probability of recovery is 25%. The overall probability of large kidney stone is 44%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.90
P(Y=1 | V1=1, X=0) = 0.32
P(Y=1 | V1=1, X=1) = 0.25
P(V1=1) = 0.44
0.56 * (0.90 - 0.96) + 0.44 * (0.25 - 0.32) = -0.06
-0.06 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 55%. For patients who do not speak english, the probability of recovery is 40%. For patients who speak english, the probability of recovery is 84%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.84
0.55*0.84 - 0.45*0.40 = 0.64
0.64 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 55%. The probability of not speaking english and recovery is 18%. The probability of speaking english and recovery is 47%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.47
0.47/0.55 - 0.18/0.45 = 0.44
0.44 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 94%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 18%. For patients who have large kidney stones and speak english, the probability of recovery is 7%. The overall probability of large kidney stone is 57%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.18
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.57
0.43 * (0.81 - 0.94) + 0.57 * (0.07 - 0.18) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 48%. For patients who do not speak english, the probability of recovery is 29%. For patients who speak english, the probability of recovery is 61%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.61
0.48*0.61 - 0.52*0.29 = 0.45
0.45 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 48%. The probability of not speaking english and recovery is 15%. The probability of speaking english and recovery is 30%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.30
0.30/0.48 - 0.15/0.52 = 0.32
0.32 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 48%. The probability of not speaking english and recovery is 15%. The probability of speaking english and recovery is 30%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.30
0.30/0.48 - 0.15/0.52 = 0.32
0.32 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look directly at how ability to speak english correlates with recovery in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 84%. For patients who have small kidney stones and speak english, the probability of recovery is 76%. For patients who have large kidney stones and do not speak english, the probability of recovery is 16%. For patients who have large kidney stones and speak english, the probability of recovery is 8%. The overall probability of large kidney stone is 59%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.84
P(Y=1 | V1=0, X=1) = 0.76
P(Y=1 | V1=1, X=0) = 0.16
P(Y=1 | V1=1, X=1) = 0.08
P(V1=1) = 0.59
0.41 * (0.76 - 0.84) + 0.59 * (0.08 - 0.16) = -0.07
-0.07 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 44%. The probability of not speaking english and recovery is 11%. The probability of speaking english and recovery is 30%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.30
0.30/0.44 - 0.11/0.56 = 0.47
0.47 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 96%. For patients who have small kidney stones and speak english, the probability of recovery is 83%. For patients who have large kidney stones and do not speak english, the probability of recovery is 21%. For patients who have large kidney stones and speak english, the probability of recovery is 11%. The overall probability of large kidney stone is 42%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.83
P(Y=1 | V1=1, X=0) = 0.21
P(Y=1 | V1=1, X=1) = 0.11
P(V1=1) = 0.42
0.58 * (0.83 - 0.96) + 0.42 * (0.11 - 0.21) = -0.13
-0.13 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 33%. For patients who do not speak english, the probability of recovery is 50%. For patients who speak english, the probability of recovery is 81%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.33
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.81
0.33*0.81 - 0.67*0.50 = 0.61
0.61 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22735,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 53%. For patients who do not speak english, the probability of recovery is 38%. For patients who speak english, the probability of recovery is 80%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.80
0.53*0.80 - 0.47*0.38 = 0.60
0.60 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look directly at how ability to speak english correlates with recovery in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22742,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 94%. For patients who have small kidney stones and speak english, the probability of recovery is 80%. For patients who have large kidney stones and do not speak english, the probability of recovery is 18%. For patients who have large kidney stones and speak english, the probability of recovery is 5%. The overall probability of large kidney stone is 58%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.18
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.58
0.42 * (0.80 - 0.94) + 0.58 * (0.05 - 0.18) = -0.14
-0.14 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 33%. The probability of not speaking english and recovery is 21%. The probability of speaking english and recovery is 25%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.33
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.25
0.25/0.33 - 0.21/0.67 = 0.46
0.46 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look directly at how ability to speak english correlates with recovery in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 80%. For patients who have small kidney stones and speak english, the probability of recovery is 73%. For patients who have large kidney stones and do not speak english, the probability of recovery is 9%. For patients who have large kidney stones and speak english, the probability of recovery is 1%. The overall probability of large kidney stone is 46%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.80
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.09
P(Y=1 | V1=1, X=1) = 0.01
P(V1=1) = 0.46
0.54 * (0.73 - 0.80) + 0.46 * (0.01 - 0.09) = -0.08
-0.08 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 49%. For patients who do not speak english, the probability of recovery is 18%. For patients who speak english, the probability of recovery is 71%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.71
0.49*0.71 - 0.51*0.18 = 0.44
0.44 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 49%. For patients who do not speak english, the probability of recovery is 18%. For patients who speak english, the probability of recovery is 71%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.18
P(Y=1 | X=1) = 0.71
0.49*0.71 - 0.51*0.18 = 0.44
0.44 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 90%. For patients who have small kidney stones and speak english, the probability of recovery is 79%. For patients who have large kidney stones and do not speak english, the probability of recovery is 13%. For patients who have large kidney stones and speak english, the probability of recovery is 0%. The overall probability of large kidney stone is 40%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.90
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.13
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.40
0.60 * (0.79 - 0.90) + 0.40 * (0.00 - 0.13) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 90%. For patients who have small kidney stones and speak english, the probability of recovery is 79%. For patients who have large kidney stones and do not speak english, the probability of recovery is 13%. For patients who have large kidney stones and speak english, the probability of recovery is 0%. The overall probability of large kidney stone is 40%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.90
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.13
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.40
0.60 * (0.79 - 0.90) + 0.40 * (0.00 - 0.13) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 90%. For patients who have small kidney stones and speak english, the probability of recovery is 79%. For patients who have large kidney stones and do not speak english, the probability of recovery is 13%. For patients who have large kidney stones and speak english, the probability of recovery is 0%. The overall probability of large kidney stone is 40%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.90
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.13
P(Y=1 | V1=1, X=1) = 0.00
P(V1=1) = 0.40
0.60 * (0.79 - 0.90) + 0.40 * (0.00 - 0.13) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 49%. The probability of not speaking english and recovery is 20%. The probability of speaking english and recovery is 33%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.33
0.33/0.49 - 0.20/0.51 = 0.30
0.30 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look directly at how ability to speak english correlates with recovery in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 51%. For patients who do not speak english, the probability of recovery is 24%. For patients who speak english, the probability of recovery is 71%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.71
0.51*0.71 - 0.49*0.24 = 0.49
0.49 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 51%. The probability of not speaking english and recovery is 12%. The probability of speaking english and recovery is 36%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.36
0.36/0.51 - 0.12/0.49 = 0.47
0.47 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 95%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 17%. For patients who have large kidney stones and speak english, the probability of recovery is 6%. The overall probability of large kidney stone is 54%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.17
P(Y=1 | V1=1, X=1) = 0.06
P(V1=1) = 0.54
0.46 * (0.81 - 0.95) + 0.54 * (0.06 - 0.17) = -0.13
-0.13 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22782,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 95%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 17%. For patients who have large kidney stones and speak english, the probability of recovery is 6%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.17
P(Y=1 | V1=1, X=1) = 0.06
P(V1=1) = 0.54
0.46 * (0.81 - 0.95) + 0.54 * (0.06 - 0.17) = -0.14
-0.14 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 36%. For patients who do not speak english, the probability of recovery is 31%. For patients who speak english, the probability of recovery is 78%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.78
0.36*0.78 - 0.64*0.31 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 50%. For patients who do not speak english, the probability of recovery is 32%. For patients who speak english, the probability of recovery is 79%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.79
0.50*0.79 - 0.50*0.32 = 0.57
0.57 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 50%. The probability of not speaking english and recovery is 16%. The probability of speaking english and recovery is 40%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.40
0.40/0.50 - 0.16/0.50 = 0.47
0.47 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 50%. The probability of not speaking english and recovery is 16%. The probability of speaking english and recovery is 40%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.40
0.40/0.50 - 0.16/0.50 = 0.47
0.47 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 95%. For patients who have small kidney stones and speak english, the probability of recovery is 83%. For patients who have large kidney stones and do not speak english, the probability of recovery is 20%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 41%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.83
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.41
0.59 * (0.83 - 0.95) + 0.41 * (0.09 - 0.20) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 95%. For patients who have small kidney stones and speak english, the probability of recovery is 83%. For patients who have large kidney stones and do not speak english, the probability of recovery is 20%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 41%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.83
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.41
0.59 * (0.83 - 0.95) + 0.41 * (0.09 - 0.20) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 69%. The probability of not speaking english and recovery is 8%. The probability of speaking english and recovery is 48%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.69
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.48
0.48/0.69 - 0.08/0.31 = 0.42
0.42 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 91%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 22%. For patients who have large kidney stones and speak english, the probability of recovery is 13%. The overall probability of large kidney stone is 53%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.13
P(V1=1) = 0.53
0.47 * (0.81 - 0.91) + 0.53 * (0.13 - 0.22) = -0.09
-0.09 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 91%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 22%. For patients who have large kidney stones and speak english, the probability of recovery is 13%. The overall probability of large kidney stone is 53%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.13
P(V1=1) = 0.53
0.47 * (0.81 - 0.91) + 0.53 * (0.13 - 0.22) = -0.09
-0.09 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 91%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 22%. For patients who have large kidney stones and speak english, the probability of recovery is 13%. The overall probability of large kidney stone is 53%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.13
P(V1=1) = 0.53
0.47 * (0.81 - 0.91) + 0.53 * (0.13 - 0.22) = -0.09
-0.09 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22815,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 47%. For patients who do not speak english, the probability of recovery is 27%. For patients who speak english, the probability of recovery is 75%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.47
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.75
0.47*0.75 - 0.53*0.27 = 0.50
0.50 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22823,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 98%. For patients who have small kidney stones and speak english, the probability of recovery is 87%. For patients who have large kidney stones and do not speak english, the probability of recovery is 25%. For patients who have large kidney stones and speak english, the probability of recovery is 10%. The overall probability of large kidney stone is 44%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.87
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.44
0.56 * (0.87 - 0.98) + 0.44 * (0.10 - 0.25) = -0.11
-0.11 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 52%. For patients who do not speak english, the probability of recovery is 48%. For patients who speak english, the probability of recovery is 71%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.71
0.52*0.71 - 0.48*0.48 = 0.60
0.60 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 52%. The probability of not speaking english and recovery is 23%. The probability of speaking english and recovery is 37%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.37
0.37/0.52 - 0.23/0.48 = 0.23
0.23 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 86%. For patients who have small kidney stones and speak english, the probability of recovery is 75%. For patients who have large kidney stones and do not speak english, the probability of recovery is 19%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 55%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.86
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.19
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.55
0.45 * (0.75 - 0.86) + 0.55 * (0.09 - 0.19) = -0.10
-0.10 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22833,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 86%. For patients who have small kidney stones and speak english, the probability of recovery is 75%. For patients who have large kidney stones and do not speak english, the probability of recovery is 19%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 55%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.86
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.19
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.55
0.45 * (0.75 - 0.86) + 0.55 * (0.09 - 0.19) = -0.11
-0.11 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22834,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 38%. For patients who do not speak english, the probability of recovery is 26%. For patients who speak english, the probability of recovery is 75%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.38
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.75
0.38*0.75 - 0.62*0.26 = 0.45
0.45 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 38%. The probability of not speaking english and recovery is 16%. The probability of speaking english and recovery is 29%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.29
0.29/0.38 - 0.16/0.62 = 0.49
0.49 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look directly at how ability to speak english correlates with recovery in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 92%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 19%. For patients who have large kidney stones and speak english, the probability of recovery is 7%. The overall probability of large kidney stone is 57%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.92
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.19
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.57
0.43 * (0.81 - 0.92) + 0.57 * (0.07 - 0.19) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 39%. The probability of not speaking english and recovery is 19%. The probability of speaking english and recovery is 27%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.27
0.27/0.39 - 0.19/0.61 = 0.39
0.39 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 39%. The probability of not speaking english and recovery is 19%. The probability of speaking english and recovery is 27%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.27
0.27/0.39 - 0.19/0.61 = 0.39
0.39 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22848,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look directly at how ability to speak english correlates with recovery in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 93%. For patients who have small kidney stones and speak english, the probability of recovery is 85%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 6%. The overall probability of large kidney stone is 50%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.93
P(Y=1 | V1=0, X=1) = 0.85
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.06
P(V1=1) = 0.50
0.50 * (0.85 - 0.93) + 0.50 * (0.06 - 0.23) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22853,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 93%. For patients who have small kidney stones and speak english, the probability of recovery is 85%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 6%. The overall probability of large kidney stone is 50%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.93
P(Y=1 | V1=0, X=1) = 0.85
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.06
P(V1=1) = 0.50
0.50 * (0.85 - 0.93) + 0.50 * (0.06 - 0.23) = -0.09
-0.09 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 51%. For patients who do not speak english, the probability of recovery is 32%. For patients who speak english, the probability of recovery is 74%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.51
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.74
0.51*0.74 - 0.49*0.32 = 0.52
0.52 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 51%. The probability of not speaking english and recovery is 16%. The probability of speaking english and recovery is 38%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.51
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.38
0.38/0.51 - 0.16/0.49 = 0.42
0.42 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22858,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look directly at how ability to speak english correlates with recovery in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 99%. For patients who have small kidney stones and speak english, the probability of recovery is 88%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 59%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.88
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.59
0.41 * (0.88 - 0.99) + 0.59 * (0.09 - 0.23) = -0.13
-0.13 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 99%. For patients who have small kidney stones and speak english, the probability of recovery is 88%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 59%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.88
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.59
0.41 * (0.88 - 0.99) + 0.59 * (0.09 - 0.23) = -0.13
-0.13 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 99%. For patients who have small kidney stones and speak english, the probability of recovery is 88%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 59%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.88
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.59
0.41 * (0.88 - 0.99) + 0.59 * (0.09 - 0.23) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 50%. For patients who do not speak english, the probability of recovery is 33%. For patients who speak english, the probability of recovery is 64%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.64
0.50*0.64 - 0.50*0.33 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 50%. The probability of not speaking english and recovery is 17%. The probability of speaking english and recovery is 32%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.32
0.32/0.50 - 0.17/0.50 = 0.30
0.30 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look directly at how ability to speak english correlates with recovery in general. Method 2: We look at this correlation case by case according to kidney stone size.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 86%. For patients who have small kidney stones and speak english, the probability of recovery is 80%. For patients who have large kidney stones and do not speak english, the probability of recovery is 24%. For patients who have large kidney stones and speak english, the probability of recovery is 12%. The overall probability of large kidney stone is 54%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.86
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.54
0.46 * (0.80 - 0.86) + 0.54 * (0.12 - 0.24) = -0.09
-0.09 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 86%. For patients who have small kidney stones and speak english, the probability of recovery is 80%. For patients who have large kidney stones and do not speak english, the probability of recovery is 24%. For patients who have large kidney stones and speak english, the probability of recovery is 12%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.86
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.54
0.46 * (0.80 - 0.86) + 0.54 * (0.12 - 0.24) = -0.07
-0.07 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22874,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 48%. For patients who do not speak english, the probability of recovery is 25%. For patients who speak english, the probability of recovery is 75%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.75
0.48*0.75 - 0.52*0.25 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 48%. The probability of not speaking english and recovery is 13%. The probability of speaking english and recovery is 36%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.36
0.36/0.48 - 0.13/0.52 = 0.50
0.50 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22877,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 48%. The probability of not speaking english and recovery is 13%. The probability of speaking english and recovery is 36%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.36
0.36/0.48 - 0.13/0.52 = 0.50
0.50 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 92%. For patients who have small kidney stones and speak english, the probability of recovery is 77%. For patients who have large kidney stones and do not speak english, the probability of recovery is 12%. For patients who have large kidney stones and speak english, the probability of recovery is 1%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.92
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.12
P(Y=1 | V1=1, X=1) = 0.01
P(V1=1) = 0.54
0.46 * (0.77 - 0.92) + 0.54 * (0.01 - 0.12) = -0.13
-0.13 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 92%. For patients who have small kidney stones and speak english, the probability of recovery is 77%. For patients who have large kidney stones and do not speak english, the probability of recovery is 12%. For patients who have large kidney stones and speak english, the probability of recovery is 1%. The overall probability of large kidney stone is 54%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.92
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.12
P(Y=1 | V1=1, X=1) = 0.01
P(V1=1) = 0.54
0.46 * (0.77 - 0.92) + 0.54 * (0.01 - 0.12) = -0.15
-0.15 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 83%. For patients who have small kidney stones and speak english, the probability of recovery is 75%. For patients who have large kidney stones and do not speak english, the probability of recovery is 15%. For patients who have large kidney stones and speak english, the probability of recovery is 5%. The overall probability of large kidney stone is 47%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.83
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.15
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.47
0.53 * (0.75 - 0.83) + 0.47 * (0.05 - 0.15) = -0.09
-0.09 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22892,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 83%. For patients who have small kidney stones and speak english, the probability of recovery is 75%. For patients who have large kidney stones and do not speak english, the probability of recovery is 15%. For patients who have large kidney stones and speak english, the probability of recovery is 5%. The overall probability of large kidney stone is 47%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.83
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.15
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.47
0.53 * (0.75 - 0.83) + 0.47 * (0.05 - 0.15) = -0.09
-0.09 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 52%. The probability of not speaking english and recovery is 11%. The probability of speaking english and recovery is 36%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.36
0.36/0.52 - 0.11/0.48 = 0.45
0.45 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22897,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 52%. The probability of not speaking english and recovery is 11%. The probability of speaking english and recovery is 36%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.36
0.36/0.52 - 0.11/0.48 = 0.45
0.45 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 99%. For patients who have small kidney stones and speak english, the probability of recovery is 85%. For patients who have large kidney stones and do not speak english, the probability of recovery is 20%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 41%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.85
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.41
0.59 * (0.85 - 0.99) + 0.41 * (0.09 - 0.20) = -0.14
-0.14 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 99%. For patients who have small kidney stones and speak english, the probability of recovery is 85%. For patients who have large kidney stones and do not speak english, the probability of recovery is 20%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 41%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.85
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.41
0.59 * (0.85 - 0.99) + 0.41 * (0.09 - 0.20) = -0.14
-0.14 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 52%. For patients who do not speak english, the probability of recovery is 45%. For patients who speak english, the probability of recovery is 73%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.45
P(Y=1 | X=1) = 0.73
0.52*0.73 - 0.48*0.45 = 0.60
0.60 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 52%. The probability of not speaking english and recovery is 21%. The probability of speaking english and recovery is 38%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.38
0.38/0.52 - 0.21/0.48 = 0.29
0.29 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 88%. For patients who have small kidney stones and speak english, the probability of recovery is 77%. For patients who have large kidney stones and do not speak english, the probability of recovery is 20%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 41%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.88
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.41
0.59 * (0.77 - 0.88) + 0.41 * (0.09 - 0.20) = -0.10
-0.10 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 92%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 17%. For patients who have large kidney stones and speak english, the probability of recovery is 5%. The overall probability of large kidney stone is 49%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.92
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.17
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.49
0.51 * (0.81 - 0.92) + 0.49 * (0.05 - 0.17) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 92%. For patients who have small kidney stones and speak english, the probability of recovery is 81%. For patients who have large kidney stones and do not speak english, the probability of recovery is 17%. For patients who have large kidney stones and speak english, the probability of recovery is 5%. The overall probability of large kidney stone is 49%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.92
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.17
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.49
0.51 * (0.81 - 0.92) + 0.49 * (0.05 - 0.17) = -0.12
-0.12 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 63%. For patients who do not speak english, the probability of recovery is 25%. For patients who speak english, the probability of recovery is 62%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.62
0.63*0.62 - 0.37*0.25 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 63%. For patients who do not speak english, the probability of recovery is 25%. For patients who speak english, the probability of recovery is 62%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.62
0.63*0.62 - 0.37*0.25 = 0.48
0.48 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 63%. The probability of not speaking english and recovery is 9%. The probability of speaking english and recovery is 39%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.39
0.39/0.63 - 0.09/0.37 = 0.37
0.37 > 0",confounding,simpson_kidneystone,1,correlation,P(Y | X)
22933,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 88%. For patients who have small kidney stones and speak english, the probability of recovery is 72%. For patients who have large kidney stones and do not speak english, the probability of recovery is 16%. For patients who have large kidney stones and speak english, the probability of recovery is 4%. The overall probability of large kidney stone is 41%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.88
P(Y=1 | V1=0, X=1) = 0.72
P(Y=1 | V1=1, X=0) = 0.16
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.41
0.59 * (0.72 - 0.88) + 0.41 * (0.04 - 0.16) = -0.16
-0.16 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 53%. For patients who do not speak english, the probability of recovery is 27%. For patients who speak english, the probability of recovery is 70%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.70
0.53*0.70 - 0.47*0.27 = 0.51
0.51 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 97%. For patients who have small kidney stones and speak english, the probability of recovery is 84%. For patients who have large kidney stones and do not speak english, the probability of recovery is 20%. For patients who have large kidney stones and speak english, the probability of recovery is 7%. The overall probability of large kidney stone is 55%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.84
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.55
0.45 * (0.84 - 0.97) + 0.55 * (0.07 - 0.20) = -0.13
-0.13 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 97%. For patients who have small kidney stones and speak english, the probability of recovery is 84%. For patients who have large kidney stones and do not speak english, the probability of recovery is 20%. For patients who have large kidney stones and speak english, the probability of recovery is 7%. The overall probability of large kidney stone is 55%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.84
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.07
P(V1=1) = 0.55
0.45 * (0.84 - 0.97) + 0.55 * (0.07 - 0.20) = -0.13
-0.13 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 41%. For patients who do not speak english, the probability of recovery is 26%. For patients who speak english, the probability of recovery is 82%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.82
0.41*0.82 - 0.59*0.26 = 0.49
0.49 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 88%. For patients who have small kidney stones and speak english, the probability of recovery is 79%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 10%. The overall probability of large kidney stone is 45%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.88
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.45
0.55 * (0.79 - 0.88) + 0.45 * (0.10 - 0.23) = -0.11
-0.11 < 0",confounding,simpson_kidneystone,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 88%. For patients who have small kidney stones and speak english, the probability of recovery is 79%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 10%. The overall probability of large kidney stone is 45%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.88
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.45
0.55 * (0.79 - 0.88) + 0.45 * (0.10 - 0.23) = -0.09
-0.09 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 98%. For patients who have small kidney stones and speak english, the probability of recovery is 85%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 57%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.85
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.57
0.43 * (0.85 - 0.98) + 0.57 * (0.09 - 0.23) = -0.14
-0.14 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 98%. For patients who have small kidney stones and speak english, the probability of recovery is 85%. For patients who have large kidney stones and do not speak english, the probability of recovery is 23%. For patients who have large kidney stones and speak english, the probability of recovery is 9%. The overall probability of large kidney stone is 57%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.98
P(Y=1 | V1=0, X=1) = 0.85
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.09
P(V1=1) = 0.57
0.43 * (0.85 - 0.98) + 0.57 * (0.09 - 0.23) = -0.14
-0.14 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 99%. For patients who have small kidney stones and speak english, the probability of recovery is 88%. For patients who have large kidney stones and do not speak english, the probability of recovery is 32%. For patients who have large kidney stones and speak english, the probability of recovery is 18%. The overall probability of large kidney stone is 59%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.88
P(Y=1 | V1=1, X=0) = 0.32
P(Y=1 | V1=1, X=1) = 0.18
P(V1=1) = 0.59
0.41 * (0.88 - 0.99) + 0.59 * (0.18 - 0.32) = -0.11
-0.11 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. For patients who have small kidney stones and do not speak english, the probability of recovery is 99%. For patients who have small kidney stones and speak english, the probability of recovery is 88%. For patients who have large kidney stones and do not speak english, the probability of recovery is 32%. For patients who have large kidney stones and speak english, the probability of recovery is 18%. The overall probability of large kidney stone is 59%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.88
P(Y=1 | V1=1, X=0) = 0.32
P(Y=1 | V1=1, X=1) = 0.18
P(V1=1) = 0.59
0.41 * (0.88 - 0.99) + 0.59 * (0.18 - 0.32) = -0.11
-0.11 < 0",confounding,simpson_kidneystone,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22974,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 45%. For patients who do not speak english, the probability of recovery is 35%. For patients who speak english, the probability of recovery is 78%.",yes,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.78
0.45*0.78 - 0.55*0.35 = 0.54
0.54 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. The overall probability of speaking english is 45%. For patients who do not speak english, the probability of recovery is 35%. For patients who speak english, the probability of recovery is 78%.",no,"Let V1 = kidney stone size; X = ability to speak english; Y = recovery.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.78
0.45*0.78 - 0.55*0.35 = 0.54
0.54 > 0",confounding,simpson_kidneystone,1,marginal,P(Y)
22979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on ability to speak english and recovery. Ability to speak english has a direct effect on recovery. Method 1: We look at how ability to speak english correlates with recovery case by case according to kidney stone size. Method 2: We look directly at how ability to speak english correlates with recovery in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_kidneystone,2,backadj,[backdoor adjustment set for Y given X]
22981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 91%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 81%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 20%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 10%. The overall probability of pre-conditions is 43%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.43
0.57 * (0.81 - 0.91) + 0.43 * (0.10 - 0.20) = -0.10
-0.10 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 91%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 81%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 20%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 10%. The overall probability of pre-conditions is 43%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.20
P(Y=1 | V1=1, X=1) = 0.10
P(V1=1) = 0.43
0.57 * (0.81 - 0.91) + 0.43 * (0.10 - 0.20) = -0.10
-0.10 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
22985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 52%. For people who do not have a brother, the probability of recovering from the disease is 34%. For people who have a brother, the probability of recovering from the disease is 75%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.75
0.52*0.75 - 0.48*0.34 = 0.55
0.55 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
22988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
22991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 95%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 75%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 24%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 3%. The overall probability of pre-conditions is 41%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.41
0.59 * (0.75 - 0.95) + 0.41 * (0.03 - 0.24) = -0.20
-0.20 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
22994,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 67%. For people who do not have a brother, the probability of recovering from the disease is 33%. For people who have a brother, the probability of recovering from the disease is 62%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.67
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.62
0.67*0.62 - 0.33*0.33 = 0.52
0.52 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
22995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 67%. For people who do not have a brother, the probability of recovering from the disease is 33%. For people who have a brother, the probability of recovering from the disease is 62%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.67
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.62
0.67*0.62 - 0.33*0.33 = 0.52
0.52 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
22996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 67%. The probability of not having a brother and recovering from the disease is 11%. The probability of having a brother and recovering from the disease is 42%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.67
P(Y=1, X=0=1) = 0.11
P(Y=1, X=1=1) = 0.42
0.42/0.67 - 0.11/0.33 = 0.29
0.29 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
22999,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look at how having a brother correlates with disease case by case according to pre-conditions. Method 2: We look directly at how having a brother correlates with disease in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 99%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 79%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 30%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 12%. The overall probability of pre-conditions is 51%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.30
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.51
0.49 * (0.79 - 0.99) + 0.51 * (0.12 - 0.30) = -0.19
-0.19 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23002,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 99%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 79%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 30%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 12%. The overall probability of pre-conditions is 51%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.30
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.51
0.49 * (0.79 - 0.99) + 0.51 * (0.12 - 0.30) = -0.20
-0.20 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 49%. For people who do not have a brother, the probability of recovering from the disease is 34%. For people who have a brother, the probability of recovering from the disease is 75%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.75
0.49*0.75 - 0.51*0.34 = 0.55
0.55 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23006,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 49%. The probability of not having a brother and recovering from the disease is 17%. The probability of having a brother and recovering from the disease is 37%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.37
0.37/0.49 - 0.17/0.51 = 0.41
0.41 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look at how having a brother correlates with disease case by case according to pre-conditions. Method 2: We look directly at how having a brother correlates with disease in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 85%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 75%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 15%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 8%. The overall probability of pre-conditions is 45%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.85
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.15
P(Y=1 | V1=1, X=1) = 0.08
P(V1=1) = 0.45
0.55 * (0.75 - 0.85) + 0.45 * (0.08 - 0.15) = -0.09
-0.09 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23012,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 85%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 75%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 15%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 8%. The overall probability of pre-conditions is 45%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.85
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.15
P(Y=1 | V1=1, X=1) = 0.08
P(V1=1) = 0.45
0.55 * (0.75 - 0.85) + 0.45 * (0.08 - 0.15) = -0.10
-0.10 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 58%. For people who do not have a brother, the probability of recovering from the disease is 20%. For people who have a brother, the probability of recovering from the disease is 68%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.58
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.68
0.58*0.68 - 0.42*0.20 = 0.48
0.48 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23021,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 99%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 77%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 25%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 4%. The overall probability of pre-conditions is 49%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.49
0.51 * (0.77 - 0.99) + 0.49 * (0.04 - 0.25) = -0.22
-0.22 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 53%. For people who do not have a brother, the probability of recovering from the disease is 38%. For people who have a brother, the probability of recovering from the disease is 62%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.62
0.53*0.62 - 0.47*0.38 = 0.51
0.51 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 53%. For people who do not have a brother, the probability of recovering from the disease is 38%. For people who have a brother, the probability of recovering from the disease is 62%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.62
0.53*0.62 - 0.47*0.38 = 0.51
0.51 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 87%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 73%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 23%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 12%. The overall probability of pre-conditions is 48%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.87
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.48
0.52 * (0.73 - 0.87) + 0.48 * (0.12 - 0.23) = -0.12
-0.12 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 87%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 73%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 23%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 12%. The overall probability of pre-conditions is 48%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.87
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.48
0.52 * (0.73 - 0.87) + 0.48 * (0.12 - 0.23) = -0.12
-0.12 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 87%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 73%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 23%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 12%. The overall probability of pre-conditions is 48%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.87
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.12
P(V1=1) = 0.48
0.52 * (0.73 - 0.87) + 0.48 * (0.12 - 0.23) = -0.14
-0.14 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 50%. For people who do not have a brother, the probability of recovering from the disease is 30%. For people who have a brother, the probability of recovering from the disease is 68%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.68
0.50*0.68 - 0.50*0.30 = 0.50
0.50 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 50%. For people who do not have a brother, the probability of recovering from the disease is 30%. For people who have a brother, the probability of recovering from the disease is 68%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.68
0.50*0.68 - 0.50*0.30 = 0.50
0.50 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 93%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 81%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 24%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 13%. The overall probability of pre-conditions is 46%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.93
P(Y=1 | V1=0, X=1) = 0.81
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.13
P(V1=1) = 0.46
0.54 * (0.81 - 0.93) + 0.46 * (0.13 - 0.24) = -0.12
-0.12 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 99%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 78%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 25%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 3%. The overall probability of pre-conditions is 42%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.78
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.42
0.58 * (0.78 - 0.99) + 0.42 * (0.03 - 0.25) = -0.21
-0.21 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 99%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 78%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 25%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 3%. The overall probability of pre-conditions is 42%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.99
P(Y=1 | V1=0, X=1) = 0.78
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.42
0.58 * (0.78 - 0.99) + 0.42 * (0.03 - 0.25) = -0.21
-0.21 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 49%. The probability of not having a brother and recovering from the disease is 22%. The probability of having a brother and recovering from the disease is 36%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.36
0.36/0.49 - 0.22/0.51 = 0.32
0.32 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 49%. The probability of not having a brother and recovering from the disease is 22%. The probability of having a brother and recovering from the disease is 36%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.36
0.36/0.49 - 0.22/0.51 = 0.32
0.32 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23058,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look at how having a brother correlates with disease case by case according to pre-conditions. Method 2: We look directly at how having a brother correlates with disease in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 96%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 80%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 35%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 17%. The overall probability of pre-conditions is 56%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.17
P(V1=1) = 0.56
0.44 * (0.80 - 0.96) + 0.56 * (0.17 - 0.35) = -0.17
-0.17 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23062,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 96%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 80%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 35%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 17%. The overall probability of pre-conditions is 56%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.17
P(V1=1) = 0.56
0.44 * (0.80 - 0.96) + 0.56 * (0.17 - 0.35) = -0.16
-0.16 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 96%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 80%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 35%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 17%. The overall probability of pre-conditions is 56%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.35
P(Y=1 | V1=1, X=1) = 0.17
P(V1=1) = 0.56
0.44 * (0.80 - 0.96) + 0.56 * (0.17 - 0.35) = -0.16
-0.16 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 46%. For people who do not have a brother, the probability of recovering from the disease is 38%. For people who have a brother, the probability of recovering from the disease is 73%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.46
P(Y=1 | X=0) = 0.38
P(Y=1 | X=1) = 0.73
0.46*0.73 - 0.54*0.38 = 0.54
0.54 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 72%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 63%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 8%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 2%. The overall probability of pre-conditions is 58%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.72
P(Y=1 | V1=0, X=1) = 0.63
P(Y=1 | V1=1, X=0) = 0.08
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.58
0.42 * (0.63 - 0.72) + 0.58 * (0.02 - 0.08) = -0.09
-0.09 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 48%. For people who do not have a brother, the probability of recovering from the disease is 12%. For people who have a brother, the probability of recovering from the disease is 51%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.51
0.48*0.51 - 0.52*0.12 = 0.31
0.31 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 96%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 76%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 25%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 4%. The overall probability of pre-conditions is 54%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.96
P(Y=1 | V1=0, X=1) = 0.76
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.54
0.46 * (0.76 - 0.96) + 0.54 * (0.04 - 0.25) = -0.21
-0.21 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 53%. For people who do not have a brother, the probability of recovering from the disease is 29%. For people who have a brother, the probability of recovering from the disease is 62%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.62
0.53*0.62 - 0.47*0.29 = 0.46
0.46 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23093,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 92%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 79%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 27%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 14%. The overall probability of pre-conditions is 58%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.92
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.14
P(V1=1) = 0.58
0.42 * (0.79 - 0.92) + 0.58 * (0.14 - 0.27) = -0.13
-0.13 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 38%. The probability of not having a brother and recovering from the disease is 20%. The probability of having a brother and recovering from the disease is 28%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.28
0.28/0.38 - 0.20/0.62 = 0.43
0.43 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23110,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 95%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 75%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 23%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 2%. The overall probability of pre-conditions is 47%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.47
0.53 * (0.75 - 0.95) + 0.47 * (0.02 - 0.23) = -0.21
-0.21 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 95%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 75%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 23%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 2%. The overall probability of pre-conditions is 47%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.23
P(Y=1 | V1=1, X=1) = 0.02
P(V1=1) = 0.47
0.53 * (0.75 - 0.95) + 0.47 * (0.02 - 0.23) = -0.21
-0.21 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 57%. For people who do not have a brother, the probability of recovering from the disease is 32%. For people who have a brother, the probability of recovering from the disease is 63%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.63
0.57*0.63 - 0.43*0.32 = 0.50
0.50 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 57%. For people who do not have a brother, the probability of recovering from the disease is 32%. For people who have a brother, the probability of recovering from the disease is 63%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.63
0.57*0.63 - 0.43*0.32 = 0.50
0.50 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23117,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 57%. The probability of not having a brother and recovering from the disease is 14%. The probability of having a brother and recovering from the disease is 36%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.36
0.36/0.57 - 0.14/0.43 = 0.31
0.31 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look at how having a brother correlates with disease case by case according to pre-conditions. Method 2: We look directly at how having a brother correlates with disease in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 52%. For people who do not have a brother, the probability of recovering from the disease is 24%. For people who have a brother, the probability of recovering from the disease is 65%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.65
0.52*0.65 - 0.48*0.24 = 0.46
0.46 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 91%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 84%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 27%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 19%. The overall probability of pre-conditions is 53%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.84
P(Y=1 | V1=1, X=0) = 0.27
P(Y=1 | V1=1, X=1) = 0.19
P(V1=1) = 0.53
0.47 * (0.84 - 0.91) + 0.53 * (0.19 - 0.27) = -0.08
-0.08 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 48%. For people who do not have a brother, the probability of recovering from the disease is 33%. For people who have a brother, the probability of recovering from the disease is 76%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.76
0.48*0.76 - 0.52*0.33 = 0.53
0.53 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 48%. The probability of not having a brother and recovering from the disease is 17%. The probability of having a brother and recovering from the disease is 36%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.36
0.36/0.48 - 0.17/0.52 = 0.43
0.43 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 44%. For people who do not have a brother, the probability of recovering from the disease is 48%. For people who have a brother, the probability of recovering from the disease is 69%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.48
P(Y=1 | X=1) = 0.69
0.44*0.69 - 0.56*0.48 = 0.57
0.57 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 44%. The probability of not having a brother and recovering from the disease is 27%. The probability of having a brother and recovering from the disease is 31%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.31
0.31/0.44 - 0.27/0.56 = 0.21
0.21 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 44%. The probability of not having a brother and recovering from the disease is 27%. The probability of having a brother and recovering from the disease is 31%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.44
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.31
0.31/0.44 - 0.27/0.56 = 0.21
0.21 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look at how having a brother correlates with disease case by case according to pre-conditions. Method 2: We look directly at how having a brother correlates with disease in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 94%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 75%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 19%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 1%. The overall probability of pre-conditions is 51%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.19
P(Y=1 | V1=1, X=1) = 0.01
P(V1=1) = 0.51
0.49 * (0.75 - 0.94) + 0.51 * (0.01 - 0.19) = -0.19
-0.19 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 43%. For people who do not have a brother, the probability of recovering from the disease is 29%. For people who have a brother, the probability of recovering from the disease is 73%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.73
0.43*0.73 - 0.57*0.29 = 0.48
0.48 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23157,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 43%. The probability of not having a brother and recovering from the disease is 17%. The probability of having a brother and recovering from the disease is 31%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.43
P(Y=1, X=0=1) = 0.17
P(Y=1, X=1=1) = 0.31
0.31/0.43 - 0.17/0.57 = 0.44
0.44 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23166,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 46%. The probability of not having a brother and recovering from the disease is 15%. The probability of having a brother and recovering from the disease is 31%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.46
P(Y=1, X=0=1) = 0.15
P(Y=1, X=1=1) = 0.31
0.31/0.46 - 0.15/0.54 = 0.39
0.39 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23169,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look at how having a brother correlates with disease case by case according to pre-conditions. Method 2: We look directly at how having a brother correlates with disease in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 97%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 75%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 25%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 3%. The overall probability of pre-conditions is 60%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.75
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.60
0.40 * (0.75 - 0.97) + 0.60 * (0.03 - 0.25) = -0.22
-0.22 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 37%. For people who do not have a brother, the probability of recovering from the disease is 32%. For people who have a brother, the probability of recovering from the disease is 69%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.69
0.37*0.69 - 0.63*0.32 = 0.46
0.46 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23177,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 37%. The probability of not having a brother and recovering from the disease is 20%. The probability of having a brother and recovering from the disease is 26%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.26
0.26/0.37 - 0.20/0.63 = 0.37
0.37 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23181,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 87%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 73%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 22%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 4%. The overall probability of pre-conditions is 45%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.87
P(Y=1 | V1=0, X=1) = 0.73
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.45
0.55 * (0.73 - 0.87) + 0.45 * (0.04 - 0.22) = -0.16
-0.16 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23194,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 34%. For people who do not have a brother, the probability of recovering from the disease is 28%. For people who have a brother, the probability of recovering from the disease is 74%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.34
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.74
0.34*0.74 - 0.66*0.28 = 0.44
0.44 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 34%. The probability of not having a brother and recovering from the disease is 19%. The probability of having a brother and recovering from the disease is 25%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.34
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.25
0.25/0.34 - 0.19/0.66 = 0.46
0.46 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 94%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 74%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 24%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 3%. The overall probability of pre-conditions is 42%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.42
0.58 * (0.74 - 0.94) + 0.42 * (0.03 - 0.24) = -0.20
-0.20 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23203,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 94%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 74%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 24%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 3%. The overall probability of pre-conditions is 42%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.94
P(Y=1 | V1=0, X=1) = 0.74
P(Y=1 | V1=1, X=0) = 0.24
P(Y=1 | V1=1, X=1) = 0.03
P(V1=1) = 0.42
0.58 * (0.74 - 0.94) + 0.42 * (0.03 - 0.24) = -0.20
-0.20 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 49%. For people who do not have a brother, the probability of recovering from the disease is 40%. For people who have a brother, the probability of recovering from the disease is 69%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.49
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.69
0.49*0.69 - 0.51*0.40 = 0.54
0.54 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 49%. The probability of not having a brother and recovering from the disease is 20%. The probability of having a brother and recovering from the disease is 34%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.34
0.34/0.49 - 0.20/0.51 = 0.29
0.29 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 49%. The probability of not having a brother and recovering from the disease is 20%. The probability of having a brother and recovering from the disease is 34%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.34
0.34/0.49 - 0.20/0.51 = 0.29
0.29 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 90%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 77%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 32%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 17%. The overall probability of pre-conditions is 50%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.90
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.32
P(Y=1 | V1=1, X=1) = 0.17
P(V1=1) = 0.50
0.50 * (0.77 - 0.90) + 0.50 * (0.17 - 0.32) = -0.14
-0.14 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 49%. The probability of not having a brother and recovering from the disease is 18%. The probability of having a brother and recovering from the disease is 36%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.49
P(Y=1, X=0=1) = 0.18
P(Y=1, X=1=1) = 0.36
0.36/0.49 - 0.18/0.51 = 0.38
0.38 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 91%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 84%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 21%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 16%. The overall probability of pre-conditions is 44%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.84
P(Y=1 | V1=1, X=0) = 0.21
P(Y=1 | V1=1, X=1) = 0.16
P(V1=1) = 0.44
0.56 * (0.84 - 0.91) + 0.44 * (0.16 - 0.21) = -0.07
-0.07 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 91%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 84%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 21%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 16%. The overall probability of pre-conditions is 44%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.91
P(Y=1 | V1=0, X=1) = 0.84
P(Y=1 | V1=1, X=0) = 0.21
P(Y=1 | V1=1, X=1) = 0.16
P(V1=1) = 0.44
0.56 * (0.84 - 0.91) + 0.44 * (0.16 - 0.21) = -0.07
-0.07 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 62%. The probability of not having a brother and recovering from the disease is 8%. The probability of having a brother and recovering from the disease is 48%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.62
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.48
0.48/0.62 - 0.08/0.38 = 0.56
0.56 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 62%. The probability of not having a brother and recovering from the disease is 8%. The probability of having a brother and recovering from the disease is 48%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.62
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.48
0.48/0.62 - 0.08/0.38 = 0.56
0.56 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 97%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 77%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 25%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 4%. The overall probability of pre-conditions is 55%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.55
0.45 * (0.77 - 0.97) + 0.55 * (0.04 - 0.25) = -0.21
-0.21 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 97%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 77%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 25%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 4%. The overall probability of pre-conditions is 55%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.55
0.45 * (0.77 - 0.97) + 0.55 * (0.04 - 0.25) = -0.20
-0.20 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 97%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 77%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 25%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 4%. The overall probability of pre-conditions is 55%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.97
P(Y=1 | V1=0, X=1) = 0.77
P(Y=1 | V1=1, X=0) = 0.25
P(Y=1 | V1=1, X=1) = 0.04
P(V1=1) = 0.55
0.45 * (0.77 - 0.97) + 0.55 * (0.04 - 0.25) = -0.20
-0.20 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 44%. For people who do not have a brother, the probability of recovering from the disease is 31%. For people who have a brother, the probability of recovering from the disease is 69%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.44
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.69
0.44*0.69 - 0.56*0.31 = 0.48
0.48 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23243,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 83%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 68%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 19%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 5%. The overall probability of pre-conditions is 53%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.83
P(Y=1 | V1=0, X=1) = 0.68
P(Y=1 | V1=1, X=0) = 0.19
P(Y=1 | V1=1, X=1) = 0.05
P(V1=1) = 0.53
0.47 * (0.68 - 0.83) + 0.53 * (0.05 - 0.19) = -0.15
-0.15 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 53%. The probability of not having a brother and recovering from the disease is 9%. The probability of having a brother and recovering from the disease is 32%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.32
0.32/0.53 - 0.09/0.47 = 0.41
0.41 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 89%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 79%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 22%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 15%. The overall probability of pre-conditions is 54%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.89
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.15
P(V1=1) = 0.54
0.46 * (0.79 - 0.89) + 0.54 * (0.15 - 0.22) = -0.09
-0.09 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 89%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 79%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 22%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 15%. The overall probability of pre-conditions is 54%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.89
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.15
P(V1=1) = 0.54
0.46 * (0.79 - 0.89) + 0.54 * (0.15 - 0.22) = -0.10
-0.10 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 89%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 79%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 22%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 15%. The overall probability of pre-conditions is 54%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.89
P(Y=1 | V1=0, X=1) = 0.79
P(Y=1 | V1=1, X=0) = 0.22
P(Y=1 | V1=1, X=1) = 0.15
P(V1=1) = 0.54
0.46 * (0.79 - 0.89) + 0.54 * (0.15 - 0.22) = -0.10
-0.10 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 52%. For people who do not have a brother, the probability of recovering from the disease is 28%. For people who have a brother, the probability of recovering from the disease is 67%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.67
0.52*0.67 - 0.48*0.28 = 0.49
0.49 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 52%. The probability of not having a brother and recovering from the disease is 13%. The probability of having a brother and recovering from the disease is 35%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.52
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.35
0.35/0.52 - 0.13/0.48 = 0.40
0.40 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 100%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 80%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 28%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 8%. The overall probability of pre-conditions is 44%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 1.00
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.28
P(Y=1 | V1=1, X=1) = 0.08
P(V1=1) = 0.44
0.56 * (0.80 - 1.00) + 0.44 * (0.08 - 0.28) = -0.20
-0.20 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23264,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 66%. For people who do not have a brother, the probability of recovering from the disease is 33%. For people who have a brother, the probability of recovering from the disease is 66%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.66
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.66
0.66*0.66 - 0.34*0.33 = 0.55
0.55 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look directly at how having a brother correlates with disease in general. Method 2: We look at this correlation case by case according to pre-conditions.",no,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. Method 1: We look at how having a brother correlates with disease case by case according to pre-conditions. Method 2: We look directly at how having a brother correlates with disease in general.",yes,"nan
nan
nan
nan
nan
nan
nan",confounding,simpson_vaccine,2,backadj,[backdoor adjustment set for Y given X]
23271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 95%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 80%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 30%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 19%. The overall probability of pre-conditions is 58%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V1=v} P(V1=v)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.30
P(Y=1 | V1=1, X=1) = 0.19
P(V1=1) = 0.58
0.42 * (0.80 - 0.95) + 0.58 * (0.19 - 0.30) = -0.13
-0.13 < 0",confounding,simpson_vaccine,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 95%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 80%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 30%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 19%. The overall probability of pre-conditions is 58%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.30
P(Y=1 | V1=1, X=1) = 0.19
P(V1=1) = 0.58
0.42 * (0.80 - 0.95) + 0.58 * (0.19 - 0.30) = -0.15
-0.15 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23273,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. For people with no pre-conditions and do not have a brother, the probability of recovering from the disease is 95%. For people with no pre-conditions and have a brother, the probability of recovering from the disease is 80%. For people with pre-conditions and do not have a brother, the probability of recovering from the disease is 30%. For people with pre-conditions and have a brother, the probability of recovering from the disease is 19%. The overall probability of pre-conditions is 58%.",no,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V1=v} P(V1=v|X=1)*[P(Y=1|V1=v,X=1) - P(Y=1|V1=v, X=0)]
P(Y=1 | V1=0, X=0) = 0.95
P(Y=1 | V1=0, X=1) = 0.80
P(Y=1 | V1=1, X=0) = 0.30
P(Y=1 | V1=1, X=1) = 0.19
P(V1=1) = 0.58
0.42 * (0.80 - 0.95) + 0.58 * (0.19 - 0.30) = -0.15
-0.15 < 0",confounding,simpson_vaccine,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 39%. For people who do not have a brother, the probability of recovering from the disease is 33%. For people who have a brother, the probability of recovering from the disease is 80%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.80
0.39*0.80 - 0.61*0.33 = 0.52
0.52 > 0",confounding,simpson_vaccine,1,marginal,P(Y)
23276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on having a brother and disease. Having a brother has a direct effect on disease. The overall probability of having a brother is 39%. The probability of not having a brother and recovering from the disease is 20%. The probability of having a brother and recovering from the disease is 31%.",yes,"Let V1 = pre-conditions; X = having a brother; Y = disease.
V1->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.31
0.31/0.39 - 0.20/0.61 = 0.47
0.47 > 0",confounding,simpson_vaccine,1,correlation,P(Y | X)
23281,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 53%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.53 - 0.70 = -0.18
-0.18 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 60%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 86%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 36%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 61%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 43%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 14%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 71%. For infants who have a sister and with good health, the probability of normal infant birth weight is 49%. The overall probability of good health is 15%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.86
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.43
P(V3=1 | X=0, V2=1) = 0.14
P(V3=1 | X=1, V2=0) = 0.71
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.15
0.15 * 0.86 * (0.49 - 0.71)+ 0.85 * 0.86 * (0.14 - 0.43)= 0.06
0.06 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23287,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 60%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 86%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 36%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 61%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 43%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 14%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 71%. For infants who have a sister and with good health, the probability of normal infant birth weight is 49%. The overall probability of good health is 15%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.60
P(Y=1 | X=0, V3=1) = 0.86
P(Y=1 | X=1, V3=0) = 0.36
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.43
P(V3=1 | X=0, V2=1) = 0.14
P(V3=1 | X=1, V2=0) = 0.71
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.15
0.15 * (0.61 - 0.36) * 0.14 + 0.85 * (0.86 - 0.60) * 0.71 = -0.24
-0.24 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23288,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 94%. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 53%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.94*0.53 - 0.06*0.70 = 0.54
0.54 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23290,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 94%. The probability of not having a sister and high infant mortality is 4%. The probability of having a sister and high infant mortality is 49%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.94
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.49
0.49/0.94 - 0.04/0.06 = -0.18
-0.18 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23294,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 61%. For infants who have a sister, the probability of high infant mortality is 32%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.32
0.32 - 0.61 = -0.28
-0.28 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23297,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 61%. For infants who have a sister, the probability of high infant mortality is 32%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.32
0.32 - 0.61 = -0.28
-0.28 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 48%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 72%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 16%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 37%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 52%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 26%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 78%. For infants who have a sister and with good health, the probability of normal infant birth weight is 57%. The overall probability of good health is 1%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.01
0.01 * 0.72 * (0.57 - 0.78)+ 0.99 * 0.72 * (0.26 - 0.52)= 0.06
0.06 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 48%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 72%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 16%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 37%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 52%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 26%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 78%. For infants who have a sister and with good health, the probability of normal infant birth weight is 57%. The overall probability of good health is 1%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.01
0.01 * (0.37 - 0.16) * 0.26 + 0.99 * (0.72 - 0.48) * 0.78 = -0.34
-0.34 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 48%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 72%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 16%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 37%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 52%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 26%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 78%. For infants who have a sister and with good health, the probability of normal infant birth weight is 57%. The overall probability of good health is 1%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.48
P(Y=1 | X=0, V3=1) = 0.72
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.01
0.01 * (0.37 - 0.16) * 0.26 + 0.99 * (0.72 - 0.48) * 0.78 = -0.34
-0.34 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23304,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 98%. The probability of not having a sister and high infant mortality is 1%. The probability of having a sister and high infant mortality is 32%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.32
0.32/0.98 - 0.01/0.02 = -0.28
-0.28 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23305,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 98%. The probability of not having a sister and high infant mortality is 1%. The probability of having a sister and high infant mortality is 32%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.32
0.32/0.98 - 0.01/0.02 = -0.28
-0.28 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23307,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 83%. For infants who have a sister, the probability of high infant mortality is 65%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.65
0.65 - 0.83 = -0.19
-0.19 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23310,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 83%. For infants who have a sister, the probability of high infant mortality is 65%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.65
0.65 - 0.83 = -0.19
-0.19 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 69%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 94%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 33%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 68%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 63%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 36%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 95%. For infants who have a sister and with good health, the probability of normal infant birth weight is 63%. The overall probability of good health is 16%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.69
P(Y=1 | X=0, V3=1) = 0.94
P(Y=1 | X=1, V3=0) = 0.33
P(Y=1 | X=1, V3=1) = 0.68
P(V3=1 | X=0, V2=0) = 0.63
P(V3=1 | X=0, V2=1) = 0.36
P(V3=1 | X=1, V2=0) = 0.95
P(V3=1 | X=1, V2=1) = 0.63
P(V2=1) = 0.16
0.16 * (0.68 - 0.33) * 0.36 + 0.84 * (0.94 - 0.69) * 0.95 = -0.26
-0.26 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23316,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 81%. For infants who do not have a sister, the probability of high infant mortality is 83%. For infants who have a sister, the probability of high infant mortality is 65%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.83
P(Y=1 | X=1) = 0.65
0.81*0.65 - 0.19*0.83 = 0.68
0.68 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 56%. For infants who have a sister, the probability of high infant mortality is 31%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.31
0.31 - 0.56 = -0.25
-0.25 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23323,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 56%. For infants who have a sister, the probability of high infant mortality is 31%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.31
0.31 - 0.56 = -0.25
-0.25 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23324,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 56%. For infants who have a sister, the probability of high infant mortality is 31%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.31
0.31 - 0.56 = -0.25
-0.25 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 57%. For infants who have a sister, the probability of high infant mortality is 39%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.39
0.39 - 0.57 = -0.18
-0.18 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 46%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 74%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 18%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 49%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 45%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 22%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 72%. For infants who have a sister and with good health, the probability of normal infant birth weight is 50%. The overall probability of good health is 14%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.18
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.45
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.14
0.14 * 0.74 * (0.50 - 0.72)+ 0.86 * 0.74 * (0.22 - 0.45)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 46%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 74%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 18%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 49%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 45%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 22%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 72%. For infants who have a sister and with good health, the probability of normal infant birth weight is 50%. The overall probability of good health is 14%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.74
P(Y=1 | X=1, V3=0) = 0.18
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.45
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.14
0.14 * (0.49 - 0.18) * 0.22 + 0.86 * (0.74 - 0.46) * 0.72 = -0.26
-0.26 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 96%. For infants who do not have a sister, the probability of high infant mortality is 57%. For infants who have a sister, the probability of high infant mortality is 39%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.39
0.96*0.39 - 0.04*0.57 = 0.40
0.40 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 96%. For infants who do not have a sister, the probability of high infant mortality is 57%. For infants who have a sister, the probability of high infant mortality is 39%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.39
0.96*0.39 - 0.04*0.57 = 0.40
0.40 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 68%. For infants who have a sister, the probability of high infant mortality is 41%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.41
0.41 - 0.68 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 68%. For infants who have a sister, the probability of high infant mortality is 41%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.41
0.41 - 0.68 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 68%. For infants who have a sister, the probability of high infant mortality is 41%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.41
0.41 - 0.68 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 40%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 83%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 6%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 43%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 69%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 35%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 96%. For infants who have a sister and with good health, the probability of normal infant birth weight is 67%. The overall probability of good health is 10%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.40
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0, V2=0) = 0.69
P(V3=1 | X=0, V2=1) = 0.35
P(V3=1 | X=1, V2=0) = 0.96
P(V3=1 | X=1, V2=1) = 0.67
P(V2=1) = 0.10
0.10 * 0.83 * (0.67 - 0.96)+ 0.90 * 0.83 * (0.35 - 0.69)= 0.13
0.13 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 95%. For infants who do not have a sister, the probability of high infant mortality is 68%. For infants who have a sister, the probability of high infant mortality is 41%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.41
0.95*0.41 - 0.05*0.68 = 0.42
0.42 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 95%. The probability of not having a sister and high infant mortality is 3%. The probability of having a sister and high infant mortality is 39%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.39
0.39/0.95 - 0.03/0.05 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 88%. For infants who have a sister, the probability of high infant mortality is 64%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.88
P(Y=1 | X=1) = 0.64
0.64 - 0.88 = -0.24
-0.24 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23369,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 74%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 97%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 44%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 69%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 58%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 22%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 78%. For infants who have a sister and with good health, the probability of normal infant birth weight is 50%. The overall probability of good health is 1%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.74
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.69
P(V3=1 | X=0, V2=0) = 0.58
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.01
0.01 * 0.97 * (0.50 - 0.78)+ 0.99 * 0.97 * (0.22 - 0.58)= 0.05
0.05 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 74%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 97%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 44%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 69%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 58%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 22%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 78%. For infants who have a sister and with good health, the probability of normal infant birth weight is 50%. The overall probability of good health is 1%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.74
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.69
P(V3=1 | X=0, V2=0) = 0.58
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.78
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.01
0.01 * (0.69 - 0.44) * 0.22 + 0.99 * (0.97 - 0.74) * 0.78 = -0.29
-0.29 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 88%. The probability of not having a sister and high infant mortality is 10%. The probability of having a sister and high infant mortality is 56%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.56
0.56/0.88 - 0.10/0.12 = -0.24
-0.24 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23378,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 65%. For infants who have a sister, the probability of high infant mortality is 37%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.37
0.37 - 0.65 = -0.29
-0.29 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 65%. For infants who have a sister, the probability of high infant mortality is 37%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.37
0.37 - 0.65 = -0.29
-0.29 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 95%. For infants who do not have a sister, the probability of high infant mortality is 65%. For infants who have a sister, the probability of high infant mortality is 37%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.37
0.95*0.37 - 0.05*0.65 = 0.38
0.38 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 95%. The probability of not having a sister and high infant mortality is 3%. The probability of having a sister and high infant mortality is 35%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.35
0.35/0.95 - 0.03/0.05 = -0.29
-0.29 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 51%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 77%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 22%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 53%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 33%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 12%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 71%. For infants who have a sister and with good health, the probability of normal infant birth weight is 44%. The overall probability of good health is 12%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.51
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.22
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0, V2=0) = 0.33
P(V3=1 | X=0, V2=1) = 0.12
P(V3=1 | X=1, V2=0) = 0.71
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.12
0.12 * 0.77 * (0.44 - 0.71)+ 0.88 * 0.77 * (0.12 - 0.33)= 0.09
0.09 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 51%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 77%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 22%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 53%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 33%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 12%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 71%. For infants who have a sister and with good health, the probability of normal infant birth weight is 44%. The overall probability of good health is 12%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.51
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.22
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0, V2=0) = 0.33
P(V3=1 | X=0, V2=1) = 0.12
P(V3=1 | X=1, V2=0) = 0.71
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.12
0.12 * (0.53 - 0.22) * 0.12 + 0.88 * (0.77 - 0.51) * 0.71 = -0.26
-0.26 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 58%. For infants who have a sister, the probability of high infant mortality is 36%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.36
0.36 - 0.58 = -0.21
-0.21 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 43%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 69%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 16%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 39%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 60%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 28%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 91%. For infants who have a sister and with good health, the probability of normal infant birth weight is 70%. The overall probability of good health is 10%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.60
P(V3=1 | X=0, V2=1) = 0.28
P(V3=1 | X=1, V2=0) = 0.91
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.10
0.10 * 0.69 * (0.70 - 0.91)+ 0.90 * 0.69 * (0.28 - 0.60)= 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23411,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 43%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 69%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 16%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 39%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 60%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 28%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 91%. For infants who have a sister and with good health, the probability of normal infant birth weight is 70%. The overall probability of good health is 10%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.60
P(V3=1 | X=0, V2=1) = 0.28
P(V3=1 | X=1, V2=0) = 0.91
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.10
0.10 * 0.69 * (0.70 - 0.91)+ 0.90 * 0.69 * (0.28 - 0.60)= 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 43%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 69%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 16%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 39%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 60%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 28%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 91%. For infants who have a sister and with good health, the probability of normal infant birth weight is 70%. The overall probability of good health is 10%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.43
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.16
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.60
P(V3=1 | X=0, V2=1) = 0.28
P(V3=1 | X=1, V2=0) = 0.91
P(V3=1 | X=1, V2=1) = 0.70
P(V2=1) = 0.10
0.10 * (0.39 - 0.16) * 0.28 + 0.90 * (0.69 - 0.43) * 0.91 = -0.29
-0.29 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 83%. The probability of not having a sister and high infant mortality is 10%. The probability of having a sister and high infant mortality is 30%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.30
0.30/0.83 - 0.10/0.17 = -0.21
-0.21 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 68%. For infants who have a sister, the probability of high infant mortality is 47%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.47
0.47 - 0.68 = -0.21
-0.21 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 68%. For infants who have a sister, the probability of high infant mortality is 47%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.47
0.47 - 0.68 = -0.21
-0.21 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 57%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 79%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 30%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 54%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 50%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 28%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 73%. For infants who have a sister and with good health, the probability of normal infant birth weight is 49%. The overall probability of good health is 1%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.79
P(Y=1 | X=1, V3=0) = 0.30
P(Y=1 | X=1, V3=1) = 0.54
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.28
P(V3=1 | X=1, V2=0) = 0.73
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.01
0.01 * 0.79 * (0.49 - 0.73)+ 0.99 * 0.79 * (0.28 - 0.50)= 0.05
0.05 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 57%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 79%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 30%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 54%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 50%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 28%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 73%. For infants who have a sister and with good health, the probability of normal infant birth weight is 49%. The overall probability of good health is 1%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.79
P(Y=1 | X=1, V3=0) = 0.30
P(Y=1 | X=1, V3=1) = 0.54
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.28
P(V3=1 | X=1, V2=0) = 0.73
P(V3=1 | X=1, V2=1) = 0.49
P(V2=1) = 0.01
0.01 * (0.54 - 0.30) * 0.28 + 0.99 * (0.79 - 0.57) * 0.73 = -0.26
-0.26 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 83%. For infants who do not have a sister, the probability of high infant mortality is 68%. For infants who have a sister, the probability of high infant mortality is 47%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.83
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.47
0.83*0.47 - 0.17*0.68 = 0.51
0.51 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 83%. The probability of not having a sister and high infant mortality is 12%. The probability of having a sister and high infant mortality is 39%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.83
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.39
0.39/0.83 - 0.12/0.17 = -0.21
-0.21 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23432,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23435,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 54%. For infants who have a sister, the probability of high infant mortality is 31%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.31
0.31 - 0.54 = -0.23
-0.23 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 54%. For infants who have a sister, the probability of high infant mortality is 31%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.31
0.31 - 0.54 = -0.23
-0.23 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 32%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 73%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 4%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 37%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 55%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 24%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 83%. For infants who have a sister and with good health, the probability of normal infant birth weight is 57%. The overall probability of good health is 6%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.32
P(Y=1 | X=0, V3=1) = 0.73
P(Y=1 | X=1, V3=0) = 0.04
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.55
P(V3=1 | X=0, V2=1) = 0.24
P(V3=1 | X=1, V2=0) = 0.83
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.06
0.06 * 0.73 * (0.57 - 0.83)+ 0.94 * 0.73 * (0.24 - 0.55)= 0.11
0.11 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 87%. For infants who do not have a sister, the probability of high infant mortality is 54%. For infants who have a sister, the probability of high infant mortality is 31%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.31
0.87*0.31 - 0.13*0.54 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 87%. For infants who do not have a sister, the probability of high infant mortality is 54%. For infants who have a sister, the probability of high infant mortality is 31%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.31
0.87*0.31 - 0.13*0.54 = 0.34
0.34 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 67%. For infants who have a sister, the probability of high infant mortality is 47%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.47
0.47 - 0.67 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 67%. For infants who have a sister, the probability of high infant mortality is 47%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.47
0.47 - 0.67 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 57%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 83%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 31%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 54%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 41%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 12%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 71%. For infants who have a sister and with good health, the probability of normal infant birth weight is 40%. The overall probability of good health is 6%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.31
P(Y=1 | X=1, V3=1) = 0.54
P(V3=1 | X=0, V2=0) = 0.41
P(V3=1 | X=0, V2=1) = 0.12
P(V3=1 | X=1, V2=0) = 0.71
P(V3=1 | X=1, V2=1) = 0.40
P(V2=1) = 0.06
0.06 * 0.83 * (0.40 - 0.71)+ 0.94 * 0.83 * (0.12 - 0.41)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 90%. For infants who do not have a sister, the probability of high infant mortality is 67%. For infants who have a sister, the probability of high infant mortality is 47%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.47
0.90*0.47 - 0.10*0.67 = 0.49
0.49 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23457,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 90%. For infants who do not have a sister, the probability of high infant mortality is 67%. For infants who have a sister, the probability of high infant mortality is 47%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.47
0.90*0.47 - 0.10*0.67 = 0.49
0.49 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 59%. For infants who have a sister, the probability of high infant mortality is 26%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.26
0.26 - 0.59 = -0.33
-0.33 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 59%. For infants who have a sister, the probability of high infant mortality is 26%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.26
0.26 - 0.59 = -0.33
-0.33 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 40%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 85%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 6%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 32%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 44%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 21%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 77%. For infants who have a sister and with good health, the probability of normal infant birth weight is 54%. The overall probability of good health is 6%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.40
P(Y=1 | X=0, V3=1) = 0.85
P(Y=1 | X=1, V3=0) = 0.06
P(Y=1 | X=1, V3=1) = 0.32
P(V3=1 | X=0, V2=0) = 0.44
P(V3=1 | X=0, V2=1) = 0.21
P(V3=1 | X=1, V2=0) = 0.77
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.06
0.06 * (0.32 - 0.06) * 0.21 + 0.94 * (0.85 - 0.40) * 0.77 = -0.42
-0.42 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 80%. For infants who have a sister, the probability of high infant mortality is 61%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.61
0.61 - 0.80 = -0.19
-0.19 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 67%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 97%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 39%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 71%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 51%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 17%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 72%. For infants who have a sister and with good health, the probability of normal infant birth weight is 46%. The overall probability of good health is 19%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.17
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.19
0.19 * 0.97 * (0.46 - 0.72)+ 0.81 * 0.97 * (0.17 - 0.51)= 0.05
0.05 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 67%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 97%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 39%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 71%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 51%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 17%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 72%. For infants who have a sister and with good health, the probability of normal infant birth weight is 46%. The overall probability of good health is 19%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.17
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.19
0.19 * 0.97 * (0.46 - 0.72)+ 0.81 * 0.97 * (0.17 - 0.51)= 0.05
0.05 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 67%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 97%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 39%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 71%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 51%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 17%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 72%. For infants who have a sister and with good health, the probability of normal infant birth weight is 46%. The overall probability of good health is 19%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.67
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.71
P(V3=1 | X=0, V2=0) = 0.51
P(V3=1 | X=0, V2=1) = 0.17
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.19
0.19 * (0.71 - 0.39) * 0.17 + 0.81 * (0.97 - 0.67) * 0.72 = -0.26
-0.26 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23485,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 94%. For infants who do not have a sister, the probability of high infant mortality is 80%. For infants who have a sister, the probability of high infant mortality is 61%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.80
P(Y=1 | X=1) = 0.61
0.94*0.61 - 0.06*0.80 = 0.62
0.62 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 65%. For infants who have a sister, the probability of high infant mortality is 44%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.44
0.44 - 0.65 = -0.21
-0.21 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23492,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 65%. For infants who have a sister, the probability of high infant mortality is 44%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.44
0.44 - 0.65 = -0.21
-0.21 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23496,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 55%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 80%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 25%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 50%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 44%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 22%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 84%. For infants who have a sister and with good health, the probability of normal infant birth weight is 54%. The overall probability of good health is 17%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.55
P(Y=1 | X=0, V3=1) = 0.80
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.50
P(V3=1 | X=0, V2=0) = 0.44
P(V3=1 | X=0, V2=1) = 0.22
P(V3=1 | X=1, V2=0) = 0.84
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.17
0.17 * (0.50 - 0.25) * 0.22 + 0.83 * (0.80 - 0.55) * 0.84 = -0.30
-0.30 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 85%. For infants who have a sister, the probability of high infant mortality is 65%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.65
0.65 - 0.85 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 81%. For infants who do not have a sister, the probability of high infant mortality is 85%. For infants who have a sister, the probability of high infant mortality is 65%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.85
P(Y=1 | X=1) = 0.65
0.81*0.65 - 0.19*0.85 = 0.68
0.68 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 81%. The probability of not having a sister and high infant mortality is 16%. The probability of having a sister and high infant mortality is 52%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.16
P(Y=1, X=1=1) = 0.52
0.52/0.81 - 0.16/0.19 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 59%. For infants who have a sister, the probability of high infant mortality is 43%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.43
0.43 - 0.59 = -0.16
-0.16 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 59%. For infants who have a sister, the probability of high infant mortality is 43%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.43
0.43 - 0.59 = -0.16
-0.16 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 42%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 69%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 20%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 44%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 62%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 39%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 95%. For infants who have a sister and with good health, the probability of normal infant birth weight is 72%. The overall probability of good health is 3%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.20
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.95
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.03
0.03 * (0.44 - 0.20) * 0.39 + 0.97 * (0.69 - 0.42) * 0.95 = -0.24
-0.24 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 42%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 69%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 20%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 44%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 62%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 39%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 95%. For infants who have a sister and with good health, the probability of normal infant birth weight is 72%. The overall probability of good health is 3%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.42
P(Y=1 | X=0, V3=1) = 0.69
P(Y=1 | X=1, V3=0) = 0.20
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.95
P(V3=1 | X=1, V2=1) = 0.72
P(V2=1) = 0.03
0.03 * (0.44 - 0.20) * 0.39 + 0.97 * (0.69 - 0.42) * 0.95 = -0.24
-0.24 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23526,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 87%. For infants who do not have a sister, the probability of high infant mortality is 59%. For infants who have a sister, the probability of high infant mortality is 43%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.43
0.87*0.43 - 0.13*0.59 = 0.45
0.45 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23527,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 87%. For infants who do not have a sister, the probability of high infant mortality is 59%. For infants who have a sister, the probability of high infant mortality is 43%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.43
0.87*0.43 - 0.13*0.59 = 0.45
0.45 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 87%. The probability of not having a sister and high infant mortality is 8%. The probability of having a sister and high infant mortality is 37%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.87
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.37
0.37/0.87 - 0.08/0.13 = -0.16
-0.16 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23536,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 61%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 89%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 24%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 59%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 67%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 31%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 96%. For infants who have a sister and with good health, the probability of normal infant birth weight is 57%. The overall probability of good health is 13%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.61
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.24
P(Y=1 | X=1, V3=1) = 0.59
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.31
P(V3=1 | X=1, V2=0) = 0.96
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.13
0.13 * 0.89 * (0.57 - 0.96)+ 0.87 * 0.89 * (0.31 - 0.67)= 0.06
0.06 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23537,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 61%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 89%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 24%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 59%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 67%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 31%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 96%. For infants who have a sister and with good health, the probability of normal infant birth weight is 57%. The overall probability of good health is 13%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.61
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.24
P(Y=1 | X=1, V3=1) = 0.59
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.31
P(V3=1 | X=1, V2=0) = 0.96
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.13
0.13 * 0.89 * (0.57 - 0.96)+ 0.87 * 0.89 * (0.31 - 0.67)= 0.06
0.06 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 89%. For infants who do not have a sister, the probability of high infant mortality is 79%. For infants who have a sister, the probability of high infant mortality is 56%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.56
0.89*0.56 - 0.11*0.79 = 0.59
0.59 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 89%. The probability of not having a sister and high infant mortality is 9%. The probability of having a sister and high infant mortality is 50%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.50
0.50/0.89 - 0.09/0.11 = -0.22
-0.22 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 52%. For infants who have a sister, the probability of high infant mortality is 32%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.32
0.32 - 0.52 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23548,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 52%. For infants who have a sister, the probability of high infant mortality is 32%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.32
0.32 - 0.52 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 40%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 67%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 13%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 42%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 52%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 11%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 73%. For infants who have a sister and with good health, the probability of normal infant birth weight is 44%. The overall probability of good health is 19%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.40
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.13
P(Y=1 | X=1, V3=1) = 0.42
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.11
P(V3=1 | X=1, V2=0) = 0.73
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.19
0.19 * 0.67 * (0.44 - 0.73)+ 0.81 * 0.67 * (0.11 - 0.52)= 0.06
0.06 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 40%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 67%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 13%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 42%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 52%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 11%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 73%. For infants who have a sister and with good health, the probability of normal infant birth weight is 44%. The overall probability of good health is 19%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.40
P(Y=1 | X=0, V3=1) = 0.67
P(Y=1 | X=1, V3=0) = 0.13
P(Y=1 | X=1, V3=1) = 0.42
P(V3=1 | X=0, V2=0) = 0.52
P(V3=1 | X=0, V2=1) = 0.11
P(V3=1 | X=1, V2=0) = 0.73
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.19
0.19 * (0.42 - 0.13) * 0.11 + 0.81 * (0.67 - 0.40) * 0.73 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23554,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 94%. For infants who do not have a sister, the probability of high infant mortality is 52%. For infants who have a sister, the probability of high infant mortality is 32%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.32
0.94*0.32 - 0.06*0.52 = 0.33
0.33 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 94%. The probability of not having a sister and high infant mortality is 3%. The probability of having a sister and high infant mortality is 30%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.94
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.30
0.30/0.94 - 0.03/0.06 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23559,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 76%. For infants who have a sister, the probability of high infant mortality is 56%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.56
0.56 - 0.76 = -0.19
-0.19 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23564,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 64%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 89%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 29%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 63%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 48%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 26%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 85%. For infants who have a sister and with good health, the probability of normal infant birth weight is 54%. The overall probability of good health is 11%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.63
P(V3=1 | X=0, V2=0) = 0.48
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.11
0.11 * 0.89 * (0.54 - 0.85)+ 0.89 * 0.89 * (0.26 - 0.48)= 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 64%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 89%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 29%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 63%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 48%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 26%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 85%. For infants who have a sister and with good health, the probability of normal infant birth weight is 54%. The overall probability of good health is 11%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.63
P(V3=1 | X=0, V2=0) = 0.48
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.11
0.11 * (0.63 - 0.29) * 0.26 + 0.89 * (0.89 - 0.64) * 0.85 = -0.30
-0.30 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 64%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 89%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 29%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 63%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 48%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 26%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 85%. For infants who have a sister and with good health, the probability of normal infant birth weight is 54%. The overall probability of good health is 11%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.89
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.63
P(V3=1 | X=0, V2=0) = 0.48
P(V3=1 | X=0, V2=1) = 0.26
P(V3=1 | X=1, V2=0) = 0.85
P(V3=1 | X=1, V2=1) = 0.54
P(V2=1) = 0.11
0.11 * (0.63 - 0.29) * 0.26 + 0.89 * (0.89 - 0.64) * 0.85 = -0.30
-0.30 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 85%. For infants who do not have a sister, the probability of high infant mortality is 76%. For infants who have a sister, the probability of high infant mortality is 56%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.56
0.85*0.56 - 0.15*0.76 = 0.59
0.59 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23574,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 63%. For infants who have a sister, the probability of high infant mortality is 43%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.43
0.43 - 0.63 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 63%. For infants who have a sister, the probability of high infant mortality is 43%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.63
P(Y=1 | X=1) = 0.43
0.43 - 0.63 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 55%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 77%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 25%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 50%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 36%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 7%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 72%. For infants who have a sister and with good health, the probability of normal infant birth weight is 50%. The overall probability of good health is 4%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.55
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.50
P(V3=1 | X=0, V2=0) = 0.36
P(V3=1 | X=0, V2=1) = 0.07
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.04
0.04 * 0.77 * (0.50 - 0.72)+ 0.96 * 0.77 * (0.07 - 0.36)= 0.08
0.08 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 55%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 77%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 25%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 50%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 36%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 7%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 72%. For infants who have a sister and with good health, the probability of normal infant birth weight is 50%. The overall probability of good health is 4%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.55
P(Y=1 | X=0, V3=1) = 0.77
P(Y=1 | X=1, V3=0) = 0.25
P(Y=1 | X=1, V3=1) = 0.50
P(V3=1 | X=0, V2=0) = 0.36
P(V3=1 | X=0, V2=1) = 0.07
P(V3=1 | X=1, V2=0) = 0.72
P(V3=1 | X=1, V2=1) = 0.50
P(V2=1) = 0.04
0.04 * (0.50 - 0.25) * 0.07 + 0.96 * (0.77 - 0.55) * 0.72 = -0.29
-0.29 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 79%. For infants who have a sister, the probability of high infant mortality is 52%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.52
0.52 - 0.79 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 79%. For infants who have a sister, the probability of high infant mortality is 52%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.52
0.52 - 0.79 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 64%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 96%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 29%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 61%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 50%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 24%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 76%. For infants who have a sister and with good health, the probability of normal infant birth weight is 46%. The overall probability of good health is 17%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.96
P(Y=1 | X=1, V3=0) = 0.29
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0, V2=0) = 0.50
P(V3=1 | X=0, V2=1) = 0.24
P(V3=1 | X=1, V2=0) = 0.76
P(V3=1 | X=1, V2=1) = 0.46
P(V2=1) = 0.17
0.17 * 0.96 * (0.46 - 0.76)+ 0.83 * 0.96 * (0.24 - 0.50)= 0.07
0.07 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 84%. The probability of not having a sister and high infant mortality is 13%. The probability of having a sister and high infant mortality is 43%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.43
0.43/0.84 - 0.13/0.16 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23601,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23603,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 53%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.53 - 0.70 = -0.17
-0.17 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23604,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 53%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.53 - 0.70 = -0.17
-0.17 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 57%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 78%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 32%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 55%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 65%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 40%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 95%. For infants who have a sister and with good health, the probability of normal infant birth weight is 71%. The overall probability of good health is 14%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.78
P(Y=1 | X=1, V3=0) = 0.32
P(Y=1 | X=1, V3=1) = 0.55
P(V3=1 | X=0, V2=0) = 0.65
P(V3=1 | X=0, V2=1) = 0.40
P(V3=1 | X=1, V2=0) = 0.95
P(V3=1 | X=1, V2=1) = 0.71
P(V2=1) = 0.14
0.14 * (0.55 - 0.32) * 0.40 + 0.86 * (0.78 - 0.57) * 0.95 = -0.23
-0.23 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 80%. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 53%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.80*0.53 - 0.20*0.70 = 0.56
0.56 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 80%. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 53%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.80
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.80*0.53 - 0.20*0.70 = 0.56
0.56 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 80%. The probability of not having a sister and high infant mortality is 14%. The probability of having a sister and high infant mortality is 42%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.80
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.42
0.42/0.80 - 0.14/0.20 = -0.17
-0.17 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23613,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 80%. The probability of not having a sister and high infant mortality is 14%. The probability of having a sister and high infant mortality is 42%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.80
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.42
0.42/0.80 - 0.14/0.20 = -0.17
-0.17 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23617,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 54%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.54
0.54 - 0.70 = -0.16
-0.16 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 63%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 87%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 39%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 63%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 32%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 1%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 64%. For infants who have a sister and with good health, the probability of normal infant birth weight is 22%. The overall probability of good health is 3%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.63
P(Y=1 | X=0, V3=1) = 0.87
P(Y=1 | X=1, V3=0) = 0.39
P(Y=1 | X=1, V3=1) = 0.63
P(V3=1 | X=0, V2=0) = 0.32
P(V3=1 | X=0, V2=1) = 0.01
P(V3=1 | X=1, V2=0) = 0.64
P(V3=1 | X=1, V2=1) = 0.22
P(V2=1) = 0.03
0.03 * (0.63 - 0.39) * 0.01 + 0.97 * (0.87 - 0.63) * 0.64 = -0.23
-0.23 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 81%. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 54%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.54
0.81*0.54 - 0.19*0.70 = 0.57
0.57 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23625,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 81%. For infants who do not have a sister, the probability of high infant mortality is 70%. For infants who have a sister, the probability of high infant mortality is 54%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.54
0.81*0.54 - 0.19*0.70 = 0.57
0.57 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 81%. The probability of not having a sister and high infant mortality is 13%. The probability of having a sister and high infant mortality is 44%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.44
0.44/0.81 - 0.13/0.19 = -0.16
-0.16 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 81%. The probability of not having a sister and high infant mortality is 13%. The probability of having a sister and high infant mortality is 44%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.44
0.44/0.81 - 0.13/0.19 = -0.16
-0.16 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 68%. For infants who have a sister, the probability of high infant mortality is 53%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.53
0.53 - 0.68 = -0.15
-0.15 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 52%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 83%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 26%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 57%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 54%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 32%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 87%. For infants who have a sister and with good health, the probability of normal infant birth weight is 57%. The overall probability of good health is 2%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.52
P(Y=1 | X=0, V3=1) = 0.83
P(Y=1 | X=1, V3=0) = 0.26
P(Y=1 | X=1, V3=1) = 0.57
P(V3=1 | X=0, V2=0) = 0.54
P(V3=1 | X=0, V2=1) = 0.32
P(V3=1 | X=1, V2=0) = 0.87
P(V3=1 | X=1, V2=1) = 0.57
P(V2=1) = 0.02
0.02 * (0.57 - 0.26) * 0.32 + 0.98 * (0.83 - 0.52) * 0.87 = -0.26
-0.26 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 59%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 86%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 21%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 60%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 67%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 39%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 99%. For infants who have a sister and with good health, the probability of normal infant birth weight is 68%. The overall probability of good health is 18%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.59
P(Y=1 | X=0, V3=1) = 0.86
P(Y=1 | X=1, V3=0) = 0.21
P(Y=1 | X=1, V3=1) = 0.60
P(V3=1 | X=0, V2=0) = 0.67
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.99
P(V3=1 | X=1, V2=1) = 0.68
P(V2=1) = 0.18
0.18 * (0.60 - 0.21) * 0.39 + 0.82 * (0.86 - 0.59) * 0.99 = -0.25
-0.25 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 82%. For infants who do not have a sister, the probability of high infant mortality is 76%. For infants who have a sister, the probability of high infant mortality is 58%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.76
P(Y=1 | X=1) = 0.58
0.82*0.58 - 0.18*0.76 = 0.61
0.61 > 0",arrowhead,smoke_birthWeight,1,marginal,P(Y)
23656,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look directly at how having a sister correlates with infant mortality in general. Method 2: We look at this correlation case by case according to infant's birth weight.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 79%. For infants who have a sister, the probability of high infant mortality is 46%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.46
0.46 - 0.79 = -0.34
-0.34 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 79%. For infants who have a sister, the probability of high infant mortality is 46%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.46
0.46 - 0.79 = -0.34
-0.34 < 0",arrowhead,smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 79%. For infants who have a sister, the probability of high infant mortality is 46%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.46
0.46 - 0.79 = -0.34
-0.34 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23661,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 79%. For infants who have a sister, the probability of high infant mortality is 46%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.79
P(Y=1 | X=1) = 0.46
0.46 - 0.79 = -0.34
-0.34 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 62%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 91%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 19%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 49%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 62%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 38%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 94%. For infants who have a sister and with good health, the probability of normal infant birth weight is 58%. The overall probability of good health is 11%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.19
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.94
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.11
0.11 * 0.91 * (0.58 - 0.94)+ 0.89 * 0.91 * (0.38 - 0.62)= 0.09
0.09 > 0",arrowhead,smoke_birthWeight,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 62%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 91%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 19%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 49%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 62%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 38%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 94%. For infants who have a sister and with good health, the probability of normal infant birth weight is 58%. The overall probability of good health is 11%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.19
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.94
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.11
0.11 * (0.49 - 0.19) * 0.38 + 0.89 * (0.91 - 0.62) * 0.94 = -0.44
-0.44 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 62%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 91%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 19%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 49%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 62%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 38%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 94%. For infants who have a sister and with good health, the probability of normal infant birth weight is 58%. The overall probability of good health is 11%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.91
P(Y=1 | X=1, V3=0) = 0.19
P(Y=1 | X=1, V3=1) = 0.49
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.94
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.11
0.11 * (0.49 - 0.19) * 0.38 + 0.89 * (0.91 - 0.62) * 0.94 = -0.44
-0.44 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 94%. The probability of not having a sister and high infant mortality is 5%. The probability of having a sister and high infant mortality is 43%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.94
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.43
0.43/0.94 - 0.05/0.06 = -0.34
-0.34 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23670,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 87%. For infants who have a sister, the probability of high infant mortality is 73%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.87
P(Y=1 | X=1) = 0.73
0.73 - 0.87 = -0.14
-0.14 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 70%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 97%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 35%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 77%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 64%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 29%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 94%. For infants who have a sister and with good health, the probability of normal infant birth weight is 58%. The overall probability of good health is 6%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.64
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.94
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.06
0.06 * (0.77 - 0.35) * 0.29 + 0.94 * (0.97 - 0.70) * 0.94 = -0.24
-0.24 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 70%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 97%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 35%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 77%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 64%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 29%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 94%. For infants who have a sister and with good health, the probability of normal infant birth weight is 58%. The overall probability of good health is 6%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.97
P(Y=1 | X=1, V3=0) = 0.35
P(Y=1 | X=1, V3=1) = 0.77
P(V3=1 | X=0, V2=0) = 0.64
P(V3=1 | X=0, V2=1) = 0.29
P(V3=1 | X=1, V2=0) = 0.94
P(V3=1 | X=1, V2=1) = 0.58
P(V2=1) = 0.06
0.06 * (0.77 - 0.35) * 0.29 + 0.94 * (0.97 - 0.70) * 0.94 = -0.24
-0.24 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 86%. The probability of not having a sister and high infant mortality is 12%. The probability of having a sister and high infant mortality is 63%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.86
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.63
0.63/0.86 - 0.12/0.14 = -0.13
-0.13 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. Method 1: We look at how having a sister correlates with infant mortality case by case according to infant's birth weight. Method 2: We look directly at how having a sister correlates with infant mortality in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
23688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister, the probability of high infant mortality is 59%. For infants who have a sister, the probability of high infant mortality is 39%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.59
P(Y=1 | X=1) = 0.39
0.39 - 0.59 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23692,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 46%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 71%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 18%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 46%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 59%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 19%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 83%. For infants who have a sister and with good health, the probability of normal infant birth weight is 44%. The overall probability of good health is 18%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.18
P(Y=1 | X=1, V3=1) = 0.46
P(V3=1 | X=0, V2=0) = 0.59
P(V3=1 | X=0, V2=1) = 0.19
P(V3=1 | X=1, V2=0) = 0.83
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.18
0.18 * (0.46 - 0.18) * 0.19 + 0.82 * (0.71 - 0.46) * 0.83 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23693,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. For infants who do not have a sister and low infant birth weight, the probability of high infant mortality is 46%. For infants who do not have a sister and normal infant birth weight, the probability of high infant mortality is 71%. For infants who have a sister and low infant birth weight, the probability of high infant mortality is 18%. For infants who have a sister and normal infant birth weight, the probability of high infant mortality is 46%. For infants who do not have a sister and with poor health, the probability of normal infant birth weight is 59%. For infants who do not have a sister and with good health, the probability of normal infant birth weight is 19%. For infants who have a sister and with poor health, the probability of normal infant birth weight is 83%. For infants who have a sister and with good health, the probability of normal infant birth weight is 44%. The overall probability of good health is 18%.",yes,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.46
P(Y=1 | X=0, V3=1) = 0.71
P(Y=1 | X=1, V3=0) = 0.18
P(Y=1 | X=1, V3=1) = 0.46
P(V3=1 | X=0, V2=0) = 0.59
P(V3=1 | X=0, V2=1) = 0.19
P(V3=1 | X=1, V2=0) = 0.83
P(V3=1 | X=1, V2=1) = 0.44
P(V2=1) = 0.18
0.18 * (0.46 - 0.18) * 0.19 + 0.82 * (0.71 - 0.46) * 0.83 = -0.27
-0.27 < 0",arrowhead,smoke_birthWeight,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
23696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on infant's birth weight and infant mortality. Health condition has a direct effect on infant's birth weight and infant mortality. Infant's birth weight has a direct effect on infant mortality. Health condition is unobserved. The overall probability of having a sister is 97%. The probability of not having a sister and high infant mortality is 2%. The probability of having a sister and high infant mortality is 38%.",no,"Let V2 = health condition; X = having a sister; V3 = infant's birth weight; Y = infant mortality.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.38
0.38/0.97 - 0.02/0.03 = -0.20
-0.20 < 0",arrowhead,smoke_birthWeight,1,correlation,P(Y | X)
23703,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 80%. For nonsmokers and with high tar deposit, the probability of freckles is 54%. For smokers and with no tar deposit, the probability of freckles is 79%. For smokers and with high tar deposit, the probability of freckles is 53%. For nonsmokers, the probability of high tar deposit is 40%. For smokers, the probability of high tar deposit is 19%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0) = 0.40
P(V3=1 | X=1) = 0.19
0.53 * (0.19 - 0.40) + 0.54 * (0.81 - 0.60) = 0.05
0.05 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 40%. For smokers, the probability of high tar deposit is 19%. For nonsmokers and with no tar deposit, the probability of freckles is 80%. For nonsmokers and with high tar deposit, the probability of freckles is 54%. For smokers and with no tar deposit, the probability of freckles is 79%. For smokers and with high tar deposit, the probability of freckles is 53%. The overall probability of smoking is 36%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.40
P(V3=1 | X=1) = 0.19
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.53
P(X=1) = 0.36
0.19 - 0.40 * (0.53 * 0.36 + 0.54 * 0.64)= 0.05
0.05 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 36%. For nonsmokers, the probability of freckles is 70%. For smokers, the probability of freckles is 74%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.36
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.74
0.36*0.74 - 0.64*0.70 = 0.71
0.71 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 36%. The probability of nonsmoking and freckles is 44%. The probability of smoking and freckles is 27%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.36
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.27
0.27/0.36 - 0.44/0.64 = 0.05
0.05 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23713,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 1%. For nonsmokers and with no tar deposit, the probability of freckles is 65%. For nonsmokers and with high tar deposit, the probability of freckles is 34%. For smokers and with no tar deposit, the probability of freckles is 65%. For smokers and with high tar deposit, the probability of freckles is 34%. The overall probability of smoking is 95%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.01
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.34
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.34
P(X=1) = 0.95
(0.01 - 0.66)* (0.34 * 0.95) + (0.99 - 0.34) * (0.34 * 0.05) = 0.20
0.20 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 1%. For nonsmokers and with no tar deposit, the probability of freckles is 65%. For nonsmokers and with high tar deposit, the probability of freckles is 34%. For smokers and with no tar deposit, the probability of freckles is 65%. For smokers and with high tar deposit, the probability of freckles is 34%. The overall probability of smoking is 95%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.01
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.34
P(Y=1 | X=1, V3=0) = 0.65
P(Y=1 | X=1, V3=1) = 0.34
P(X=1) = 0.95
0.01 - 0.66 * (0.34 * 0.95 + 0.34 * 0.05)= 0.20
0.20 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 55%. For smokers, the probability of high tar deposit is 18%. For nonsmokers and with no tar deposit, the probability of freckles is 94%. For nonsmokers and with high tar deposit, the probability of freckles is 64%. For smokers and with no tar deposit, the probability of freckles is 89%. For smokers and with high tar deposit, the probability of freckles is 61%. The overall probability of smoking is 50%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.55
P(V3=1 | X=1) = 0.18
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.89
P(Y=1 | X=1, V3=1) = 0.61
P(X=1) = 0.50
(0.18 - 0.55)* (0.61 * 0.50) + (0.82 - 0.45) * (0.64 * 0.50) = 0.11
0.11 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 94%. For nonsmokers and with high tar deposit, the probability of freckles is 64%. For smokers and with no tar deposit, the probability of freckles is 89%. For smokers and with high tar deposit, the probability of freckles is 61%. For nonsmokers, the probability of high tar deposit is 55%. For smokers, the probability of high tar deposit is 18%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.89
P(Y=1 | X=1, V3=1) = 0.61
P(V3=1 | X=0) = 0.55
P(V3=1 | X=1) = 0.18
0.61 * (0.18 - 0.55) + 0.64 * (0.82 - 0.45) = 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 55%. For smokers, the probability of high tar deposit is 18%. For nonsmokers and with no tar deposit, the probability of freckles is 94%. For nonsmokers and with high tar deposit, the probability of freckles is 64%. For smokers and with no tar deposit, the probability of freckles is 89%. For smokers and with high tar deposit, the probability of freckles is 61%. The overall probability of smoking is 50%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.55
P(V3=1 | X=1) = 0.18
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.89
P(Y=1 | X=1, V3=1) = 0.61
P(X=1) = 0.50
0.18 - 0.55 * (0.61 * 0.50 + 0.64 * 0.50)= 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 55%. For smokers, the probability of high tar deposit is 18%. For nonsmokers and with no tar deposit, the probability of freckles is 94%. For nonsmokers and with high tar deposit, the probability of freckles is 64%. For smokers and with no tar deposit, the probability of freckles is 89%. For smokers and with high tar deposit, the probability of freckles is 61%. The overall probability of smoking is 50%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.55
P(V3=1 | X=1) = 0.18
P(Y=1 | X=0, V3=0) = 0.94
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.89
P(Y=1 | X=1, V3=1) = 0.61
P(X=1) = 0.50
0.18 - 0.55 * (0.61 * 0.50 + 0.64 * 0.50)= 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 50%. For nonsmokers, the probability of freckles is 77%. For smokers, the probability of freckles is 84%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.50
P(Y=1 | X=0) = 0.77
P(Y=1 | X=1) = 0.84
0.50*0.84 - 0.50*0.77 = 0.81
0.81 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23733,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 50%. The probability of nonsmoking and freckles is 39%. The probability of smoking and freckles is 42%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.50
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.42
0.42/0.50 - 0.39/0.50 = 0.07
0.07 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23736,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 86%. For smokers, the probability of high tar deposit is 51%. For nonsmokers and with no tar deposit, the probability of freckles is 77%. For nonsmokers and with high tar deposit, the probability of freckles is 42%. For smokers and with no tar deposit, the probability of freckles is 76%. For smokers and with high tar deposit, the probability of freckles is 43%. The overall probability of smoking is 82%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.86
P(V3=1 | X=1) = 0.51
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.43
P(X=1) = 0.82
(0.51 - 0.86)* (0.43 * 0.82) + (0.49 - 0.14) * (0.42 * 0.18) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 86%. For smokers, the probability of high tar deposit is 51%. For nonsmokers and with no tar deposit, the probability of freckles is 77%. For nonsmokers and with high tar deposit, the probability of freckles is 42%. For smokers and with no tar deposit, the probability of freckles is 76%. For smokers and with high tar deposit, the probability of freckles is 43%. The overall probability of smoking is 82%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.86
P(V3=1 | X=1) = 0.51
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.43
P(X=1) = 0.82
(0.51 - 0.86)* (0.43 * 0.82) + (0.49 - 0.14) * (0.42 * 0.18) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 77%. For nonsmokers and with high tar deposit, the probability of freckles is 42%. For smokers and with no tar deposit, the probability of freckles is 76%. For smokers and with high tar deposit, the probability of freckles is 43%. For nonsmokers, the probability of high tar deposit is 86%. For smokers, the probability of high tar deposit is 51%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0) = 0.86
P(V3=1 | X=1) = 0.51
0.43 * (0.51 - 0.86) + 0.42 * (0.49 - 0.14) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 82%. The probability of nonsmoking and freckles is 8%. The probability of smoking and freckles is 49%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.49
0.49/0.82 - 0.08/0.18 = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 56%. For smokers, the probability of high tar deposit is 10%. For nonsmokers and with no tar deposit, the probability of freckles is 93%. For nonsmokers and with high tar deposit, the probability of freckles is 60%. For smokers and with no tar deposit, the probability of freckles is 88%. For smokers and with high tar deposit, the probability of freckles is 54%. The overall probability of smoking is 55%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.56
P(V3=1 | X=1) = 0.10
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.88
P(Y=1 | X=1, V3=1) = 0.54
P(X=1) = 0.55
(0.10 - 0.56)* (0.54 * 0.55) + (0.90 - 0.44) * (0.60 * 0.45) = 0.15
0.15 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 93%. For nonsmokers and with high tar deposit, the probability of freckles is 60%. For smokers and with no tar deposit, the probability of freckles is 88%. For smokers and with high tar deposit, the probability of freckles is 54%. For nonsmokers, the probability of high tar deposit is 56%. For smokers, the probability of high tar deposit is 10%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.88
P(Y=1 | X=1, V3=1) = 0.54
P(V3=1 | X=0) = 0.56
P(V3=1 | X=1) = 0.10
0.54 * (0.10 - 0.56) + 0.60 * (0.90 - 0.44) = 0.16
0.16 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23753,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 56%. For smokers, the probability of high tar deposit is 10%. For nonsmokers and with no tar deposit, the probability of freckles is 93%. For nonsmokers and with high tar deposit, the probability of freckles is 60%. For smokers and with no tar deposit, the probability of freckles is 88%. For smokers and with high tar deposit, the probability of freckles is 54%. The overall probability of smoking is 55%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.56
P(V3=1 | X=1) = 0.10
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.88
P(Y=1 | X=1, V3=1) = 0.54
P(X=1) = 0.55
0.10 - 0.56 * (0.54 * 0.55 + 0.60 * 0.45)= 0.15
0.15 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 55%. For nonsmokers, the probability of freckles is 74%. For smokers, the probability of freckles is 85%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.55
P(Y=1 | X=0) = 0.74
P(Y=1 | X=1) = 0.85
0.55*0.85 - 0.45*0.74 = 0.80
0.80 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 55%. The probability of nonsmoking and freckles is 33%. The probability of smoking and freckles is 47%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.55
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.47
0.47/0.55 - 0.33/0.45 = 0.10
0.10 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 78%. For smokers, the probability of high tar deposit is 32%. For nonsmokers and with no tar deposit, the probability of freckles is 69%. For nonsmokers and with high tar deposit, the probability of freckles is 33%. For smokers and with no tar deposit, the probability of freckles is 76%. For smokers and with high tar deposit, the probability of freckles is 24%. The overall probability of smoking is 97%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.78
P(V3=1 | X=1) = 0.32
P(Y=1 | X=0, V3=0) = 0.69
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.24
P(X=1) = 0.97
(0.32 - 0.78)* (0.24 * 0.97) + (0.68 - 0.22) * (0.33 * 0.03) = 0.24
0.24 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 78%. For smokers, the probability of high tar deposit is 32%. For nonsmokers and with no tar deposit, the probability of freckles is 69%. For nonsmokers and with high tar deposit, the probability of freckles is 33%. For smokers and with no tar deposit, the probability of freckles is 76%. For smokers and with high tar deposit, the probability of freckles is 24%. The overall probability of smoking is 97%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.78
P(V3=1 | X=1) = 0.32
P(Y=1 | X=0, V3=0) = 0.69
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.76
P(Y=1 | X=1, V3=1) = 0.24
P(X=1) = 0.97
0.32 - 0.78 * (0.24 * 0.97 + 0.33 * 0.03)= 0.24
0.24 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 97%. The probability of nonsmoking and freckles is 1%. The probability of smoking and freckles is 57%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.57
0.57/0.97 - 0.01/0.03 = 0.18
0.18 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23770,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 77%. For smokers, the probability of high tar deposit is 26%. For nonsmokers and with no tar deposit, the probability of freckles is 71%. For nonsmokers and with high tar deposit, the probability of freckles is 45%. For smokers and with no tar deposit, the probability of freckles is 63%. For smokers and with high tar deposit, the probability of freckles is 37%. The overall probability of smoking is 39%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.77
P(V3=1 | X=1) = 0.26
P(Y=1 | X=0, V3=0) = 0.71
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.37
P(X=1) = 0.39
(0.26 - 0.77)* (0.37 * 0.39) + (0.74 - 0.23) * (0.45 * 0.61) = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23773,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 77%. For smokers, the probability of high tar deposit is 26%. For nonsmokers and with no tar deposit, the probability of freckles is 71%. For nonsmokers and with high tar deposit, the probability of freckles is 45%. For smokers and with no tar deposit, the probability of freckles is 63%. For smokers and with high tar deposit, the probability of freckles is 37%. The overall probability of smoking is 39%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.77
P(V3=1 | X=1) = 0.26
P(Y=1 | X=0, V3=0) = 0.71
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.37
P(X=1) = 0.39
(0.26 - 0.77)* (0.37 * 0.39) + (0.74 - 0.23) * (0.45 * 0.61) = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 71%. For nonsmokers and with high tar deposit, the probability of freckles is 45%. For smokers and with no tar deposit, the probability of freckles is 63%. For smokers and with high tar deposit, the probability of freckles is 37%. For nonsmokers, the probability of high tar deposit is 77%. For smokers, the probability of high tar deposit is 26%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.71
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0) = 0.77
P(V3=1 | X=1) = 0.26
0.37 * (0.26 - 0.77) + 0.45 * (0.74 - 0.23) = 0.13
0.13 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 77%. For smokers, the probability of high tar deposit is 26%. For nonsmokers and with no tar deposit, the probability of freckles is 71%. For nonsmokers and with high tar deposit, the probability of freckles is 45%. For smokers and with no tar deposit, the probability of freckles is 63%. For smokers and with high tar deposit, the probability of freckles is 37%. The overall probability of smoking is 39%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.77
P(V3=1 | X=1) = 0.26
P(Y=1 | X=0, V3=0) = 0.71
P(Y=1 | X=0, V3=1) = 0.45
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.37
P(X=1) = 0.39
0.26 - 0.77 * (0.37 * 0.39 + 0.45 * 0.61)= 0.13
0.13 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 39%. For nonsmokers, the probability of freckles is 51%. For smokers, the probability of freckles is 57%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.57
0.39*0.57 - 0.61*0.51 = 0.53
0.53 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 39%. The probability of nonsmoking and freckles is 31%. The probability of smoking and freckles is 22%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.22
0.22/0.39 - 0.31/0.61 = 0.05
0.05 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 69%. For smokers, the probability of high tar deposit is 3%. For nonsmokers and with no tar deposit, the probability of freckles is 72%. For nonsmokers and with high tar deposit, the probability of freckles is 19%. For smokers and with no tar deposit, the probability of freckles is 69%. For smokers and with high tar deposit, the probability of freckles is 18%. The overall probability of smoking is 70%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.69
P(V3=1 | X=1) = 0.03
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.18
P(X=1) = 0.70
(0.03 - 0.69)* (0.18 * 0.70) + (0.97 - 0.31) * (0.19 * 0.30) = 0.34
0.34 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 69%. For smokers, the probability of high tar deposit is 3%. For nonsmokers and with no tar deposit, the probability of freckles is 72%. For nonsmokers and with high tar deposit, the probability of freckles is 19%. For smokers and with no tar deposit, the probability of freckles is 69%. For smokers and with high tar deposit, the probability of freckles is 18%. The overall probability of smoking is 70%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.69
P(V3=1 | X=1) = 0.03
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.18
P(X=1) = 0.70
0.03 - 0.69 * (0.18 * 0.70 + 0.19 * 0.30)= 0.34
0.34 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 69%. For smokers, the probability of high tar deposit is 3%. For nonsmokers and with no tar deposit, the probability of freckles is 72%. For nonsmokers and with high tar deposit, the probability of freckles is 19%. For smokers and with no tar deposit, the probability of freckles is 69%. For smokers and with high tar deposit, the probability of freckles is 18%. The overall probability of smoking is 70%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.69
P(V3=1 | X=1) = 0.03
P(Y=1 | X=0, V3=0) = 0.72
P(Y=1 | X=0, V3=1) = 0.19
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.18
P(X=1) = 0.70
0.03 - 0.69 * (0.18 * 0.70 + 0.19 * 0.30)= 0.34
0.34 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23794,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 61%. For smokers, the probability of high tar deposit is 33%. For nonsmokers and with no tar deposit, the probability of freckles is 76%. For nonsmokers and with high tar deposit, the probability of freckles is 38%. For smokers and with no tar deposit, the probability of freckles is 60%. For smokers and with high tar deposit, the probability of freckles is 26%. The overall probability of smoking is 10%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.61
P(V3=1 | X=1) = 0.33
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.26
P(X=1) = 0.10
(0.33 - 0.61)* (0.26 * 0.10) + (0.67 - 0.39) * (0.38 * 0.90) = 0.10
0.10 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 76%. For nonsmokers and with high tar deposit, the probability of freckles is 38%. For smokers and with no tar deposit, the probability of freckles is 60%. For smokers and with high tar deposit, the probability of freckles is 26%. For nonsmokers, the probability of high tar deposit is 61%. For smokers, the probability of high tar deposit is 33%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.38
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.26
P(V3=1 | X=0) = 0.61
P(V3=1 | X=1) = 0.33
0.26 * (0.33 - 0.61) + 0.38 * (0.67 - 0.39) = 0.09
0.09 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 10%. For nonsmokers, the probability of freckles is 53%. For smokers, the probability of freckles is 49%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.10
P(Y=1 | X=0) = 0.53
P(Y=1 | X=1) = 0.49
0.10*0.49 - 0.90*0.53 = 0.53
0.53 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 10%. The probability of nonsmoking and freckles is 48%. The probability of smoking and freckles is 5%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.10
P(Y=1, X=0=1) = 0.48
P(Y=1, X=1=1) = 0.05
0.05/0.10 - 0.48/0.90 = -0.04
-0.04 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 70%. For nonsmokers and with high tar deposit, the probability of freckles is 21%. For smokers and with no tar deposit, the probability of freckles is 68%. For smokers and with high tar deposit, the probability of freckles is 18%. For nonsmokers, the probability of high tar deposit is 73%. For smokers, the probability of high tar deposit is 23%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.21
P(Y=1 | X=1, V3=0) = 0.68
P(Y=1 | X=1, V3=1) = 0.18
P(V3=1 | X=0) = 0.73
P(V3=1 | X=1) = 0.23
0.18 * (0.23 - 0.73) + 0.21 * (0.77 - 0.27) = 0.25
0.25 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 73%. For smokers, the probability of high tar deposit is 23%. For nonsmokers and with no tar deposit, the probability of freckles is 70%. For nonsmokers and with high tar deposit, the probability of freckles is 21%. For smokers and with no tar deposit, the probability of freckles is 68%. For smokers and with high tar deposit, the probability of freckles is 18%. The overall probability of smoking is 64%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.73
P(V3=1 | X=1) = 0.23
P(Y=1 | X=0, V3=0) = 0.70
P(Y=1 | X=0, V3=1) = 0.21
P(Y=1 | X=1, V3=0) = 0.68
P(Y=1 | X=1, V3=1) = 0.18
P(X=1) = 0.64
0.23 - 0.73 * (0.18 * 0.64 + 0.21 * 0.36)= 0.25
0.25 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 64%. The probability of nonsmoking and freckles is 12%. The probability of smoking and freckles is 36%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.64
P(Y=1, X=0=1) = 0.12
P(Y=1, X=1=1) = 0.36
0.36/0.64 - 0.12/0.36 = 0.22
0.22 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 56%. For smokers, the probability of high tar deposit is 32%. For nonsmokers and with no tar deposit, the probability of freckles is 76%. For nonsmokers and with high tar deposit, the probability of freckles is 43%. For smokers and with no tar deposit, the probability of freckles is 67%. For smokers and with high tar deposit, the probability of freckles is 32%. The overall probability of smoking is 37%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.56
P(V3=1 | X=1) = 0.32
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.43
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.32
P(X=1) = 0.37
(0.32 - 0.56)* (0.32 * 0.37) + (0.68 - 0.44) * (0.43 * 0.63) = 0.08
0.08 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 56%. For smokers, the probability of high tar deposit is 32%. For nonsmokers and with no tar deposit, the probability of freckles is 76%. For nonsmokers and with high tar deposit, the probability of freckles is 43%. For smokers and with no tar deposit, the probability of freckles is 67%. For smokers and with high tar deposit, the probability of freckles is 32%. The overall probability of smoking is 37%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.56
P(V3=1 | X=1) = 0.32
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.43
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.32
P(X=1) = 0.37
0.32 - 0.56 * (0.32 * 0.37 + 0.43 * 0.63)= 0.08
0.08 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 37%. For nonsmokers, the probability of freckles is 57%. For smokers, the probability of freckles is 56%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.56
0.37*0.56 - 0.63*0.57 = 0.57
0.57 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 37%. The probability of nonsmoking and freckles is 36%. The probability of smoking and freckles is 21%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.36
P(Y=1, X=1=1) = 0.21
0.21/0.37 - 0.36/0.63 = -0.02
-0.02 < 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23833,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 78%. For smokers, the probability of high tar deposit is 28%. For nonsmokers and with no tar deposit, the probability of freckles is 76%. For nonsmokers and with high tar deposit, the probability of freckles is 33%. For smokers and with no tar deposit, the probability of freckles is 77%. For smokers and with high tar deposit, the probability of freckles is 34%. The overall probability of smoking is 63%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.78
P(V3=1 | X=1) = 0.28
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.77
P(Y=1 | X=1, V3=1) = 0.34
P(X=1) = 0.63
(0.28 - 0.78)* (0.34 * 0.63) + (0.72 - 0.22) * (0.33 * 0.37) = 0.21
0.21 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 78%. For smokers, the probability of high tar deposit is 28%. For nonsmokers and with no tar deposit, the probability of freckles is 76%. For nonsmokers and with high tar deposit, the probability of freckles is 33%. For smokers and with no tar deposit, the probability of freckles is 77%. For smokers and with high tar deposit, the probability of freckles is 34%. The overall probability of smoking is 63%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.78
P(V3=1 | X=1) = 0.28
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.77
P(Y=1 | X=1, V3=1) = 0.34
P(X=1) = 0.63
0.28 - 0.78 * (0.34 * 0.63 + 0.33 * 0.37)= 0.21
0.21 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 96%. For nonsmokers, the probability of freckles is 46%. For smokers, the probability of freckles is 68%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.68
0.96*0.68 - 0.04*0.46 = 0.67
0.67 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 96%. The probability of nonsmoking and freckles is 2%. The probability of smoking and freckles is 65%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.65
0.65/0.96 - 0.02/0.04 = 0.22
0.22 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 57%. For smokers, the probability of high tar deposit is 1%. For nonsmokers and with no tar deposit, the probability of freckles is 97%. For nonsmokers and with high tar deposit, the probability of freckles is 58%. For smokers and with no tar deposit, the probability of freckles is 92%. For smokers and with high tar deposit, the probability of freckles is 54%. The overall probability of smoking is 45%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.57
P(V3=1 | X=1) = 0.01
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.54
P(X=1) = 0.45
(0.01 - 0.57)* (0.54 * 0.45) + (0.99 - 0.43) * (0.58 * 0.55) = 0.22
0.22 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 57%. For smokers, the probability of high tar deposit is 1%. For nonsmokers and with no tar deposit, the probability of freckles is 97%. For nonsmokers and with high tar deposit, the probability of freckles is 58%. For smokers and with no tar deposit, the probability of freckles is 92%. For smokers and with high tar deposit, the probability of freckles is 54%. The overall probability of smoking is 45%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.57
P(V3=1 | X=1) = 0.01
P(Y=1 | X=0, V3=0) = 0.97
P(Y=1 | X=0, V3=1) = 0.58
P(Y=1 | X=1, V3=0) = 0.92
P(Y=1 | X=1, V3=1) = 0.54
P(X=1) = 0.45
0.01 - 0.57 * (0.54 * 0.45 + 0.58 * 0.55)= 0.22
0.22 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23874,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 45%. For nonsmokers, the probability of freckles is 75%. For smokers, the probability of freckles is 92%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.92
0.45*0.92 - 0.55*0.75 = 0.83
0.83 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 45%. The probability of nonsmoking and freckles is 42%. The probability of smoking and freckles is 41%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.42
P(Y=1, X=1=1) = 0.41
0.41/0.45 - 0.42/0.55 = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 8%. For nonsmokers and with no tar deposit, the probability of freckles is 84%. For nonsmokers and with high tar deposit, the probability of freckles is 33%. For smokers and with no tar deposit, the probability of freckles is 82%. For smokers and with high tar deposit, the probability of freckles is 33%. The overall probability of smoking is 57%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.08
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.33
P(X=1) = 0.57
(0.08 - 0.66)* (0.33 * 0.57) + (0.92 - 0.34) * (0.33 * 0.43) = 0.29
0.29 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 84%. For nonsmokers and with high tar deposit, the probability of freckles is 33%. For smokers and with no tar deposit, the probability of freckles is 82%. For smokers and with high tar deposit, the probability of freckles is 33%. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 8%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.33
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.08
0.33 * (0.08 - 0.66) + 0.33 * (0.92 - 0.34) = 0.29
0.29 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 57%. For nonsmokers, the probability of freckles is 51%. For smokers, the probability of freckles is 78%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.57
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.78
0.57*0.78 - 0.43*0.51 = 0.67
0.67 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23888,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 57%. The probability of nonsmoking and freckles is 22%. The probability of smoking and freckles is 45%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.45
0.45/0.57 - 0.22/0.43 = 0.28
0.28 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23889,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 57%. The probability of nonsmoking and freckles is 22%. The probability of smoking and freckles is 45%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.57
P(Y=1, X=0=1) = 0.22
P(Y=1, X=1=1) = 0.45
0.45/0.57 - 0.22/0.43 = 0.28
0.28 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 63%. For smokers, the probability of high tar deposit is 26%. For nonsmokers and with no tar deposit, the probability of freckles is 61%. For nonsmokers and with high tar deposit, the probability of freckles is 27%. For smokers and with no tar deposit, the probability of freckles is 44%. For smokers and with high tar deposit, the probability of freckles is 14%. The overall probability of smoking is 21%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.63
P(V3=1 | X=1) = 0.26
P(Y=1 | X=0, V3=0) = 0.61
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.44
P(Y=1 | X=1, V3=1) = 0.14
P(X=1) = 0.21
0.26 - 0.63 * (0.14 * 0.21 + 0.27 * 0.79)= 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23905,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 69%. For smokers, the probability of high tar deposit is 12%. For nonsmokers and with no tar deposit, the probability of freckles is 57%. For nonsmokers and with high tar deposit, the probability of freckles is 27%. For smokers and with no tar deposit, the probability of freckles is 56%. For smokers and with high tar deposit, the probability of freckles is 29%. The overall probability of smoking is 86%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.69
P(V3=1 | X=1) = 0.12
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.29
P(X=1) = 0.86
(0.12 - 0.69)* (0.29 * 0.86) + (0.88 - 0.31) * (0.27 * 0.14) = 0.16
0.16 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 57%. For nonsmokers and with high tar deposit, the probability of freckles is 27%. For smokers and with no tar deposit, the probability of freckles is 56%. For smokers and with high tar deposit, the probability of freckles is 29%. For nonsmokers, the probability of high tar deposit is 69%. For smokers, the probability of high tar deposit is 12%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.29
P(V3=1 | X=0) = 0.69
P(V3=1 | X=1) = 0.12
0.29 * (0.12 - 0.69) + 0.27 * (0.88 - 0.31) = 0.16
0.16 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 69%. For smokers, the probability of high tar deposit is 12%. For nonsmokers and with no tar deposit, the probability of freckles is 57%. For nonsmokers and with high tar deposit, the probability of freckles is 27%. For smokers and with no tar deposit, the probability of freckles is 56%. For smokers and with high tar deposit, the probability of freckles is 29%. The overall probability of smoking is 86%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.69
P(V3=1 | X=1) = 0.12
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.27
P(Y=1 | X=1, V3=0) = 0.56
P(Y=1 | X=1, V3=1) = 0.29
P(X=1) = 0.86
0.12 - 0.69 * (0.29 * 0.86 + 0.27 * 0.14)= 0.16
0.16 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 86%. For nonsmokers, the probability of freckles is 37%. For smokers, the probability of freckles is 53%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.53
0.86*0.53 - 0.14*0.37 = 0.51
0.51 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 53%. For nonsmokers and with high tar deposit, the probability of freckles is 31%. For smokers and with no tar deposit, the probability of freckles is 51%. For smokers and with high tar deposit, the probability of freckles is 29%. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 18%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.29
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.18
0.29 * (0.18 - 0.66) + 0.31 * (0.82 - 0.34) = 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 53%. For nonsmokers and with high tar deposit, the probability of freckles is 31%. For smokers and with no tar deposit, the probability of freckles is 51%. For smokers and with high tar deposit, the probability of freckles is 29%. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 18%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.29
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.18
0.29 * (0.18 - 0.66) + 0.31 * (0.82 - 0.34) = 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 18%. For nonsmokers and with no tar deposit, the probability of freckles is 53%. For nonsmokers and with high tar deposit, the probability of freckles is 31%. For smokers and with no tar deposit, the probability of freckles is 51%. For smokers and with high tar deposit, the probability of freckles is 29%. The overall probability of smoking is 41%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.18
P(Y=1 | X=0, V3=0) = 0.53
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.51
P(Y=1 | X=1, V3=1) = 0.29
P(X=1) = 0.41
0.18 - 0.66 * (0.29 * 0.41 + 0.31 * 0.59)= 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 41%. The probability of nonsmoking and freckles is 23%. The probability of smoking and freckles is 19%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.41
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.19
0.19/0.41 - 0.23/0.59 = 0.08
0.08 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 36%. For smokers, the probability of high tar deposit is 2%. For nonsmokers and with no tar deposit, the probability of freckles is 80%. For nonsmokers and with high tar deposit, the probability of freckles is 46%. For smokers and with no tar deposit, the probability of freckles is 78%. For smokers and with high tar deposit, the probability of freckles is 44%. The overall probability of smoking is 63%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.36
P(V3=1 | X=1) = 0.02
P(Y=1 | X=0, V3=0) = 0.80
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.44
P(X=1) = 0.63
(0.02 - 0.36)* (0.44 * 0.63) + (0.98 - 0.64) * (0.46 * 0.37) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 63%. For nonsmokers, the probability of freckles is 67%. For smokers, the probability of freckles is 77%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.77
0.63*0.77 - 0.37*0.67 = 0.74
0.74 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 70%. For smokers, the probability of high tar deposit is 24%. For nonsmokers and with no tar deposit, the probability of freckles is 90%. For nonsmokers and with high tar deposit, the probability of freckles is 64%. For smokers and with no tar deposit, the probability of freckles is 84%. For smokers and with high tar deposit, the probability of freckles is 59%. The overall probability of smoking is 45%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.70
P(V3=1 | X=1) = 0.24
P(Y=1 | X=0, V3=0) = 0.90
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.59
P(X=1) = 0.45
0.24 - 0.70 * (0.59 * 0.45 + 0.64 * 0.55)= 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 45%. For nonsmokers, the probability of freckles is 72%. For smokers, the probability of freckles is 78%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.45
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.78
0.45*0.78 - 0.55*0.72 = 0.75
0.75 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 45%. The probability of nonsmoking and freckles is 39%. The probability of smoking and freckles is 35%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.45
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.35
0.35/0.45 - 0.39/0.55 = 0.06
0.06 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 62%. For nonsmokers and with high tar deposit, the probability of freckles is 28%. For smokers and with no tar deposit, the probability of freckles is 61%. For smokers and with high tar deposit, the probability of freckles is 27%. For nonsmokers, the probability of high tar deposit is 97%. For smokers, the probability of high tar deposit is 45%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.28
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0) = 0.97
P(V3=1 | X=1) = 0.45
0.27 * (0.45 - 0.97) + 0.28 * (0.55 - 0.03) = 0.18
0.18 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 62%. For nonsmokers and with high tar deposit, the probability of freckles is 28%. For smokers and with no tar deposit, the probability of freckles is 61%. For smokers and with high tar deposit, the probability of freckles is 27%. For nonsmokers, the probability of high tar deposit is 97%. For smokers, the probability of high tar deposit is 45%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.28
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.27
P(V3=1 | X=0) = 0.97
P(V3=1 | X=1) = 0.45
0.27 * (0.45 - 0.97) + 0.28 * (0.55 - 0.03) = 0.18
0.18 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 97%. For smokers, the probability of high tar deposit is 45%. For nonsmokers and with no tar deposit, the probability of freckles is 62%. For nonsmokers and with high tar deposit, the probability of freckles is 28%. For smokers and with no tar deposit, the probability of freckles is 61%. For smokers and with high tar deposit, the probability of freckles is 27%. The overall probability of smoking is 86%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.97
P(V3=1 | X=1) = 0.45
P(Y=1 | X=0, V3=0) = 0.62
P(Y=1 | X=0, V3=1) = 0.28
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.27
P(X=1) = 0.86
0.45 - 0.97 * (0.27 * 0.86 + 0.28 * 0.14)= 0.18
0.18 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 86%. For nonsmokers, the probability of freckles is 29%. For smokers, the probability of freckles is 46%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.86
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.46
0.86*0.46 - 0.14*0.29 = 0.43
0.43 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 86%. The probability of nonsmoking and freckles is 4%. The probability of smoking and freckles is 39%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.86
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.39
0.39/0.86 - 0.04/0.14 = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
23964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 29%. For nonsmokers and with no tar deposit, the probability of freckles is 79%. For nonsmokers and with high tar deposit, the probability of freckles is 49%. For smokers and with no tar deposit, the probability of freckles is 73%. For smokers and with high tar deposit, the probability of freckles is 41%. The overall probability of smoking is 37%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.29
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.41
P(X=1) = 0.37
(0.29 - 0.66)* (0.41 * 0.37) + (0.71 - 0.34) * (0.49 * 0.63) = 0.11
0.11 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 79%. For nonsmokers and with high tar deposit, the probability of freckles is 49%. For smokers and with no tar deposit, the probability of freckles is 73%. For smokers and with high tar deposit, the probability of freckles is 41%. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 29%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.41
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.29
0.41 * (0.29 - 0.66) + 0.49 * (0.71 - 0.34) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 29%. For nonsmokers and with no tar deposit, the probability of freckles is 79%. For nonsmokers and with high tar deposit, the probability of freckles is 49%. For smokers and with no tar deposit, the probability of freckles is 73%. For smokers and with high tar deposit, the probability of freckles is 41%. The overall probability of smoking is 37%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.29
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.41
P(X=1) = 0.37
0.29 - 0.66 * (0.41 * 0.37 + 0.49 * 0.63)= 0.11
0.11 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 85%. For smokers, the probability of high tar deposit is 11%. For nonsmokers and with no tar deposit, the probability of freckles is 75%. For nonsmokers and with high tar deposit, the probability of freckles is 35%. For smokers and with no tar deposit, the probability of freckles is 74%. For smokers and with high tar deposit, the probability of freckles is 36%. The overall probability of smoking is 53%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.85
P(V3=1 | X=1) = 0.11
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.74
P(Y=1 | X=1, V3=1) = 0.36
P(X=1) = 0.53
(0.11 - 0.85)* (0.36 * 0.53) + (0.89 - 0.15) * (0.35 * 0.47) = 0.29
0.29 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 75%. For nonsmokers and with high tar deposit, the probability of freckles is 35%. For smokers and with no tar deposit, the probability of freckles is 74%. For smokers and with high tar deposit, the probability of freckles is 36%. For nonsmokers, the probability of high tar deposit is 85%. For smokers, the probability of high tar deposit is 11%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.35
P(Y=1 | X=1, V3=0) = 0.74
P(Y=1 | X=1, V3=1) = 0.36
P(V3=1 | X=0) = 0.85
P(V3=1 | X=1) = 0.11
0.36 * (0.11 - 0.85) + 0.35 * (0.89 - 0.15) = 0.28
0.28 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 53%. For nonsmokers, the probability of freckles is 41%. For smokers, the probability of freckles is 69%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.69
0.53*0.69 - 0.47*0.41 = 0.56
0.56 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23983,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 53%. For nonsmokers, the probability of freckles is 41%. For smokers, the probability of freckles is 69%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.53
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.69
0.53*0.69 - 0.47*0.41 = 0.56
0.56 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
23984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 53%. The probability of nonsmoking and freckles is 19%. The probability of smoking and freckles is 37%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.37
0.37/0.53 - 0.19/0.47 = 0.29
0.29 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 53%. The probability of nonsmoking and freckles is 19%. The probability of smoking and freckles is 37%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.53
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.37
0.37/0.53 - 0.19/0.47 = 0.29
0.29 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
23988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 79%. For smokers, the probability of high tar deposit is 40%. For nonsmokers and with no tar deposit, the probability of freckles is 79%. For nonsmokers and with high tar deposit, the probability of freckles is 49%. For smokers and with no tar deposit, the probability of freckles is 71%. For smokers and with high tar deposit, the probability of freckles is 40%. The overall probability of smoking is 45%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.79
P(V3=1 | X=1) = 0.40
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.40
P(X=1) = 0.45
(0.40 - 0.79)* (0.40 * 0.45) + (0.60 - 0.21) * (0.49 * 0.55) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23989,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 79%. For smokers, the probability of high tar deposit is 40%. For nonsmokers and with no tar deposit, the probability of freckles is 79%. For nonsmokers and with high tar deposit, the probability of freckles is 49%. For smokers and with no tar deposit, the probability of freckles is 71%. For smokers and with high tar deposit, the probability of freckles is 40%. The overall probability of smoking is 45%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.79
P(V3=1 | X=1) = 0.40
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.40
P(X=1) = 0.45
(0.40 - 0.79)* (0.40 * 0.45) + (0.60 - 0.21) * (0.49 * 0.55) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
23990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 79%. For nonsmokers and with high tar deposit, the probability of freckles is 49%. For smokers and with no tar deposit, the probability of freckles is 71%. For smokers and with high tar deposit, the probability of freckles is 40%. For nonsmokers, the probability of high tar deposit is 79%. For smokers, the probability of high tar deposit is 40%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0) = 0.79
P(V3=1 | X=1) = 0.40
0.40 * (0.40 - 0.79) + 0.49 * (0.60 - 0.21) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
23992,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 79%. For smokers, the probability of high tar deposit is 40%. For nonsmokers and with no tar deposit, the probability of freckles is 79%. For nonsmokers and with high tar deposit, the probability of freckles is 49%. For smokers and with no tar deposit, the probability of freckles is 71%. For smokers and with high tar deposit, the probability of freckles is 40%. The overall probability of smoking is 45%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.79
P(V3=1 | X=1) = 0.40
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.40
P(X=1) = 0.45
0.40 - 0.79 * (0.40 * 0.45 + 0.49 * 0.55)= 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
23998,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look directly at how smoking correlates with freckles in general. Method 2: We look at this correlation case by case according to gender.",no,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
24000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 44%. For smokers, the probability of high tar deposit is 22%. For nonsmokers and with no tar deposit, the probability of freckles is 75%. For nonsmokers and with high tar deposit, the probability of freckles is 42%. For smokers and with no tar deposit, the probability of freckles is 75%. For smokers and with high tar deposit, the probability of freckles is 42%. The overall probability of smoking is 60%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.44
P(V3=1 | X=1) = 0.22
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.75
P(Y=1 | X=1, V3=1) = 0.42
P(X=1) = 0.60
(0.22 - 0.44)* (0.42 * 0.60) + (0.78 - 0.56) * (0.42 * 0.40) = 0.07
0.07 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 82%. For nonsmokers and with high tar deposit, the probability of freckles is 56%. For smokers and with no tar deposit, the probability of freckles is 79%. For smokers and with high tar deposit, the probability of freckles is 53%. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 32%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.32
0.53 * (0.32 - 0.66) + 0.56 * (0.68 - 0.34) = 0.09
0.09 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 82%. For nonsmokers and with high tar deposit, the probability of freckles is 56%. For smokers and with no tar deposit, the probability of freckles is 79%. For smokers and with high tar deposit, the probability of freckles is 53%. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 32%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.53
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.32
0.53 * (0.32 - 0.66) + 0.56 * (0.68 - 0.34) = 0.09
0.09 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 66%. For smokers, the probability of high tar deposit is 32%. For nonsmokers and with no tar deposit, the probability of freckles is 82%. For nonsmokers and with high tar deposit, the probability of freckles is 56%. For smokers and with no tar deposit, the probability of freckles is 79%. For smokers and with high tar deposit, the probability of freckles is 53%. The overall probability of smoking is 37%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.66
P(V3=1 | X=1) = 0.32
P(Y=1 | X=0, V3=0) = 0.82
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.79
P(Y=1 | X=1, V3=1) = 0.53
P(X=1) = 0.37
0.32 - 0.66 * (0.53 * 0.37 + 0.56 * 0.63)= 0.09
0.09 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 37%. For nonsmokers, the probability of freckles is 65%. For smokers, the probability of freckles is 71%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.37
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.71
0.37*0.71 - 0.63*0.65 = 0.67
0.67 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
24020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 37%. The probability of nonsmoking and freckles is 41%. The probability of smoking and freckles is 26%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.37
P(Y=1, X=0=1) = 0.41
P(Y=1, X=1=1) = 0.26
0.26/0.37 - 0.41/0.63 = 0.06
0.06 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
24025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 80%. For smokers, the probability of high tar deposit is 3%. For nonsmokers and with no tar deposit, the probability of freckles is 57%. For nonsmokers and with high tar deposit, the probability of freckles is 18%. For smokers and with no tar deposit, the probability of freckles is 59%. For smokers and with high tar deposit, the probability of freckles is 22%. The overall probability of smoking is 75%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.80
P(V3=1 | X=1) = 0.03
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.18
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.22
P(X=1) = 0.75
(0.03 - 0.80)* (0.22 * 0.75) + (0.97 - 0.20) * (0.18 * 0.25) = 0.29
0.29 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 57%. For nonsmokers and with high tar deposit, the probability of freckles is 18%. For smokers and with no tar deposit, the probability of freckles is 59%. For smokers and with high tar deposit, the probability of freckles is 22%. For nonsmokers, the probability of high tar deposit is 80%. For smokers, the probability of high tar deposit is 3%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.18
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.22
P(V3=1 | X=0) = 0.80
P(V3=1 | X=1) = 0.03
0.22 * (0.03 - 0.80) + 0.18 * (0.97 - 0.20) = 0.29
0.29 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 75%. For nonsmokers, the probability of freckles is 26%. For smokers, the probability of freckles is 58%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.75
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.58
0.75*0.58 - 0.25*0.26 = 0.51
0.51 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
24031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 75%. For nonsmokers, the probability of freckles is 26%. For smokers, the probability of freckles is 58%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.75
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.58
0.75*0.58 - 0.25*0.26 = 0.51
0.51 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
24032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 75%. The probability of nonsmoking and freckles is 6%. The probability of smoking and freckles is 44%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.75
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.44
0.44/0.75 - 0.06/0.25 = 0.32
0.32 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
24033,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 75%. The probability of nonsmoking and freckles is 6%. The probability of smoking and freckles is 44%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.75
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.44
0.44/0.75 - 0.06/0.25 = 0.32
0.32 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
24039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 65%. For nonsmokers and with high tar deposit, the probability of freckles is 33%. For smokers and with no tar deposit, the probability of freckles is 66%. For smokers and with high tar deposit, the probability of freckles is 34%. For nonsmokers, the probability of high tar deposit is 70%. For smokers, the probability of high tar deposit is 19%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0) = 0.70
P(V3=1 | X=1) = 0.19
0.34 * (0.19 - 0.70) + 0.33 * (0.81 - 0.30) = 0.16
0.16 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 70%. For smokers, the probability of high tar deposit is 19%. For nonsmokers and with no tar deposit, the probability of freckles is 65%. For nonsmokers and with high tar deposit, the probability of freckles is 33%. For smokers and with no tar deposit, the probability of freckles is 66%. For smokers and with high tar deposit, the probability of freckles is 34%. The overall probability of smoking is 56%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.70
P(V3=1 | X=1) = 0.19
P(Y=1 | X=0, V3=0) = 0.65
P(Y=1 | X=0, V3=1) = 0.33
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.34
P(X=1) = 0.56
0.19 - 0.70 * (0.34 * 0.56 + 0.33 * 0.44)= 0.16
0.16 > 0",frontdoor,smoking_frontdoor,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 56%. For nonsmokers, the probability of freckles is 43%. For smokers, the probability of freckles is 60%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.56
P(Y=1 | X=0) = 0.43
P(Y=1 | X=1) = 0.60
0.56*0.60 - 0.44*0.43 = 0.52
0.52 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
24044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 56%. The probability of nonsmoking and freckles is 19%. The probability of smoking and freckles is 33%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.56
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.33
0.33/0.56 - 0.19/0.44 = 0.17
0.17 > 0",frontdoor,smoking_frontdoor,1,correlation,P(Y | X)
24047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. Method 1: We look at how smoking correlates with freckles case by case according to gender. Method 2: We look directly at how smoking correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",frontdoor,smoking_frontdoor,2,backadj,[backdoor adjustment set for Y given X]
24048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 74%. For smokers, the probability of high tar deposit is 29%. For nonsmokers and with no tar deposit, the probability of freckles is 85%. For nonsmokers and with high tar deposit, the probability of freckles is 59%. For smokers and with no tar deposit, the probability of freckles is 84%. For smokers and with high tar deposit, the probability of freckles is 58%. The overall probability of smoking is 63%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.74
P(V3=1 | X=1) = 0.29
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.58
P(X=1) = 0.63
(0.29 - 0.74)* (0.58 * 0.63) + (0.71 - 0.26) * (0.59 * 0.37) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers, the probability of high tar deposit is 74%. For smokers, the probability of high tar deposit is 29%. For nonsmokers and with no tar deposit, the probability of freckles is 85%. For nonsmokers and with high tar deposit, the probability of freckles is 59%. For smokers and with no tar deposit, the probability of freckles is 84%. For smokers and with high tar deposit, the probability of freckles is 58%. The overall probability of smoking is 63%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
\sum_{V3 = v} [P(V3 = v|X = 1) - P(V3 = v|X = 0)] * [\sum_{X = h} P(Y = 1|X = h,V3 = v)*P(X = h)]
P(V3=1 | X=0) = 0.74
P(V3=1 | X=1) = 0.29
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.58
P(X=1) = 0.63
(0.29 - 0.74)* (0.58 * 0.63) + (0.71 - 0.26) * (0.59 * 0.37) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 85%. For nonsmokers and with high tar deposit, the probability of freckles is 59%. For smokers and with no tar deposit, the probability of freckles is 84%. For smokers and with high tar deposit, the probability of freckles is 58%. For nonsmokers, the probability of high tar deposit is 74%. For smokers, the probability of high tar deposit is 29%.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0) = 0.74
P(V3=1 | X=1) = 0.29
0.58 * (0.29 - 0.74) + 0.59 * (0.71 - 0.26) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. For nonsmokers and with no tar deposit, the probability of freckles is 85%. For nonsmokers and with high tar deposit, the probability of freckles is 59%. For smokers and with no tar deposit, the probability of freckles is 84%. For smokers and with high tar deposit, the probability of freckles is 58%. For nonsmokers, the probability of high tar deposit is 74%. For smokers, the probability of high tar deposit is 29%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
\sum_{V3=v}P(Y=1|X=1,V3=v)*[P(V3=v|X=1)-P(V3=v|X=0)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.59
P(Y=1 | X=1, V3=0) = 0.84
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0) = 0.74
P(V3=1 | X=1) = 0.29
0.58 * (0.29 - 0.74) + 0.59 * (0.71 - 0.26) = 0.12
0.12 > 0",frontdoor,smoking_frontdoor,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and freckles. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on freckles. Gender is unobserved. The overall probability of smoking is 63%. For nonsmokers, the probability of freckles is 66%. For smokers, the probability of freckles is 77%.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = freckles.
V1->X,X->V3,V1->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.66
P(Y=1 | X=1) = 0.77
0.63*0.77 - 0.37*0.66 = 0.73
0.73 > 0",frontdoor,smoking_frontdoor,1,marginal,P(Y)
24061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 62%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.62
0.62 - 0.54 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 62%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.62
0.62 - 0.54 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 54%. For people who do not have a brother and smokers, the probability of lung cancer is 55%. For people who have a brother and nonsmokers, the probability of lung cancer is 69%. For people who have a brother and smokers, the probability of lung cancer is 51%. For people who do not have a brother and with low pollution, the probability of smoking is 95%. For people who do not have a brother and with high pollution, the probability of smoking is 37%. For people who have a brother and with low pollution, the probability of smoking is 58%. For people who have a brother and with high pollution, the probability of smoking is 9%. The overall probability of high pollution is 40%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.95
P(V3=1 | X=0, V2=1) = 0.37
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.40
0.40 * 0.55 * (0.09 - 0.58)+ 0.60 * 0.55 * (0.37 - 0.95)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 54%. For people who do not have a brother and smokers, the probability of lung cancer is 55%. For people who have a brother and nonsmokers, the probability of lung cancer is 69%. For people who have a brother and smokers, the probability of lung cancer is 51%. For people who do not have a brother and with low pollution, the probability of smoking is 95%. For people who do not have a brother and with high pollution, the probability of smoking is 37%. For people who have a brother and with low pollution, the probability of smoking is 58%. For people who have a brother and with high pollution, the probability of smoking is 9%. The overall probability of high pollution is 40%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.95
P(V3=1 | X=0, V2=1) = 0.37
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.40
0.40 * 0.55 * (0.09 - 0.58)+ 0.60 * 0.55 * (0.37 - 0.95)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 54%. For people who do not have a brother and smokers, the probability of lung cancer is 55%. For people who have a brother and nonsmokers, the probability of lung cancer is 69%. For people who have a brother and smokers, the probability of lung cancer is 51%. For people who do not have a brother and with low pollution, the probability of smoking is 95%. For people who do not have a brother and with high pollution, the probability of smoking is 37%. For people who have a brother and with low pollution, the probability of smoking is 58%. For people who have a brother and with high pollution, the probability of smoking is 9%. The overall probability of high pollution is 40%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.54
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.95
P(V3=1 | X=0, V2=1) = 0.37
P(V3=1 | X=1, V2=0) = 0.58
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.40
0.40 * (0.51 - 0.69) * 0.37 + 0.60 * (0.55 - 0.54) * 0.58 = -0.03
-0.03 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 92%. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 62%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.92
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.62
0.92*0.62 - 0.08*0.54 = 0.62
0.62 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 64%. For people who have a brother, the probability of lung cancer is 45%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.45
0.45 - 0.64 = -0.18
-0.18 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24083,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 81%. For people who do not have a brother, the probability of lung cancer is 64%. For people who have a brother, the probability of lung cancer is 45%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.45
0.81*0.45 - 0.19*0.64 = 0.49
0.49 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24086,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 61%. For people who have a brother, the probability of lung cancer is 76%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.76
0.76 - 0.61 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 61%. For people who have a brother, the probability of lung cancer is 76%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.76
0.76 - 0.61 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24092,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 68%. For people who do not have a brother and smokers, the probability of lung cancer is 54%. For people who have a brother and nonsmokers, the probability of lung cancer is 82%. For people who have a brother and smokers, the probability of lung cancer is 58%. For people who do not have a brother and with low pollution, the probability of smoking is 60%. For people who do not have a brother and with high pollution, the probability of smoking is 36%. For people who have a brother and with low pollution, the probability of smoking is 34%. For people who have a brother and with high pollution, the probability of smoking is 2%. The overall probability of high pollution is 41%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.60
P(V3=1 | X=0, V2=1) = 0.36
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.02
P(V2=1) = 0.41
0.41 * 0.54 * (0.02 - 0.34)+ 0.59 * 0.54 * (0.36 - 0.60)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24093,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 68%. For people who do not have a brother and smokers, the probability of lung cancer is 54%. For people who have a brother and nonsmokers, the probability of lung cancer is 82%. For people who have a brother and smokers, the probability of lung cancer is 58%. For people who do not have a brother and with low pollution, the probability of smoking is 60%. For people who do not have a brother and with high pollution, the probability of smoking is 36%. For people who have a brother and with low pollution, the probability of smoking is 34%. For people who have a brother and with high pollution, the probability of smoking is 2%. The overall probability of high pollution is 41%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.60
P(V3=1 | X=0, V2=1) = 0.36
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.02
P(V2=1) = 0.41
0.41 * 0.54 * (0.02 - 0.34)+ 0.59 * 0.54 * (0.36 - 0.60)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 68%. For people who do not have a brother and smokers, the probability of lung cancer is 54%. For people who have a brother and nonsmokers, the probability of lung cancer is 82%. For people who have a brother and smokers, the probability of lung cancer is 58%. For people who do not have a brother and with low pollution, the probability of smoking is 60%. For people who do not have a brother and with high pollution, the probability of smoking is 36%. For people who have a brother and with low pollution, the probability of smoking is 34%. For people who have a brother and with high pollution, the probability of smoking is 2%. The overall probability of high pollution is 41%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.58
P(V3=1 | X=0, V2=0) = 0.60
P(V3=1 | X=0, V2=1) = 0.36
P(V3=1 | X=1, V2=0) = 0.34
P(V3=1 | X=1, V2=1) = 0.02
P(V2=1) = 0.41
0.41 * (0.58 - 0.82) * 0.36 + 0.59 * (0.54 - 0.68) * 0.34 = 0.03
0.03 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 97%. For people who do not have a brother, the probability of lung cancer is 61%. For people who have a brother, the probability of lung cancer is 76%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.76
0.97*0.76 - 0.03*0.61 = 0.75
0.75 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 97%. The probability of not having a brother and lung cancer is 2%. The probability of having a brother and lung cancer is 74%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.97
P(Y=1, X=0=1) = 0.02
P(Y=1, X=1=1) = 0.74
0.74/0.97 - 0.02/0.03 = 0.16
0.16 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 39%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.39
0.39 - 0.54 = -0.15
-0.15 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 77%. For people who do not have a brother and smokers, the probability of lung cancer is 52%. For people who have a brother and nonsmokers, the probability of lung cancer is 58%. For people who have a brother and smokers, the probability of lung cancer is 29%. For people who do not have a brother and with low pollution, the probability of smoking is 94%. For people who do not have a brother and with high pollution, the probability of smoking is 64%. For people who have a brother and with low pollution, the probability of smoking is 68%. For people who have a brother and with high pollution, the probability of smoking is 36%. The overall probability of high pollution is 5%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.29
P(V3=1 | X=0, V2=0) = 0.94
P(V3=1 | X=0, V2=1) = 0.64
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.05
0.05 * 0.52 * (0.36 - 0.68)+ 0.95 * 0.52 * (0.64 - 0.94)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 77%. For people who do not have a brother and smokers, the probability of lung cancer is 52%. For people who have a brother and nonsmokers, the probability of lung cancer is 58%. For people who have a brother and smokers, the probability of lung cancer is 29%. For people who do not have a brother and with low pollution, the probability of smoking is 94%. For people who do not have a brother and with high pollution, the probability of smoking is 64%. For people who have a brother and with low pollution, the probability of smoking is 68%. For people who have a brother and with high pollution, the probability of smoking is 36%. The overall probability of high pollution is 5%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.77
P(Y=1 | X=0, V3=1) = 0.52
P(Y=1 | X=1, V3=0) = 0.58
P(Y=1 | X=1, V3=1) = 0.29
P(V3=1 | X=0, V2=0) = 0.94
P(V3=1 | X=0, V2=1) = 0.64
P(V3=1 | X=1, V2=0) = 0.68
P(V3=1 | X=1, V2=1) = 0.36
P(V2=1) = 0.05
0.05 * (0.29 - 0.58) * 0.64 + 0.95 * (0.52 - 0.77) * 0.68 = -0.24
-0.24 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 88%. The probability of not having a brother and lung cancer is 7%. The probability of having a brother and lung cancer is 34%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.34
0.34/0.88 - 0.07/0.12 = -0.16
-0.16 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 88%. The probability of not having a brother and lung cancer is 7%. The probability of having a brother and lung cancer is 34%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.34
0.34/0.88 - 0.07/0.12 = -0.16
-0.16 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 46%. For people who have a brother, the probability of lung cancer is 61%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.46
P(Y=1 | X=1) = 0.61
0.61 - 0.46 = 0.15
0.15 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 61%. For people who do not have a brother and smokers, the probability of lung cancer is 31%. For people who have a brother and nonsmokers, the probability of lung cancer is 69%. For people who have a brother and smokers, the probability of lung cancer is 32%. For people who do not have a brother and with low pollution, the probability of smoking is 62%. For people who do not have a brother and with high pollution, the probability of smoking is 34%. For people who have a brother and with low pollution, the probability of smoking is 31%. For people who have a brother and with high pollution, the probability of smoking is 9%. The overall probability of high pollution is 44%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.61
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.32
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.44
0.44 * 0.31 * (0.09 - 0.31)+ 0.56 * 0.31 * (0.34 - 0.62)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 61%. For people who do not have a brother and smokers, the probability of lung cancer is 31%. For people who have a brother and nonsmokers, the probability of lung cancer is 69%. For people who have a brother and smokers, the probability of lung cancer is 32%. For people who do not have a brother and with low pollution, the probability of smoking is 62%. For people who do not have a brother and with high pollution, the probability of smoking is 34%. For people who have a brother and with low pollution, the probability of smoking is 31%. For people who have a brother and with high pollution, the probability of smoking is 9%. The overall probability of high pollution is 44%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.61
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.32
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.44
0.44 * 0.31 * (0.09 - 0.31)+ 0.56 * 0.31 * (0.34 - 0.62)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24122,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 61%. For people who do not have a brother and smokers, the probability of lung cancer is 31%. For people who have a brother and nonsmokers, the probability of lung cancer is 69%. For people who have a brother and smokers, the probability of lung cancer is 32%. For people who do not have a brother and with low pollution, the probability of smoking is 62%. For people who do not have a brother and with high pollution, the probability of smoking is 34%. For people who have a brother and with low pollution, the probability of smoking is 31%. For people who have a brother and with high pollution, the probability of smoking is 9%. The overall probability of high pollution is 44%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.61
P(Y=1 | X=0, V3=1) = 0.31
P(Y=1 | X=1, V3=0) = 0.69
P(Y=1 | X=1, V3=1) = 0.32
P(V3=1 | X=0, V2=0) = 0.62
P(V3=1 | X=0, V2=1) = 0.34
P(V3=1 | X=1, V2=0) = 0.31
P(V3=1 | X=1, V2=1) = 0.09
P(V2=1) = 0.44
0.44 * (0.32 - 0.69) * 0.34 + 0.56 * (0.31 - 0.61) * 0.31 = 0.02
0.02 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24129,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 70%. For people who have a brother, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.56
0.56 - 0.70 = -0.14
-0.14 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 84%. For people who do not have a brother and smokers, the probability of lung cancer is 65%. For people who have a brother and nonsmokers, the probability of lung cancer is 64%. For people who have a brother and smokers, the probability of lung cancer is 46%. For people who do not have a brother and with low pollution, the probability of smoking is 80%. For people who do not have a brother and with high pollution, the probability of smoking is 46%. For people who have a brother and with low pollution, the probability of smoking is 50%. For people who have a brother and with high pollution, the probability of smoking is 20%. The overall probability of high pollution is 18%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.65
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.46
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.50
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.18
0.18 * 0.65 * (0.20 - 0.50)+ 0.82 * 0.65 * (0.46 - 0.80)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 87%. For people who do not have a brother, the probability of lung cancer is 70%. For people who have a brother, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.56
0.87*0.56 - 0.13*0.70 = 0.58
0.58 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 87%. The probability of not having a brother and lung cancer is 9%. The probability of having a brother and lung cancer is 49%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.87
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.49
0.49/0.87 - 0.09/0.13 = -0.14
-0.14 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 68%. For people who do not have a brother and smokers, the probability of lung cancer is 46%. For people who have a brother and nonsmokers, the probability of lung cancer is 71%. For people who have a brother and smokers, the probability of lung cancer is 44%. For people who do not have a brother and with low pollution, the probability of smoking is 73%. For people who do not have a brother and with high pollution, the probability of smoking is 42%. For people who have a brother and with low pollution, the probability of smoking is 49%. For people who have a brother and with high pollution, the probability of smoking is 17%. The overall probability of high pollution is 53%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.42
P(V3=1 | X=1, V2=0) = 0.49
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.53
0.53 * 0.46 * (0.17 - 0.49)+ 0.47 * 0.46 * (0.42 - 0.73)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24150,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 68%. For people who do not have a brother and smokers, the probability of lung cancer is 46%. For people who have a brother and nonsmokers, the probability of lung cancer is 71%. For people who have a brother and smokers, the probability of lung cancer is 44%. For people who do not have a brother and with low pollution, the probability of smoking is 73%. For people who do not have a brother and with high pollution, the probability of smoking is 42%. For people who have a brother and with low pollution, the probability of smoking is 49%. For people who have a brother and with high pollution, the probability of smoking is 17%. The overall probability of high pollution is 53%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.42
P(V3=1 | X=1, V2=0) = 0.49
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.53
0.53 * (0.44 - 0.71) * 0.42 + 0.47 * (0.46 - 0.68) * 0.49 = -0.02
-0.02 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 68%. For people who do not have a brother and smokers, the probability of lung cancer is 46%. For people who have a brother and nonsmokers, the probability of lung cancer is 71%. For people who have a brother and smokers, the probability of lung cancer is 44%. For people who do not have a brother and with low pollution, the probability of smoking is 73%. For people who do not have a brother and with high pollution, the probability of smoking is 42%. For people who have a brother and with low pollution, the probability of smoking is 49%. For people who have a brother and with high pollution, the probability of smoking is 17%. The overall probability of high pollution is 53%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.68
P(Y=1 | X=0, V3=1) = 0.46
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.73
P(V3=1 | X=0, V2=1) = 0.42
P(V3=1 | X=1, V2=0) = 0.49
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.53
0.53 * (0.44 - 0.71) * 0.42 + 0.47 * (0.46 - 0.68) * 0.49 = -0.02
-0.02 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 82%. For people who do not have a brother, the probability of lung cancer is 55%. For people who have a brother, the probability of lung cancer is 62%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.62
0.82*0.62 - 0.18*0.55 = 0.60
0.60 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 82%. The probability of not having a brother and lung cancer is 10%. The probability of having a brother and lung cancer is 51%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.51
0.51/0.82 - 0.10/0.18 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 82%. The probability of not having a brother and lung cancer is 10%. The probability of having a brother and lung cancer is 51%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.51
0.51/0.82 - 0.10/0.18 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 60%. For people who have a brother, the probability of lung cancer is 42%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.42
0.42 - 0.60 = -0.18
-0.18 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 76%. For people who do not have a brother and smokers, the probability of lung cancer is 55%. For people who have a brother and nonsmokers, the probability of lung cancer is 53%. For people who have a brother and smokers, the probability of lung cancer is 31%. For people who do not have a brother and with low pollution, the probability of smoking is 82%. For people who do not have a brother and with high pollution, the probability of smoking is 51%. For people who have a brother and with low pollution, the probability of smoking is 56%. For people who have a brother and with high pollution, the probability of smoking is 31%. The overall probability of high pollution is 19%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.55
P(Y=1 | X=1, V3=0) = 0.53
P(Y=1 | X=1, V3=1) = 0.31
P(V3=1 | X=0, V2=0) = 0.82
P(V3=1 | X=0, V2=1) = 0.51
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.31
P(V2=1) = 0.19
0.19 * (0.31 - 0.53) * 0.51 + 0.81 * (0.55 - 0.76) * 0.56 = -0.25
-0.25 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24167,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 81%. For people who do not have a brother, the probability of lung cancer is 60%. For people who have a brother, the probability of lung cancer is 42%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.42
0.81*0.42 - 0.19*0.60 = 0.45
0.45 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24173,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 42%. For people who have a brother, the probability of lung cancer is 52%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.52
0.52 - 0.42 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24177,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 59%. For people who do not have a brother and smokers, the probability of lung cancer is 36%. For people who have a brother and nonsmokers, the probability of lung cancer is 67%. For people who have a brother and smokers, the probability of lung cancer is 33%. For people who do not have a brother and with low pollution, the probability of smoking is 89%. For people who do not have a brother and with high pollution, the probability of smoking is 56%. For people who have a brother and with low pollution, the probability of smoking is 60%. For people who have a brother and with high pollution, the probability of smoking is 25%. The overall probability of high pollution is 47%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.59
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.33
P(V3=1 | X=0, V2=0) = 0.89
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.60
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.47
0.47 * 0.36 * (0.25 - 0.60)+ 0.53 * 0.36 * (0.56 - 0.89)= 0.12
0.12 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 59%. For people who do not have a brother and smokers, the probability of lung cancer is 36%. For people who have a brother and nonsmokers, the probability of lung cancer is 67%. For people who have a brother and smokers, the probability of lung cancer is 33%. For people who do not have a brother and with low pollution, the probability of smoking is 89%. For people who do not have a brother and with high pollution, the probability of smoking is 56%. For people who have a brother and with low pollution, the probability of smoking is 60%. For people who have a brother and with high pollution, the probability of smoking is 25%. The overall probability of high pollution is 47%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.59
P(Y=1 | X=0, V3=1) = 0.36
P(Y=1 | X=1, V3=0) = 0.67
P(Y=1 | X=1, V3=1) = 0.33
P(V3=1 | X=0, V2=0) = 0.89
P(V3=1 | X=0, V2=1) = 0.56
P(V3=1 | X=1, V2=0) = 0.60
P(V3=1 | X=1, V2=1) = 0.25
P(V2=1) = 0.47
0.47 * (0.33 - 0.67) * 0.56 + 0.53 * (0.36 - 0.59) * 0.60 = -0.04
-0.04 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24185,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24187,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 67%. For people who have a brother, the probability of lung cancer is 52%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.52
0.52 - 0.67 = -0.15
-0.15 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 67%. For people who have a brother, the probability of lung cancer is 52%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.67
P(Y=1 | X=1) = 0.52
0.52 - 0.67 = -0.15
-0.15 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24192,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 85%. For people who do not have a brother and smokers, the probability of lung cancer is 63%. For people who have a brother and nonsmokers, the probability of lung cancer is 66%. For people who have a brother and smokers, the probability of lung cancer is 39%. For people who do not have a brother and with low pollution, the probability of smoking is 81%. For people who do not have a brother and with high pollution, the probability of smoking is 60%. For people who have a brother and with low pollution, the probability of smoking is 53%. For people who have a brother and with high pollution, the probability of smoking is 30%. The overall probability of high pollution is 7%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.81
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.30
P(V2=1) = 0.07
0.07 * (0.39 - 0.66) * 0.60 + 0.93 * (0.63 - 0.85) * 0.53 = -0.23
-0.23 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 85%. For people who do not have a brother and smokers, the probability of lung cancer is 63%. For people who have a brother and nonsmokers, the probability of lung cancer is 66%. For people who have a brother and smokers, the probability of lung cancer is 39%. For people who do not have a brother and with low pollution, the probability of smoking is 81%. For people who do not have a brother and with high pollution, the probability of smoking is 60%. For people who have a brother and with low pollution, the probability of smoking is 53%. For people who have a brother and with high pollution, the probability of smoking is 30%. The overall probability of high pollution is 7%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.63
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.39
P(V3=1 | X=0, V2=0) = 0.81
P(V3=1 | X=0, V2=1) = 0.60
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.30
P(V2=1) = 0.07
0.07 * (0.39 - 0.66) * 0.60 + 0.93 * (0.63 - 0.85) * 0.53 = -0.23
-0.23 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 61%. For people who have a brother, the probability of lung cancer is 71%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.71
0.71 - 0.61 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24202,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 61%. For people who have a brother, the probability of lung cancer is 71%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.71
0.71 - 0.61 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 75%. For people who do not have a brother and smokers, the probability of lung cancer is 57%. For people who have a brother and nonsmokers, the probability of lung cancer is 82%. For people who have a brother and smokers, the probability of lung cancer is 59%. For people who do not have a brother and with low pollution, the probability of smoking is 84%. For people who do not have a brother and with high pollution, the probability of smoking is 52%. For people who have a brother and with low pollution, the probability of smoking is 59%. For people who have a brother and with high pollution, the probability of smoking is 28%. The overall probability of high pollution is 41%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.57
P(Y=1 | X=1, V3=0) = 0.82
P(Y=1 | X=1, V3=1) = 0.59
P(V3=1 | X=0, V2=0) = 0.84
P(V3=1 | X=0, V2=1) = 0.52
P(V3=1 | X=1, V2=0) = 0.59
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.41
0.41 * (0.59 - 0.82) * 0.52 + 0.59 * (0.57 - 0.75) * 0.59 = 0.02
0.02 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24210,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 98%. The probability of not having a brother and lung cancer is 1%. The probability of having a brother and lung cancer is 70%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.70
0.70/0.98 - 0.01/0.02 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24211,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 98%. The probability of not having a brother and lung cancer is 1%. The probability of having a brother and lung cancer is 70%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.70
0.70/0.98 - 0.01/0.02 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24215,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 56%. For people who have a brother, the probability of lung cancer is 40%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.40
0.40 - 0.56 = -0.17
-0.17 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 56%. For people who have a brother, the probability of lung cancer is 40%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.40
0.40 - 0.56 = -0.17
-0.17 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 56%. For people who have a brother, the probability of lung cancer is 40%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.40
0.40 - 0.56 = -0.17
-0.17 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 75%. For people who do not have a brother and smokers, the probability of lung cancer is 49%. For people who have a brother and nonsmokers, the probability of lung cancer is 49%. For people who have a brother and smokers, the probability of lung cancer is 23%. For people who do not have a brother and with low pollution, the probability of smoking is 75%. For people who do not have a brother and with high pollution, the probability of smoking is 46%. For people who have a brother and with low pollution, the probability of smoking is 39%. For people who have a brother and with high pollution, the probability of smoking is 17%. The overall probability of high pollution is 6%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.49
P(Y=1 | X=1, V3=1) = 0.23
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.39
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.06
0.06 * (0.23 - 0.49) * 0.46 + 0.94 * (0.49 - 0.75) * 0.39 = -0.26
-0.26 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 88%. For people who do not have a brother, the probability of lung cancer is 56%. For people who have a brother, the probability of lung cancer is 40%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.40
0.88*0.40 - 0.12*0.56 = 0.42
0.42 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 88%. The probability of not having a brother and lung cancer is 7%. The probability of having a brother and lung cancer is 35%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.35
0.35/0.88 - 0.07/0.12 = -0.17
-0.17 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24228,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 56%. For people who have a brother, the probability of lung cancer is 64%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.64
0.64 - 0.56 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24231,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 56%. For people who have a brother, the probability of lung cancer is 64%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.64
0.64 - 0.56 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 94%. For people who do not have a brother, the probability of lung cancer is 56%. For people who have a brother, the probability of lung cancer is 64%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.64
0.94*0.64 - 0.06*0.56 = 0.64
0.64 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 58%. For people who have a brother, the probability of lung cancer is 41%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.41
0.41 - 0.58 = -0.16
-0.16 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 75%. For people who do not have a brother and smokers, the probability of lung cancer is 56%. For people who have a brother and nonsmokers, the probability of lung cancer is 54%. For people who have a brother and smokers, the probability of lung cancer is 30%. For people who do not have a brother and with low pollution, the probability of smoking is 93%. For people who do not have a brother and with high pollution, the probability of smoking is 68%. For people who have a brother and with low pollution, the probability of smoking is 57%. For people who have a brother and with high pollution, the probability of smoking is 27%. The overall probability of high pollution is 10%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.93
P(V3=1 | X=0, V2=1) = 0.68
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.10
0.10 * 0.56 * (0.27 - 0.57)+ 0.90 * 0.56 * (0.68 - 0.93)= 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24247,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 75%. For people who do not have a brother and smokers, the probability of lung cancer is 56%. For people who have a brother and nonsmokers, the probability of lung cancer is 54%. For people who have a brother and smokers, the probability of lung cancer is 30%. For people who do not have a brother and with low pollution, the probability of smoking is 93%. For people who do not have a brother and with high pollution, the probability of smoking is 68%. For people who have a brother and with low pollution, the probability of smoking is 57%. For people who have a brother and with high pollution, the probability of smoking is 27%. The overall probability of high pollution is 10%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.93
P(V3=1 | X=0, V2=1) = 0.68
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.10
0.10 * 0.56 * (0.27 - 0.57)+ 0.90 * 0.56 * (0.68 - 0.93)= 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24249,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 75%. For people who do not have a brother and smokers, the probability of lung cancer is 56%. For people who have a brother and nonsmokers, the probability of lung cancer is 54%. For people who have a brother and smokers, the probability of lung cancer is 30%. For people who do not have a brother and with low pollution, the probability of smoking is 93%. For people who do not have a brother and with high pollution, the probability of smoking is 68%. For people who have a brother and with low pollution, the probability of smoking is 57%. For people who have a brother and with high pollution, the probability of smoking is 27%. The overall probability of high pollution is 10%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.75
P(Y=1 | X=0, V3=1) = 0.56
P(Y=1 | X=1, V3=0) = 0.54
P(Y=1 | X=1, V3=1) = 0.30
P(V3=1 | X=0, V2=0) = 0.93
P(V3=1 | X=0, V2=1) = 0.68
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.10
0.10 * (0.30 - 0.54) * 0.68 + 0.90 * (0.56 - 0.75) * 0.57 = -0.26
-0.26 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 91%. For people who do not have a brother, the probability of lung cancer is 58%. For people who have a brother, the probability of lung cancer is 41%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.91
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.41
0.91*0.41 - 0.09*0.58 = 0.43
0.43 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 44%. For people who have a brother, the probability of lung cancer is 53%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.44
P(Y=1 | X=1) = 0.53
0.53 - 0.44 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 59%. For people who do not have a brother and smokers, the probability of lung cancer is 39%. For people who have a brother and nonsmokers, the probability of lung cancer is 59%. For people who have a brother and smokers, the probability of lung cancer is 44%. For people who do not have a brother and with low pollution, the probability of smoking is 87%. For people who do not have a brother and with high pollution, the probability of smoking is 57%. For people who have a brother and with low pollution, the probability of smoking is 52%. For people who have a brother and with high pollution, the probability of smoking is 28%. The overall probability of high pollution is 49%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.59
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.59
P(Y=1 | X=1, V3=1) = 0.44
P(V3=1 | X=0, V2=0) = 0.87
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.52
P(V3=1 | X=1, V2=1) = 0.28
P(V2=1) = 0.49
0.49 * (0.44 - 0.59) * 0.57 + 0.51 * (0.39 - 0.59) * 0.52 = 0.02
0.02 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 81%. The probability of not having a brother and lung cancer is 8%. The probability of having a brother and lung cancer is 43%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.43
0.43/0.81 - 0.08/0.19 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24271,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 72%. For people who have a brother, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.56
0.56 - 0.72 = -0.15
-0.15 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 72%. For people who have a brother, the probability of lung cancer is 56%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.56
0.56 - 0.72 = -0.15
-0.15 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 85%. For people who do not have a brother and smokers, the probability of lung cancer is 66%. For people who have a brother and nonsmokers, the probability of lung cancer is 66%. For people who have a brother and smokers, the probability of lung cancer is 40%. For people who do not have a brother and with low pollution, the probability of smoking is 74%. For people who do not have a brother and with high pollution, the probability of smoking is 46%. For people who have a brother and with low pollution, the probability of smoking is 41%. For people who have a brother and with high pollution, the probability of smoking is 20%. The overall probability of high pollution is 19%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.41
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.19
0.19 * 0.66 * (0.20 - 0.41)+ 0.81 * 0.66 * (0.46 - 0.74)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24276,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 85%. For people who do not have a brother and smokers, the probability of lung cancer is 66%. For people who have a brother and nonsmokers, the probability of lung cancer is 66%. For people who have a brother and smokers, the probability of lung cancer is 40%. For people who do not have a brother and with low pollution, the probability of smoking is 74%. For people who do not have a brother and with high pollution, the probability of smoking is 46%. For people who have a brother and with low pollution, the probability of smoking is 41%. For people who have a brother and with high pollution, the probability of smoking is 20%. The overall probability of high pollution is 19%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.85
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.74
P(V3=1 | X=0, V2=1) = 0.46
P(V3=1 | X=1, V2=0) = 0.41
P(V3=1 | X=1, V2=1) = 0.20
P(V2=1) = 0.19
0.19 * (0.40 - 0.66) * 0.46 + 0.81 * (0.66 - 0.85) * 0.41 = -0.25
-0.25 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24280,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 93%. The probability of not having a brother and lung cancer is 5%. The probability of having a brother and lung cancer is 52%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.52
0.52/0.93 - 0.05/0.07 = -0.15
-0.15 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24282,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 93%. For people who do not have a brother, the probability of lung cancer is 47%. For people who have a brother, the probability of lung cancer is 54%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.54
0.93*0.54 - 0.07*0.47 = 0.53
0.53 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24295,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 93%. The probability of not having a brother and lung cancer is 3%. The probability of having a brother and lung cancer is 51%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.93
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.51
0.51/0.93 - 0.03/0.07 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24299,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 78%. For people who have a brother, the probability of lung cancer is 58%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.58
0.58 - 0.78 = -0.20
-0.20 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24300,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 78%. For people who have a brother, the probability of lung cancer is 58%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.78
P(Y=1 | X=1) = 0.58
0.58 - 0.78 = -0.20
-0.20 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24302,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 93%. For people who do not have a brother and smokers, the probability of lung cancer is 73%. For people who have a brother and nonsmokers, the probability of lung cancer is 73%. For people who have a brother and smokers, the probability of lung cancer is 36%. For people who do not have a brother and with low pollution, the probability of smoking is 76%. For people who do not have a brother and with high pollution, the probability of smoking is 39%. For people who have a brother and with low pollution, the probability of smoking is 44%. For people who have a brother and with high pollution, the probability of smoking is 8%. The overall probability of high pollution is 11%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.93
P(Y=1 | X=0, V3=1) = 0.73
P(Y=1 | X=1, V3=0) = 0.73
P(Y=1 | X=1, V3=1) = 0.36
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.39
P(V3=1 | X=1, V2=0) = 0.44
P(V3=1 | X=1, V2=1) = 0.08
P(V2=1) = 0.11
0.11 * 0.73 * (0.08 - 0.44)+ 0.89 * 0.73 * (0.39 - 0.76)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 92%. The probability of not having a brother and lung cancer is 6%. The probability of having a brother and lung cancer is 54%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.92
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.54
0.54/0.92 - 0.06/0.08 = -0.21
-0.21 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 47%. For people who have a brother, the probability of lung cancer is 55%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.55
0.55 - 0.47 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 47%. For people who have a brother, the probability of lung cancer is 55%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.55
0.55 - 0.47 = 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24317,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 57%. For people who do not have a brother and smokers, the probability of lung cancer is 39%. For people who have a brother and nonsmokers, the probability of lung cancer is 63%. For people who have a brother and smokers, the probability of lung cancer is 42%. For people who do not have a brother and with low pollution, the probability of smoking is 75%. For people who do not have a brother and with high pollution, the probability of smoking is 44%. For people who have a brother and with low pollution, the probability of smoking is 53%. For people who have a brother and with high pollution, the probability of smoking is 24%. The overall probability of high pollution is 57%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.57
P(Y=1 | X=0, V3=1) = 0.39
P(Y=1 | X=1, V3=0) = 0.63
P(Y=1 | X=1, V3=1) = 0.42
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.44
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.57
0.57 * 0.39 * (0.24 - 0.53)+ 0.43 * 0.39 * (0.44 - 0.75)= 0.05
0.05 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24323,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 90%. The probability of not having a brother and lung cancer is 5%. The probability of having a brother and lung cancer is 50%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.50
0.50/0.90 - 0.05/0.10 = 0.09
0.09 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 61%. For people who have a brother, the probability of lung cancer is 48%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.48
0.48 - 0.61 = -0.13
-0.13 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 76%. For people who do not have a brother and smokers, the probability of lung cancer is 60%. For people who have a brother and nonsmokers, the probability of lung cancer is 61%. For people who have a brother and smokers, the probability of lung cancer is 34%. For people who do not have a brother and with low pollution, the probability of smoking is 97%. For people who do not have a brother and with high pollution, the probability of smoking is 67%. For people who have a brother and with low pollution, the probability of smoking is 53%. For people who have a brother and with high pollution, the probability of smoking is 24%. The overall probability of high pollution is 16%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.97
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.16
0.16 * 0.60 * (0.24 - 0.53)+ 0.84 * 0.60 * (0.67 - 0.97)= 0.13
0.13 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 76%. For people who do not have a brother and smokers, the probability of lung cancer is 60%. For people who have a brother and nonsmokers, the probability of lung cancer is 61%. For people who have a brother and smokers, the probability of lung cancer is 34%. For people who do not have a brother and with low pollution, the probability of smoking is 97%. For people who do not have a brother and with high pollution, the probability of smoking is 67%. For people who have a brother and with low pollution, the probability of smoking is 53%. For people who have a brother and with high pollution, the probability of smoking is 24%. The overall probability of high pollution is 16%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.97
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.16
0.16 * (0.34 - 0.61) * 0.67 + 0.84 * (0.60 - 0.76) * 0.53 = -0.26
-0.26 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 76%. For people who do not have a brother and smokers, the probability of lung cancer is 60%. For people who have a brother and nonsmokers, the probability of lung cancer is 61%. For people who have a brother and smokers, the probability of lung cancer is 34%. For people who do not have a brother and with low pollution, the probability of smoking is 97%. For people who do not have a brother and with high pollution, the probability of smoking is 67%. For people who have a brother and with low pollution, the probability of smoking is 53%. For people who have a brother and with high pollution, the probability of smoking is 24%. The overall probability of high pollution is 16%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.76
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.34
P(V3=1 | X=0, V2=0) = 0.97
P(V3=1 | X=0, V2=1) = 0.67
P(V3=1 | X=1, V2=0) = 0.53
P(V3=1 | X=1, V2=1) = 0.24
P(V2=1) = 0.16
0.16 * (0.34 - 0.61) * 0.67 + 0.84 * (0.60 - 0.76) * 0.53 = -0.26
-0.26 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 90%. For people who do not have a brother, the probability of lung cancer is 61%. For people who have a brother, the probability of lung cancer is 48%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.48
0.90*0.48 - 0.10*0.61 = 0.50
0.50 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 90%. The probability of not having a brother and lung cancer is 6%. The probability of having a brother and lung cancer is 43%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.43
0.43/0.90 - 0.06/0.10 = -0.13
-0.13 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 90%. The probability of not having a brother and lung cancer is 6%. The probability of having a brother and lung cancer is 43%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.43
0.43/0.90 - 0.06/0.10 = -0.13
-0.13 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24339,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 47%. For people who have a brother, the probability of lung cancer is 53%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.53
0.53 - 0.47 = 0.06
0.06 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 56%. For people who do not have a brother and smokers, the probability of lung cancer is 42%. For people who have a brother and nonsmokers, the probability of lung cancer is 60%. For people who have a brother and smokers, the probability of lung cancer is 40%. For people who do not have a brother and with low pollution, the probability of smoking is 76%. For people who do not have a brother and with high pollution, the probability of smoking is 48%. For people who have a brother and with low pollution, the probability of smoking is 46%. For people who have a brother and with high pollution, the probability of smoking is 21%. The overall probability of high pollution is 41%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.56
P(Y=1 | X=0, V3=1) = 0.42
P(Y=1 | X=1, V3=0) = 0.60
P(Y=1 | X=1, V3=1) = 0.40
P(V3=1 | X=0, V2=0) = 0.76
P(V3=1 | X=0, V2=1) = 0.48
P(V3=1 | X=1, V2=0) = 0.46
P(V3=1 | X=1, V2=1) = 0.21
P(V2=1) = 0.41
0.41 * 0.42 * (0.21 - 0.46)+ 0.59 * 0.42 * (0.48 - 0.76)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24349,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 89%. For people who do not have a brother, the probability of lung cancer is 47%. For people who have a brother, the probability of lung cancer is 53%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.47
P(Y=1 | X=1) = 0.53
0.89*0.53 - 0.11*0.47 = 0.52
0.52 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24350,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 89%. The probability of not having a brother and lung cancer is 5%. The probability of having a brother and lung cancer is 47%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.47
0.47/0.89 - 0.05/0.11 = 0.06
0.06 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 89%. The probability of not having a brother and lung cancer is 5%. The probability of having a brother and lung cancer is 47%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.47
0.47/0.89 - 0.05/0.11 = 0.06
0.06 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 68%. For people who have a brother, the probability of lung cancer is 46%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.46
0.46 - 0.68 = -0.22
-0.22 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 68%. For people who have a brother, the probability of lung cancer is 46%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.46
0.46 - 0.68 = -0.22
-0.22 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 68%. For people who have a brother, the probability of lung cancer is 46%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.46
0.46 - 0.68 = -0.22
-0.22 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 68%. For people who have a brother, the probability of lung cancer is 46%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.46
0.46 - 0.68 = -0.22
-0.22 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 84%. For people who do not have a brother and smokers, the probability of lung cancer is 66%. For people who have a brother and nonsmokers, the probability of lung cancer is 61%. For people who have a brother and smokers, the probability of lung cancer is 33%. For people who do not have a brother and with low pollution, the probability of smoking is 88%. For people who do not have a brother and with high pollution, the probability of smoking is 63%. For people who have a brother and with low pollution, the probability of smoking is 56%. For people who have a brother and with high pollution, the probability of smoking is 17%. The overall probability of high pollution is 7%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.33
P(V3=1 | X=0, V2=0) = 0.88
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.07
0.07 * 0.66 * (0.17 - 0.56)+ 0.93 * 0.66 * (0.63 - 0.88)= 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 84%. For people who do not have a brother and smokers, the probability of lung cancer is 66%. For people who have a brother and nonsmokers, the probability of lung cancer is 61%. For people who have a brother and smokers, the probability of lung cancer is 33%. For people who do not have a brother and with low pollution, the probability of smoking is 88%. For people who do not have a brother and with high pollution, the probability of smoking is 63%. For people who have a brother and with low pollution, the probability of smoking is 56%. For people who have a brother and with high pollution, the probability of smoking is 17%. The overall probability of high pollution is 7%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.61
P(Y=1 | X=1, V3=1) = 0.33
P(V3=1 | X=0, V2=0) = 0.88
P(V3=1 | X=0, V2=1) = 0.63
P(V3=1 | X=1, V2=0) = 0.56
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.07
0.07 * (0.33 - 0.61) * 0.63 + 0.93 * (0.66 - 0.84) * 0.56 = -0.32
-0.32 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 97%. For people who do not have a brother, the probability of lung cancer is 68%. For people who have a brother, the probability of lung cancer is 46%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.97
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.46
0.97*0.46 - 0.03*0.68 = 0.47
0.47 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 57%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.57
0.57 - 0.54 = 0.02
0.02 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 57%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.57
0.57 - 0.54 = 0.02
0.02 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 73%. For people who do not have a brother and smokers, the probability of lung cancer is 49%. For people who have a brother and nonsmokers, the probability of lung cancer is 66%. For people who have a brother and smokers, the probability of lung cancer is 43%. For people who do not have a brother and with low pollution, the probability of smoking is 83%. For people who do not have a brother and with high pollution, the probability of smoking is 55%. For people who have a brother and with low pollution, the probability of smoking is 57%. For people who have a brother and with high pollution, the probability of smoking is 29%. The overall probability of high pollution is 44%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.73
P(Y=1 | X=0, V3=1) = 0.49
P(Y=1 | X=1, V3=0) = 0.66
P(Y=1 | X=1, V3=1) = 0.43
P(V3=1 | X=0, V2=0) = 0.83
P(V3=1 | X=0, V2=1) = 0.55
P(V3=1 | X=1, V2=0) = 0.57
P(V3=1 | X=1, V2=1) = 0.29
P(V2=1) = 0.44
0.44 * 0.49 * (0.29 - 0.57)+ 0.56 * 0.49 * (0.55 - 0.83)= 0.08
0.08 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 94%. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 57%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.57
0.94*0.57 - 0.06*0.54 = 0.57
0.57 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 94%. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 57%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.94
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.57
0.94*0.57 - 0.06*0.54 = 0.57
0.57 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 54%. For people who have a brother, the probability of lung cancer is 38%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.38
0.38 - 0.54 = -0.16
-0.16 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 55%. For people who have a brother, the probability of lung cancer is 65%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.65
0.65 - 0.55 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 55%. For people who have a brother, the probability of lung cancer is 65%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.65
0.65 - 0.55 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 55%. For people who have a brother, the probability of lung cancer is 65%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.65
0.65 - 0.55 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 55%. For people who have a brother, the probability of lung cancer is 65%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.65
0.65 - 0.55 = 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 64%. For people who do not have a brother and smokers, the probability of lung cancer is 47%. For people who have a brother and nonsmokers, the probability of lung cancer is 71%. For people who have a brother and smokers, the probability of lung cancer is 51%. For people who do not have a brother and with low pollution, the probability of smoking is 75%. For people who do not have a brother and with high pollution, the probability of smoking is 38%. For people who have a brother and with low pollution, the probability of smoking is 45%. For people who have a brother and with high pollution, the probability of smoking is 17%. The overall probability of high pollution is 53%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.64
P(Y=1 | X=0, V3=1) = 0.47
P(Y=1 | X=1, V3=0) = 0.71
P(Y=1 | X=1, V3=1) = 0.51
P(V3=1 | X=0, V2=0) = 0.75
P(V3=1 | X=0, V2=1) = 0.38
P(V3=1 | X=1, V2=0) = 0.45
P(V3=1 | X=1, V2=1) = 0.17
P(V2=1) = 0.53
0.53 * (0.51 - 0.71) * 0.38 + 0.47 * (0.47 - 0.64) * 0.45 = 0.02
0.02 > 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 90%. For people who do not have a brother, the probability of lung cancer is 55%. For people who have a brother, the probability of lung cancer is 65%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.90
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.65
0.90*0.65 - 0.10*0.55 = 0.64
0.64 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 90%. The probability of not having a brother and lung cancer is 5%. The probability of having a brother and lung cancer is 59%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.90
P(Y=1, X=0=1) = 0.05
P(Y=1, X=1=1) = 0.59
0.59/0.90 - 0.05/0.10 = 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 65%. For people who have a brother, the probability of lung cancer is 49%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.49
0.49 - 0.65 = -0.16
-0.16 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24411,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 65%. For people who have a brother, the probability of lung cancer is 49%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.49
0.49 - 0.65 = -0.16
-0.16 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 79%. For people who do not have a brother and smokers, the probability of lung cancer is 64%. For people who have a brother and nonsmokers, the probability of lung cancer is 62%. For people who have a brother and smokers, the probability of lung cancer is 38%. For people who do not have a brother and with low pollution, the probability of smoking is 92%. For people who do not have a brother and with high pollution, the probability of smoking is 64%. For people who have a brother and with low pollution, the probability of smoking is 55%. For people who have a brother and with high pollution, the probability of smoking is 29%. The overall probability of high pollution is 11%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.79
P(Y=1 | X=0, V3=1) = 0.64
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.38
P(V3=1 | X=0, V2=0) = 0.92
P(V3=1 | X=0, V2=1) = 0.64
P(V3=1 | X=1, V2=0) = 0.55
P(V3=1 | X=1, V2=1) = 0.29
P(V2=1) = 0.11
0.11 * (0.38 - 0.62) * 0.64 + 0.89 * (0.64 - 0.79) * 0.55 = -0.25
-0.25 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 89%. For people who do not have a brother, the probability of lung cancer is 65%. For people who have a brother, the probability of lung cancer is 49%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.89
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.49
0.89*0.49 - 0.11*0.65 = 0.51
0.51 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 89%. The probability of not having a brother and lung cancer is 7%. The probability of having a brother and lung cancer is 44%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.89
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.44
0.44/0.89 - 0.07/0.11 = -0.16
-0.16 < 0",arrowhead,smoking_gene_cancer,1,correlation,P(Y | X)
24436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look at how having a brother correlates with lung cancer case by case according to smoking. Method 2: We look directly at how having a brother correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 70%. For people who have a brother, the probability of lung cancer is 53%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.53 - 0.70 = -0.17
-0.17 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 70%. For people who have a brother, the probability of lung cancer is 53%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.53 - 0.70 = -0.17
-0.17 < 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 70%. For people who have a brother, the probability of lung cancer is 53%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.53 - 0.70 = -0.17
-0.17 < 0",arrowhead,smoking_gene_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 88%. For people who do not have a brother and smokers, the probability of lung cancer is 66%. For people who have a brother and nonsmokers, the probability of lung cancer is 64%. For people who have a brother and smokers, the probability of lung cancer is 41%. For people who do not have a brother and with low pollution, the probability of smoking is 83%. For people who do not have a brother and with high pollution, the probability of smoking is 47%. For people who have a brother and with low pollution, the probability of smoking is 47%. For people who have a brother and with high pollution, the probability of smoking is 19%. The overall probability of high pollution is 3%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k}[P(Y=1|X=1,V3=v)-P(Y=1|X=0,V3=v)]*P(V3=v|X=0,V2=k)*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.88
P(Y=1 | X=0, V3=1) = 0.66
P(Y=1 | X=1, V3=0) = 0.64
P(Y=1 | X=1, V3=1) = 0.41
P(V3=1 | X=0, V2=0) = 0.83
P(V3=1 | X=0, V2=1) = 0.47
P(V3=1 | X=1, V2=0) = 0.47
P(V3=1 | X=1, V2=1) = 0.19
P(V2=1) = 0.03
0.03 * (0.41 - 0.64) * 0.47 + 0.97 * (0.66 - 0.88) * 0.47 = -0.25
-0.25 < 0",arrowhead,smoking_gene_cancer,3,nde,"E[Y_{X=1, V3=0} - Y_{X=0, V3=0}]"
24446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 93%. For people who do not have a brother, the probability of lung cancer is 70%. For people who have a brother, the probability of lung cancer is 53%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.93
P(Y=1 | X=0) = 0.70
P(Y=1 | X=1) = 0.53
0.93*0.53 - 0.07*0.70 = 0.54
0.54 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 62%. For people who have a brother, the probability of lung cancer is 70%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.70
0.70 - 0.62 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother, the probability of lung cancer is 62%. For people who have a brother, the probability of lung cancer is 70%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.70
0.70 - 0.62 = 0.07
0.07 > 0",arrowhead,smoking_gene_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24457,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 83%. For people who do not have a brother and smokers, the probability of lung cancer is 54%. For people who have a brother and nonsmokers, the probability of lung cancer is 78%. For people who have a brother and smokers, the probability of lung cancer is 57%. For people who do not have a brother and with low pollution, the probability of smoking is 80%. For people who do not have a brother and with high pollution, the probability of smoking is 57%. For people who have a brother and with low pollution, the probability of smoking is 48%. For people who have a brother and with high pollution, the probability of smoking is 27%. The overall probability of high pollution is 46%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.83
P(Y=1 | X=0, V3=1) = 0.54
P(Y=1 | X=1, V3=0) = 0.78
P(Y=1 | X=1, V3=1) = 0.57
P(V3=1 | X=0, V2=0) = 0.80
P(V3=1 | X=0, V2=1) = 0.57
P(V3=1 | X=1, V2=0) = 0.48
P(V3=1 | X=1, V2=1) = 0.27
P(V2=1) = 0.46
0.46 * 0.54 * (0.27 - 0.48)+ 0.54 * 0.54 * (0.57 - 0.80)= 0.11
0.11 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 85%. For people who do not have a brother, the probability of lung cancer is 62%. For people who have a brother, the probability of lung cancer is 70%.",yes,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.70
0.85*0.70 - 0.15*0.62 = 0.69
0.69 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. The overall probability of having a brother is 85%. For people who do not have a brother, the probability of lung cancer is 62%. For people who have a brother, the probability of lung cancer is 70%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.70
0.85*0.70 - 0.15*0.62 = 0.69
0.69 > 0",arrowhead,smoking_gene_cancer,1,marginal,P(Y)
24471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. For people who do not have a brother and nonsmokers, the probability of lung cancer is 84%. For people who do not have a brother and smokers, the probability of lung cancer is 60%. For people who have a brother and nonsmokers, the probability of lung cancer is 62%. For people who have a brother and smokers, the probability of lung cancer is 37%. For people who do not have a brother and with low pollution, the probability of smoking is 70%. For people who do not have a brother and with high pollution, the probability of smoking is 45%. For people who have a brother and with low pollution, the probability of smoking is 35%. For people who have a brother and with high pollution, the probability of smoking is 10%. The overall probability of high pollution is 17%.",no,"Let V2 = pollution; X = having a brother; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]
\sum_{V3=v} [\sum_{V2=k} P(Y=1|X=0,V3=v)*[P(V3=v|X=1,V2=k)-P(V3=v|X=0,V2=k)]*P(V2=k)]
P(Y=1 | X=0, V3=0) = 0.84
P(Y=1 | X=0, V3=1) = 0.60
P(Y=1 | X=1, V3=0) = 0.62
P(Y=1 | X=1, V3=1) = 0.37
P(V3=1 | X=0, V2=0) = 0.70
P(V3=1 | X=0, V2=1) = 0.45
P(V3=1 | X=1, V2=0) = 0.35
P(V3=1 | X=1, V2=1) = 0.10
P(V2=1) = 0.17
0.17 * 0.60 * (0.10 - 0.35)+ 0.83 * 0.60 * (0.45 - 0.70)= 0.10
0.10 > 0",arrowhead,smoking_gene_cancer,3,nie,"E[Y_{X=0, V3=1} - Y_{X=0, V3=0}]"
24479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. Method 1: We look directly at how having a brother correlates with lung cancer in general. Method 2: We look at this correlation case by case according to smoking.",yes,"nan
nan
nan
nan
nan
nan
nan",arrowhead,smoking_gene_cancer,2,backadj,[backdoor adjustment set for Y given X]
24480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 28%. For people who have a sister, the probability of lung cancer is 46%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.46
0.46 - 0.28 = 0.18
0.18 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 28%. For people who have a sister, the probability of lung cancer is 46%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.46
0.46 - 0.28 = 0.18
0.18 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24492,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 24%. For people who have a sister, the probability of lung cancer is 48%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.48
0.48 - 0.24 = 0.25
0.25 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24497,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 24%. For people who have a sister, the probability of lung cancer is 48%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.48
0.48 - 0.24 = 0.25
0.25 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 98%. For people who do not have a sister, the probability of lung cancer is 24%. For people who have a sister, the probability of lung cancer is 48%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.98
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.48
0.98*0.48 - 0.02*0.24 = 0.48
0.48 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 62%. For people who have a sister, the probability of lung cancer is 52%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.52
0.52 - 0.62 = -0.10
-0.10 < 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 62%. For people who have a sister, the probability of lung cancer is 52%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.52
0.52 - 0.62 = -0.10
-0.10 < 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 62%. For people who have a sister, the probability of lung cancer is 52%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.52
0.52 - 0.62 = -0.10
-0.10 < 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 85%. For people who do not have a sister, the probability of lung cancer is 62%. For people who have a sister, the probability of lung cancer is 52%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.52
0.85*0.52 - 0.15*0.62 = 0.53
0.53 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 85%. For people who do not have a sister, the probability of lung cancer is 62%. For people who have a sister, the probability of lung cancer is 52%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.85
P(Y=1 | X=0) = 0.62
P(Y=1 | X=1) = 0.52
0.85*0.52 - 0.15*0.62 = 0.53
0.53 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24513,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 85%. The probability of not having a sister and lung cancer is 9%. The probability of having a sister and lung cancer is 44%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.85
P(Y=1, X=0=1) = 0.09
P(Y=1, X=1=1) = 0.44
0.44/0.85 - 0.09/0.15 = -0.10
-0.10 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24514,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24518,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 64%. For people who have a sister, the probability of lung cancer is 80%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.80
0.80 - 0.64 = 0.17
0.17 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24519,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 64%. For people who have a sister, the probability of lung cancer is 80%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.80
0.80 - 0.64 = 0.17
0.17 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 64%. For people who have a sister, the probability of lung cancer is 80%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.80
0.80 - 0.64 = 0.17
0.17 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 16%. The probability of not having a sister and lung cancer is 54%. The probability of having a sister and lung cancer is 13%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.13
0.13/0.16 - 0.54/0.84 = 0.17
0.17 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 16%. The probability of not having a sister and lung cancer is 54%. The probability of having a sister and lung cancer is 13%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.54
P(Y=1, X=1=1) = 0.13
0.13/0.16 - 0.54/0.84 = 0.17
0.17 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 34%. For people who have a sister, the probability of lung cancer is 44%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.44
0.44 - 0.34 = 0.10
0.10 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24532,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 34%. For people who have a sister, the probability of lung cancer is 44%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.34
P(Y=1 | X=1) = 0.44
0.44 - 0.34 = 0.10
0.10 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24539,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 84%. For people who do not have a sister, the probability of lung cancer is 28%. For people who have a sister, the probability of lung cancer is 5%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.05
0.84*0.05 - 0.16*0.28 = 0.09
0.09 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 84%. For people who do not have a sister, the probability of lung cancer is 28%. For people who have a sister, the probability of lung cancer is 5%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.84
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.05
0.84*0.05 - 0.16*0.28 = 0.09
0.09 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 84%. The probability of not having a sister and lung cancer is 4%. The probability of having a sister and lung cancer is 4%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.84
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.04
0.04/0.84 - 0.04/0.16 = -0.23
-0.23 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24550,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24554,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 57%. For people who have a sister, the probability of lung cancer is 76%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.76
0.76 - 0.57 = 0.18
0.18 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 57%. For people who have a sister, the probability of lung cancer is 76%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.76
0.76 - 0.57 = 0.18
0.18 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 57%. For people who have a sister, the probability of lung cancer is 76%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.76
0.76 - 0.57 = 0.18
0.18 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24558,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 9%. For people who do not have a sister, the probability of lung cancer is 57%. For people who have a sister, the probability of lung cancer is 76%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.09
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.76
0.09*0.76 - 0.91*0.57 = 0.59
0.59 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 9%. The probability of not having a sister and lung cancer is 52%. The probability of having a sister and lung cancer is 7%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.52
P(Y=1, X=1=1) = 0.07
0.07/0.09 - 0.52/0.91 = 0.18
0.18 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24565,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 27%. For people who have a sister, the probability of lung cancer is 57%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.57
0.57 - 0.27 = 0.30
0.30 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 27%. For people who have a sister, the probability of lung cancer is 57%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.57
0.57 - 0.27 = 0.30
0.30 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 27%. For people who have a sister, the probability of lung cancer is 57%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.57
0.57 - 0.27 = 0.30
0.30 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24570,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 99%. For people who do not have a sister, the probability of lung cancer is 27%. For people who have a sister, the probability of lung cancer is 57%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.57
0.99*0.57 - 0.01*0.27 = 0.56
0.56 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 99%. For people who do not have a sister, the probability of lung cancer is 27%. For people who have a sister, the probability of lung cancer is 57%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.99
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.57
0.99*0.57 - 0.01*0.27 = 0.56
0.56 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24573,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 99%. The probability of not having a sister and lung cancer is 0%. The probability of having a sister and lung cancer is 56%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.56
0.56/0.99 - 0.00/0.01 = 0.30
0.30 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 41%. For people who have a sister, the probability of lung cancer is 32%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.41
P(Y=1 | X=1) = 0.32
0.32 - 0.41 = -0.09
-0.09 < 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 98%. The probability of not having a sister and lung cancer is 1%. The probability of having a sister and lung cancer is 32%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.98
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.32
0.32/0.98 - 0.01/0.02 = -0.09
-0.09 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24592,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 29%. For people who have a sister, the probability of lung cancer is 64%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.64
0.64 - 0.29 = 0.35
0.35 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 29%. For people who have a sister, the probability of lung cancer is 64%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.64
0.64 - 0.29 = 0.35
0.35 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 8%. For people who do not have a sister, the probability of lung cancer is 29%. For people who have a sister, the probability of lung cancer is 64%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.08
P(Y=1 | X=0) = 0.29
P(Y=1 | X=1) = 0.64
0.08*0.64 - 0.92*0.29 = 0.32
0.32 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24597,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 8%. The probability of not having a sister and lung cancer is 27%. The probability of having a sister and lung cancer is 5%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.08
P(Y=1, X=0=1) = 0.27
P(Y=1, X=1=1) = 0.05
0.05/0.08 - 0.27/0.92 = 0.35
0.35 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24600,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 20%. For people who have a sister, the probability of lung cancer is 80%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.20
P(Y=1 | X=1) = 0.80
0.80 - 0.20 = 0.60
0.60 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24609,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 99%. The probability of not having a sister and lung cancer is 0%. The probability of having a sister and lung cancer is 79%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.99
P(Y=1, X=0=1) = 0.00
P(Y=1, X=1=1) = 0.79
0.79/0.99 - 0.00/0.01 = 0.60
0.60 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24611,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24619,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 87%. For people who do not have a sister, the probability of lung cancer is 75%. For people who have a sister, the probability of lung cancer is 43%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.87
P(Y=1 | X=0) = 0.75
P(Y=1 | X=1) = 0.43
0.87*0.43 - 0.13*0.75 = 0.47
0.47 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 28%. For people who have a sister, the probability of lung cancer is 54%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.54
0.54 - 0.28 = 0.25
0.25 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 28%. For people who have a sister, the probability of lung cancer is 54%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.54
0.54 - 0.28 = 0.25
0.25 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24630,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 13%. For people who do not have a sister, the probability of lung cancer is 28%. For people who have a sister, the probability of lung cancer is 54%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.54
0.13*0.54 - 0.87*0.28 = 0.32
0.32 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 13%. The probability of not having a sister and lung cancer is 25%. The probability of having a sister and lung cancer is 7%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.25
P(Y=1, X=1=1) = 0.07
0.07/0.13 - 0.25/0.87 = 0.25
0.25 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 73%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.73
0.73 - 0.33 = 0.39
0.39 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24638,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 73%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.73
0.73 - 0.33 = 0.39
0.39 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24641,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 73%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.73
0.73 - 0.33 = 0.39
0.39 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 82%. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 73%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.73
0.82*0.73 - 0.18*0.33 = 0.66
0.66 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 82%. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 73%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.73
0.82*0.73 - 0.18*0.33 = 0.66
0.66 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24645,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 82%. The probability of not having a sister and lung cancer is 6%. The probability of having a sister and lung cancer is 60%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.82
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.60
0.60/0.82 - 0.06/0.18 = 0.39
0.39 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 32%. For people who have a sister, the probability of lung cancer is 14%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.14
0.14 - 0.32 = -0.18
-0.18 < 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 32%. For people who have a sister, the probability of lung cancer is 14%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.14
0.14 - 0.32 = -0.18
-0.18 < 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 32%. For people who have a sister, the probability of lung cancer is 14%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.14
0.14 - 0.32 = -0.18
-0.18 < 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 32%. For people who have a sister, the probability of lung cancer is 14%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.14
0.14 - 0.32 = -0.18
-0.18 < 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24652,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 32%. For people who have a sister, the probability of lung cancer is 14%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.14
0.14 - 0.32 = -0.18
-0.18 < 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24653,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 32%. For people who have a sister, the probability of lung cancer is 14%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.32
P(Y=1 | X=1) = 0.14
0.14 - 0.32 = -0.18
-0.18 < 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24656,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 81%. The probability of not having a sister and lung cancer is 6%. The probability of having a sister and lung cancer is 11%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.11
0.11/0.81 - 0.06/0.19 = -0.18
-0.18 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 81%. The probability of not having a sister and lung cancer is 6%. The probability of having a sister and lung cancer is 11%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.81
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.11
0.11/0.81 - 0.06/0.19 = -0.18
-0.18 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24661,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 64%. For people who have a sister, the probability of lung cancer is 89%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.89
0.89 - 0.64 = 0.25
0.25 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 64%. For people who have a sister, the probability of lung cancer is 89%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.89
0.89 - 0.64 = 0.25
0.25 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24663,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 64%. For people who have a sister, the probability of lung cancer is 89%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.89
0.89 - 0.64 = 0.25
0.25 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 64%. For people who have a sister, the probability of lung cancer is 89%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.89
0.89 - 0.64 = 0.25
0.25 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 15%. For people who do not have a sister, the probability of lung cancer is 64%. For people who have a sister, the probability of lung cancer is 89%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.64
P(Y=1 | X=1) = 0.89
0.15*0.89 - 0.85*0.64 = 0.68
0.68 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 15%. The probability of not having a sister and lung cancer is 55%. The probability of having a sister and lung cancer is 13%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.55
P(Y=1, X=1=1) = 0.13
0.13/0.15 - 0.55/0.85 = 0.25
0.25 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 61%. For people who have a sister, the probability of lung cancer is 81%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.81
0.81 - 0.61 = 0.20
0.20 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24687,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 69%. For people who have a sister, the probability of lung cancer is 54%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.54
0.54 - 0.69 = -0.15
-0.15 < 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 69%. For people who have a sister, the probability of lung cancer is 54%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.54
0.54 - 0.69 = -0.15
-0.15 < 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 82%. For people who do not have a sister, the probability of lung cancer is 69%. For people who have a sister, the probability of lung cancer is 54%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.82
P(Y=1 | X=0) = 0.69
P(Y=1 | X=1) = 0.54
0.82*0.54 - 0.18*0.69 = 0.57
0.57 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 72%. For people who have a sister, the probability of lung cancer is 93%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.93
0.93 - 0.72 = 0.21
0.21 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 72%. For people who have a sister, the probability of lung cancer is 93%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.93
0.93 - 0.72 = 0.21
0.21 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 72%. For people who have a sister, the probability of lung cancer is 93%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.93
0.93 - 0.72 = 0.21
0.21 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 72%. For people who have a sister, the probability of lung cancer is 93%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.72
P(Y=1 | X=1) = 0.93
0.93 - 0.72 = 0.21
0.21 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 13%. The probability of not having a sister and lung cancer is 62%. The probability of having a sister and lung cancer is 13%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.62
P(Y=1, X=1=1) = 0.13
0.13/0.13 - 0.62/0.87 = 0.21
0.21 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 56%. For people who have a sister, the probability of lung cancer is 71%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.71
0.71 - 0.56 = 0.15
0.15 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 54%. For people who have a sister, the probability of lung cancer is 21%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.21
0.21 - 0.54 = -0.33
-0.33 < 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 95%. For people who do not have a sister, the probability of lung cancer is 54%. For people who have a sister, the probability of lung cancer is 21%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.54
P(Y=1 | X=1) = 0.21
0.95*0.21 - 0.05*0.54 = 0.23
0.23 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 95%. The probability of not having a sister and lung cancer is 3%. The probability of having a sister and lung cancer is 20%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.03
P(Y=1, X=1=1) = 0.20
0.20/0.95 - 0.03/0.05 = -0.33
-0.33 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24733,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 55%. For people who have a sister, the probability of lung cancer is 65%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.65
0.65 - 0.55 = 0.10
0.10 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24735,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 55%. For people who have a sister, the probability of lung cancer is 65%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.65
0.65 - 0.55 = 0.10
0.10 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 55%. For people who have a sister, the probability of lung cancer is 65%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.65
0.65 - 0.55 = 0.10
0.10 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 30%. For people who have a sister, the probability of lung cancer is 43%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.43
0.43 - 0.30 = 0.13
0.13 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 30%. For people who have a sister, the probability of lung cancer is 43%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.43
0.43 - 0.30 = 0.13
0.13 > 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 30%. For people who have a sister, the probability of lung cancer is 43%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.43
0.43 - 0.30 = 0.13
0.13 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 30%. For people who have a sister, the probability of lung cancer is 43%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.43
0.43 - 0.30 = 0.13
0.13 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24752,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 96%. The probability of not having a sister and lung cancer is 1%. The probability of having a sister and lung cancer is 41%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.41
0.41/0.96 - 0.01/0.04 = 0.13
0.13 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 56%. For people who have a sister, the probability of lung cancer is 29%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.29
0.29 - 0.56 = -0.27
-0.27 < 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 56%. For people who have a sister, the probability of lung cancer is 29%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.29
0.29 - 0.56 = -0.27
-0.27 < 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 88%. For people who do not have a sister, the probability of lung cancer is 56%. For people who have a sister, the probability of lung cancer is 29%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.88
P(Y=1 | X=0) = 0.56
P(Y=1 | X=1) = 0.29
0.88*0.29 - 0.12*0.56 = 0.32
0.32 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 88%. The probability of not having a sister and lung cancer is 7%. The probability of having a sister and lung cancer is 25%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.88
P(Y=1, X=0=1) = 0.07
P(Y=1, X=1=1) = 0.25
0.25/0.88 - 0.07/0.12 = -0.27
-0.27 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 35%. For people who have a sister, the probability of lung cancer is 51%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.51
0.51 - 0.35 = 0.17
0.17 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 35%. For people who have a sister, the probability of lung cancer is 51%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.51
0.51 - 0.35 = 0.17
0.17 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 35%. For people who have a sister, the probability of lung cancer is 51%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.51
0.51 - 0.35 = 0.17
0.17 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24773,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 35%. For people who have a sister, the probability of lung cancer is 51%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.35
P(Y=1 | X=1) = 0.51
0.51 - 0.35 = 0.17
0.17 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24777,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 9%. The probability of not having a sister and lung cancer is 31%. The probability of having a sister and lung cancer is 5%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.09
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.05
0.05/0.09 - 0.31/0.91 = 0.17
0.17 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 17%. For people who have a sister, the probability of lung cancer is 49%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.49
0.49 - 0.17 = 0.32
0.32 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 81%. For people who do not have a sister, the probability of lung cancer is 17%. For people who have a sister, the probability of lung cancer is 49%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.81
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.49
0.81*0.49 - 0.19*0.17 = 0.43
0.43 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24790,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 50%. For people who have a sister, the probability of lung cancer is 33%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.33
0.33 - 0.50 = -0.17
-0.17 < 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 80%. The probability of not having a sister and lung cancer is 10%. The probability of having a sister and lung cancer is 27%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.80
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.27
0.27/0.80 - 0.10/0.20 = -0.17
-0.17 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 80%. The probability of not having a sister and lung cancer is 10%. The probability of having a sister and lung cancer is 27%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.80
P(Y=1, X=0=1) = 0.10
P(Y=1, X=1=1) = 0.27
0.27/0.80 - 0.10/0.20 = -0.17
-0.17 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 47%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.47
0.47 - 0.33 = 0.13
0.13 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 47%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.47
0.47 - 0.33 = 0.13
0.13 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 96%. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 47%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.47
0.96*0.47 - 0.04*0.33 = 0.46
0.46 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 96%. For people who do not have a sister, the probability of lung cancer is 33%. For people who have a sister, the probability of lung cancer is 47%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.96
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.47
0.96*0.47 - 0.04*0.33 = 0.46
0.46 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 96%. The probability of not having a sister and lung cancer is 1%. The probability of having a sister and lung cancer is 45%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.96
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.45
0.45/0.96 - 0.01/0.04 = 0.13
0.13 > 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24815,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 60%. For people who have a sister, the probability of lung cancer is 74%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.74
0.74 - 0.60 = 0.14
0.14 > 0",chain,smoking_tar_cancer,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 60%. For people who have a sister, the probability of lung cancer is 74%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.74
0.74 - 0.60 = 0.14
0.14 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 60%. For people who have a sister, the probability of lung cancer is 74%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.60
P(Y=1 | X=1) = 0.74
0.74 - 0.60 = 0.14
0.14 > 0",chain,smoking_tar_cancer,3,nie,"E[Y_{X=0, V2=1} - Y_{X=0, V2=0}]"
24827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look directly at how having a sister correlates with lung cancer in general. Method 2: We look at this correlation case by case according to tar deposit.",yes,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. For people who do not have a sister, the probability of lung cancer is 73%. For people who have a sister, the probability of lung cancer is 51%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
E[Y_{X = 1} - Y_{X = 0} | X = 1]
P(Y=1|X=1) - P(Y=1|X=0)
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.51
0.51 - 0.73 = -0.23
-0.23 < 0",chain,smoking_tar_cancer,3,ett,E[Y_{X = 1} - Y_{X = 0} | X = 1]
24834,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 95%. For people who do not have a sister, the probability of lung cancer is 73%. For people who have a sister, the probability of lung cancer is 51%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.51
0.95*0.51 - 0.05*0.73 = 0.52
0.52 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24835,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 95%. For people who do not have a sister, the probability of lung cancer is 73%. For people who have a sister, the probability of lung cancer is 51%.",no,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.95
P(Y=1 | X=0) = 0.73
P(Y=1 | X=1) = 0.51
0.95*0.51 - 0.05*0.73 = 0.52
0.52 > 0",chain,smoking_tar_cancer,1,marginal,P(Y)
24837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. The overall probability of having a sister is 95%. The probability of not having a sister and lung cancer is 4%. The probability of having a sister and lung cancer is 48%.",yes,"Let X = having a sister; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.95
P(Y=1, X=0=1) = 0.04
P(Y=1, X=1=1) = 0.48
0.48/0.95 - 0.04/0.05 = -0.23
-0.23 < 0",chain,smoking_tar_cancer,1,correlation,P(Y | X)
24838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. Method 1: We look at how having a sister correlates with lung cancer case by case according to tar deposit. Method 2: We look directly at how having a sister correlates with lung cancer in general.",no,"nan
nan
nan
nan
nan
nan
nan",chain,smoking_tar_cancer,2,backadj,[backdoor adjustment set for Y given X]
24840,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 49%. For areas with high cigarette tax, the probability of normal infant birth weight is 54%. For areas with low cigarette tax, the probability of having a brother is 27%. For areas with high cigarette tax, the probability of having a brother is 50%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.27
P(X=1 | V2=1) = 0.50
(0.54 - 0.49) / (0.50 - 0.27) = 0.22
0.22 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 49%. For areas with high cigarette tax, the probability of normal infant birth weight is 54%. For areas with low cigarette tax, the probability of having a brother is 27%. For areas with high cigarette tax, the probability of having a brother is 50%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.27
P(X=1 | V2=1) = 0.50
(0.54 - 0.49) / (0.50 - 0.27) = 0.22
0.22 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 31%. For infants who do not have a brother, the probability of normal infant birth weight is 42%. For infants who have a brother, the probability of normal infant birth weight is 67%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.67
0.31*0.67 - 0.69*0.42 = 0.50
0.50 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 31%. For infants who do not have a brother, the probability of normal infant birth weight is 42%. For infants who have a brother, the probability of normal infant birth weight is 67%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.42
P(Y=1 | X=1) = 0.67
0.31*0.67 - 0.69*0.42 = 0.50
0.50 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 31%. The probability of not having a brother and normal infant birth weight is 29%. The probability of having a brother and normal infant birth weight is 21%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.21
0.21/0.31 - 0.29/0.69 = 0.25
0.25 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 63%. For infants who do not have a brother, the probability of normal infant birth weight is 17%. For infants who have a brother, the probability of normal infant birth weight is 47%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.63
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.47
0.63*0.47 - 0.37*0.17 = 0.36
0.36 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 63%. The probability of not having a brother and normal infant birth weight is 6%. The probability of having a brother and normal infant birth weight is 30%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.30
0.30/0.63 - 0.06/0.37 = 0.30
0.30 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24853,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 63%. The probability of not having a brother and normal infant birth weight is 6%. The probability of having a brother and normal infant birth weight is 30%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.63
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.30
0.30/0.63 - 0.06/0.37 = 0.30
0.30 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 22%. For areas with high cigarette tax, the probability of normal infant birth weight is 31%. For areas with low cigarette tax, the probability of having a brother is 39%. For areas with high cigarette tax, the probability of having a brother is 75%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.22
P(Y=1 | V2=1) = 0.31
P(X=1 | V2=0) = 0.39
P(X=1 | V2=1) = 0.75
(0.31 - 0.22) / (0.75 - 0.39) = 0.23
0.23 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 40%. The probability of not having a brother and normal infant birth weight is 6%. The probability of having a brother and normal infant birth weight is 17%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.17
0.17/0.40 - 0.06/0.60 = 0.31
0.31 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24866,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 26%. For infants who do not have a brother, the probability of normal infant birth weight is 26%. For infants who have a brother, the probability of normal infant birth weight is 61%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.61
0.26*0.61 - 0.74*0.26 = 0.35
0.35 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 26%. For infants who do not have a brother, the probability of normal infant birth weight is 26%. For infants who have a brother, the probability of normal infant birth weight is 61%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.26
P(Y=1 | X=1) = 0.61
0.26*0.61 - 0.74*0.26 = 0.35
0.35 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 40%. The probability of not having a brother and normal infant birth weight is 6%. The probability of having a brother and normal infant birth weight is 15%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.15
0.15/0.40 - 0.06/0.60 = 0.28
0.28 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 28%. For infants who do not have a brother, the probability of normal infant birth weight is 40%. For infants who have a brother, the probability of normal infant birth weight is 67%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.28
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.67
0.28*0.67 - 0.72*0.40 = 0.47
0.47 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24884,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 28%. The probability of not having a brother and normal infant birth weight is 29%. The probability of having a brother and normal infant birth weight is 19%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.28
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.19
0.19/0.28 - 0.29/0.72 = 0.27
0.27 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 28%. The probability of not having a brother and normal infant birth weight is 29%. The probability of having a brother and normal infant birth weight is 19%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.28
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.19
0.19/0.28 - 0.29/0.72 = 0.27
0.27 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24890,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 15%. For infants who do not have a brother, the probability of normal infant birth weight is 7%. For infants who have a brother, the probability of normal infant birth weight is 47%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.15
P(Y=1 | X=0) = 0.07
P(Y=1 | X=1) = 0.47
0.15*0.47 - 0.85*0.07 = 0.13
0.13 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 15%. The probability of not having a brother and normal infant birth weight is 6%. The probability of having a brother and normal infant birth weight is 7%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.15
P(Y=1, X=0=1) = 0.06
P(Y=1, X=1=1) = 0.07
0.07/0.15 - 0.06/0.85 = 0.39
0.39 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24895,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24897,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 20%. For areas with high cigarette tax, the probability of normal infant birth weight is 41%. For areas with low cigarette tax, the probability of having a brother is 22%. For areas with high cigarette tax, the probability of having a brother is 70%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.20
P(Y=1 | V2=1) = 0.41
P(X=1 | V2=0) = 0.22
P(X=1 | V2=1) = 0.70
(0.41 - 0.20) / (0.70 - 0.22) = 0.44
0.44 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24901,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 25%. The probability of not having a brother and normal infant birth weight is 8%. The probability of having a brother and normal infant birth weight is 14%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.14
0.14/0.25 - 0.08/0.75 = 0.44
0.44 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look directly at how having a brother correlates with infant's birth weight in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 24%. For areas with high cigarette tax, the probability of normal infant birth weight is 33%. For areas with low cigarette tax, the probability of having a brother is 16%. For areas with high cigarette tax, the probability of having a brother is 47%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.24
P(Y=1 | V2=1) = 0.33
P(X=1 | V2=0) = 0.16
P(X=1 | V2=1) = 0.47
(0.33 - 0.24) / (0.47 - 0.16) = 0.27
0.27 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24907,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 22%. For infants who do not have a brother, the probability of normal infant birth weight is 19%. For infants who have a brother, the probability of normal infant birth weight is 49%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.19
P(Y=1 | X=1) = 0.49
0.22*0.49 - 0.78*0.19 = 0.26
0.26 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24910,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look directly at how having a brother correlates with infant's birth weight in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 12%. For areas with high cigarette tax, the probability of normal infant birth weight is 26%. For areas with low cigarette tax, the probability of having a brother is 23%. For areas with high cigarette tax, the probability of having a brother is 63%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.12
P(Y=1 | V2=1) = 0.26
P(X=1 | V2=0) = 0.23
P(X=1 | V2=1) = 0.63
(0.26 - 0.12) / (0.63 - 0.23) = 0.34
0.34 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 31%. For infants who do not have a brother, the probability of normal infant birth weight is 5%. For infants who have a brother, the probability of normal infant birth weight is 38%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.05
P(Y=1 | X=1) = 0.38
0.31*0.38 - 0.69*0.05 = 0.15
0.15 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 31%. For infants who do not have a brother, the probability of normal infant birth weight is 5%. For infants who have a brother, the probability of normal infant birth weight is 38%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.05
P(Y=1 | X=1) = 0.38
0.31*0.38 - 0.69*0.05 = 0.15
0.15 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 36%. For areas with high cigarette tax, the probability of normal infant birth weight is 42%. For areas with low cigarette tax, the probability of having a brother is 24%. For areas with high cigarette tax, the probability of having a brother is 51%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.36
P(Y=1 | V2=1) = 0.42
P(X=1 | V2=0) = 0.24
P(X=1 | V2=1) = 0.51
(0.42 - 0.36) / (0.51 - 0.24) = 0.21
0.21 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 26%. For infants who do not have a brother, the probability of normal infant birth weight is 31%. For infants who have a brother, the probability of normal infant birth weight is 53%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.31
P(Y=1 | X=1) = 0.53
0.26*0.53 - 0.74*0.31 = 0.36
0.36 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 26%. The probability of not having a brother and normal infant birth weight is 23%. The probability of having a brother and normal infant birth weight is 14%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.14
0.14/0.26 - 0.23/0.74 = 0.22
0.22 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look directly at how having a brother correlates with infant's birth weight in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24933,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 26%. The probability of not having a brother and normal infant birth weight is 29%. The probability of having a brother and normal infant birth weight is 19%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.19
0.19/0.26 - 0.29/0.74 = 0.35
0.35 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 20%. For areas with high cigarette tax, the probability of normal infant birth weight is 29%. For areas with low cigarette tax, the probability of having a brother is 11%. For areas with high cigarette tax, the probability of having a brother is 44%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.20
P(Y=1 | V2=1) = 0.29
P(X=1 | V2=0) = 0.11
P(X=1 | V2=1) = 0.44
(0.29 - 0.20) / (0.44 - 0.11) = 0.26
0.26 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 14%. For infants who do not have a brother, the probability of normal infant birth weight is 17%. For infants who have a brother, the probability of normal infant birth weight is 45%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.17
P(Y=1 | X=1) = 0.45
0.14*0.45 - 0.86*0.17 = 0.21
0.21 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 14%. The probability of not having a brother and normal infant birth weight is 14%. The probability of having a brother and normal infant birth weight is 6%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.14
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.06
0.06/0.14 - 0.14/0.86 = 0.29
0.29 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look directly at how having a brother correlates with infant's birth weight in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 43%. For areas with high cigarette tax, the probability of normal infant birth weight is 59%. For areas with low cigarette tax, the probability of having a brother is 11%. For areas with high cigarette tax, the probability of having a brother is 48%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.43
P(Y=1 | V2=1) = 0.59
P(X=1 | V2=0) = 0.11
P(X=1 | V2=1) = 0.48
(0.59 - 0.43) / (0.48 - 0.11) = 0.44
0.44 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 17%. The probability of not having a brother and normal infant birth weight is 31%. The probability of having a brother and normal infant birth weight is 14%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.14
0.14/0.17 - 0.31/0.83 = 0.44
0.44 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 17%. The probability of not having a brother and normal infant birth weight is 31%. The probability of having a brother and normal infant birth weight is 14%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.17
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.14
0.14/0.17 - 0.31/0.83 = 0.44
0.44 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look directly at how having a brother correlates with infant's birth weight in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 25%. The probability of not having a brother and normal infant birth weight is 13%. The probability of having a brother and normal infant birth weight is 11%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.13
P(Y=1, X=1=1) = 0.11
0.11/0.25 - 0.13/0.75 = 0.27
0.27 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 49%. For areas with high cigarette tax, the probability of normal infant birth weight is 74%. For areas with low cigarette tax, the probability of having a brother is 37%. For areas with high cigarette tax, the probability of having a brother is 80%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.74
P(X=1 | V2=0) = 0.37
P(X=1 | V2=1) = 0.80
(0.74 - 0.49) / (0.80 - 0.37) = 0.60
0.60 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 49%. For areas with high cigarette tax, the probability of normal infant birth weight is 74%. For areas with low cigarette tax, the probability of having a brother is 37%. For areas with high cigarette tax, the probability of having a brother is 80%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.74
P(X=1 | V2=0) = 0.37
P(X=1 | V2=1) = 0.80
(0.74 - 0.49) / (0.80 - 0.37) = 0.60
0.60 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 41%. For infants who do not have a brother, the probability of normal infant birth weight is 27%. For infants who have a brother, the probability of normal infant birth weight is 87%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.87
0.41*0.87 - 0.59*0.27 = 0.51
0.51 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 41%. For infants who do not have a brother, the probability of normal infant birth weight is 27%. For infants who have a brother, the probability of normal infant birth weight is 87%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.27
P(Y=1 | X=1) = 0.87
0.41*0.87 - 0.59*0.27 = 0.51
0.51 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 30%. The probability of not having a brother and normal infant birth weight is 19%. The probability of having a brother and normal infant birth weight is 17%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.17
0.17/0.30 - 0.19/0.70 = 0.30
0.30 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 39%. For areas with high cigarette tax, the probability of normal infant birth weight is 53%. For areas with low cigarette tax, the probability of having a brother is 39%. For areas with high cigarette tax, the probability of having a brother is 77%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.39
P(Y=1 | V2=1) = 0.53
P(X=1 | V2=0) = 0.39
P(X=1 | V2=1) = 0.77
(0.53 - 0.39) / (0.77 - 0.39) = 0.36
0.36 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 41%. For infants who do not have a brother, the probability of normal infant birth weight is 25%. For infants who have a brother, the probability of normal infant birth weight is 61%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.41
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.61
0.41*0.61 - 0.59*0.25 = 0.40
0.40 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 21%. For areas with high cigarette tax, the probability of normal infant birth weight is 34%. For areas with low cigarette tax, the probability of having a brother is 24%. For areas with high cigarette tax, the probability of having a brother is 58%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.21
P(Y=1 | V2=1) = 0.34
P(X=1 | V2=0) = 0.24
P(X=1 | V2=1) = 0.58
(0.34 - 0.21) / (0.58 - 0.24) = 0.37
0.37 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 26%. The probability of not having a brother and normal infant birth weight is 8%. The probability of having a brother and normal infant birth weight is 14%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.14
0.14/0.26 - 0.08/0.74 = 0.43
0.43 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
24990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look directly at how having a brother correlates with infant's birth weight in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
24993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 77%. For areas with high cigarette tax, the probability of normal infant birth weight is 88%. For areas with low cigarette tax, the probability of having a brother is 61%. For areas with high cigarette tax, the probability of having a brother is 90%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.77
P(Y=1 | V2=1) = 0.88
P(X=1 | V2=0) = 0.61
P(X=1 | V2=1) = 0.90
(0.88 - 0.77) / (0.90 - 0.61) = 0.37
0.37 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
24995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 65%. For infants who do not have a brother, the probability of normal infant birth weight is 55%. For infants who have a brother, the probability of normal infant birth weight is 92%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.65
P(Y=1 | X=0) = 0.55
P(Y=1 | X=1) = 0.92
0.65*0.92 - 0.35*0.55 = 0.79
0.79 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
24996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 65%. The probability of not having a brother and normal infant birth weight is 19%. The probability of having a brother and normal infant birth weight is 60%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.65
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.60
0.60/0.65 - 0.19/0.35 = 0.37
0.37 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
25000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 42%. For areas with high cigarette tax, the probability of normal infant birth weight is 51%. For areas with low cigarette tax, the probability of having a brother is 31%. For areas with high cigarette tax, the probability of having a brother is 59%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.42
P(Y=1 | V2=1) = 0.51
P(X=1 | V2=0) = 0.31
P(X=1 | V2=1) = 0.59
(0.51 - 0.42) / (0.59 - 0.31) = 0.32
0.32 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 33%. The probability of not having a brother and normal infant birth weight is 20%. The probability of having a brother and normal infant birth weight is 23%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.33
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.23
0.23/0.33 - 0.20/0.67 = 0.39
0.39 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
25011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 39%. For infants who do not have a brother, the probability of normal infant birth weight is 37%. For infants who have a brother, the probability of normal infant birth weight is 73%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.73
0.39*0.73 - 0.61*0.37 = 0.51
0.51 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
25016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 36%. For areas with high cigarette tax, the probability of normal infant birth weight is 41%. For areas with low cigarette tax, the probability of having a brother is 27%. For areas with high cigarette tax, the probability of having a brother is 51%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.36
P(Y=1 | V2=1) = 0.41
P(X=1 | V2=0) = 0.27
P(X=1 | V2=1) = 0.51
(0.41 - 0.36) / (0.51 - 0.27) = 0.24
0.24 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 30%. For infants who do not have a brother, the probability of normal infant birth weight is 28%. For infants who have a brother, the probability of normal infant birth weight is 58%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.30
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.58
0.30*0.58 - 0.70*0.28 = 0.36
0.36 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
25019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 30%. For infants who do not have a brother, the probability of normal infant birth weight is 28%. For infants who have a brother, the probability of normal infant birth weight is 58%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.30
P(Y=1 | X=0) = 0.28
P(Y=1 | X=1) = 0.58
0.30*0.58 - 0.70*0.28 = 0.36
0.36 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
25020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 30%. The probability of not having a brother and normal infant birth weight is 19%. The probability of having a brother and normal infant birth weight is 17%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.19
P(Y=1, X=1=1) = 0.17
0.17/0.30 - 0.19/0.70 = 0.30
0.30 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
25024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 32%. For areas with high cigarette tax, the probability of normal infant birth weight is 50%. For areas with low cigarette tax, the probability of having a brother is 46%. For areas with high cigarette tax, the probability of having a brother is 76%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.32
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.46
P(X=1 | V2=1) = 0.76
(0.50 - 0.32) / (0.76 - 0.46) = 0.61
0.61 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 52%. For infants who do not have a brother, the probability of normal infant birth weight is 3%. For infants who have a brother, the probability of normal infant birth weight is 65%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.52
P(Y=1 | X=0) = 0.03
P(Y=1 | X=1) = 0.65
0.52*0.65 - 0.48*0.03 = 0.35
0.35 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
25032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 34%. For areas with high cigarette tax, the probability of normal infant birth weight is 42%. For areas with low cigarette tax, the probability of having a brother is 34%. For areas with high cigarette tax, the probability of having a brother is 63%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.34
P(Y=1 | V2=1) = 0.42
P(X=1 | V2=0) = 0.34
P(X=1 | V2=1) = 0.63
(0.42 - 0.34) / (0.63 - 0.34) = 0.29
0.29 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 39%. For infants who do not have a brother, the probability of normal infant birth weight is 24%. For infants who have a brother, the probability of normal infant birth weight is 54%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.39
P(Y=1 | X=0) = 0.24
P(Y=1 | X=1) = 0.54
0.39*0.54 - 0.61*0.24 = 0.36
0.36 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
25037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 39%. The probability of not having a brother and normal infant birth weight is 14%. The probability of having a brother and normal infant birth weight is 21%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.39
P(Y=1, X=0=1) = 0.14
P(Y=1, X=1=1) = 0.21
0.21/0.39 - 0.14/0.61 = 0.30
0.30 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
25039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
25041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 23%. For areas with high cigarette tax, the probability of normal infant birth weight is 46%. For areas with low cigarette tax, the probability of having a brother is 32%. For areas with high cigarette tax, the probability of having a brother is 67%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.23
P(Y=1 | V2=1) = 0.46
P(X=1 | V2=0) = 0.32
P(X=1 | V2=1) = 0.67
(0.46 - 0.23) / (0.67 - 0.32) = 0.67
0.67 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 38%. The probability of not having a brother and normal infant birth weight is 1%. The probability of having a brother and normal infant birth weight is 26%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.38
P(Y=1, X=0=1) = 0.01
P(Y=1, X=1=1) = 0.26
0.26/0.38 - 0.01/0.62 = 0.67
0.67 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
25046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look directly at how having a brother correlates with infant's birth weight in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
25047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
25049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 7%. For areas with high cigarette tax, the probability of normal infant birth weight is 22%. For areas with low cigarette tax, the probability of having a brother is 6%. For areas with high cigarette tax, the probability of having a brother is 49%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.07
P(Y=1 | V2=1) = 0.22
P(X=1 | V2=0) = 0.06
P(X=1 | V2=1) = 0.49
(0.22 - 0.07) / (0.49 - 0.06) = 0.35
0.35 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 14%. For infants who do not have a brother, the probability of normal infant birth weight is 5%. For infants who have a brother, the probability of normal infant birth weight is 42%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.14
P(Y=1 | X=0) = 0.05
P(Y=1 | X=1) = 0.42
0.14*0.42 - 0.86*0.05 = 0.10
0.10 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
25055,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look at how having a brother correlates with infant's birth weight case by case according to unobserved confounders. Method 2: We look directly at how having a brother correlates with infant's birth weight in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
25056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 66%. For areas with high cigarette tax, the probability of normal infant birth weight is 79%. For areas with low cigarette tax, the probability of having a brother is 18%. For areas with high cigarette tax, the probability of having a brother is 56%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.66
P(Y=1 | V2=1) = 0.79
P(X=1 | V2=0) = 0.18
P(X=1 | V2=1) = 0.56
(0.79 - 0.66) / (0.56 - 0.18) = 0.33
0.33 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 25%. The probability of not having a brother and normal infant birth weight is 45%. The probability of having a brother and normal infant birth weight is 23%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.23
0.23/0.25 - 0.45/0.75 = 0.33
0.33 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
25062,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. Method 1: We look directly at how having a brother correlates with infant's birth weight in general. Method 2: We look at this correlation case by case according to unobserved confounders.",no,"nan
nan
nan
nan
nan
nan
nan",IV,tax_smoke_birthWeight,2,backadj,[backdoor adjustment set for Y given X]
25066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 34%. For infants who do not have a brother, the probability of normal infant birth weight is 12%. For infants who have a brother, the probability of normal infant birth weight is 52%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.34
P(Y=1 | X=0) = 0.12
P(Y=1 | X=1) = 0.52
0.34*0.52 - 0.66*0.12 = 0.25
0.25 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
25068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 34%. The probability of not having a brother and normal infant birth weight is 8%. The probability of having a brother and normal infant birth weight is 17%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.34
P(Y=1, X=0=1) = 0.08
P(Y=1, X=1=1) = 0.17
0.17/0.34 - 0.08/0.66 = 0.40
0.40 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
25072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. For areas with low cigarette tax, the probability of normal infant birth weight is 38%. For areas with high cigarette tax, the probability of normal infant birth weight is 44%. For areas with low cigarette tax, the probability of having a brother is 28%. For areas with high cigarette tax, the probability of having a brother is 51%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.38
P(Y=1 | V2=1) = 0.44
P(X=1 | V2=0) = 0.28
P(X=1 | V2=1) = 0.51
(0.44 - 0.38) / (0.51 - 0.28) = 0.25
0.25 > 0",IV,tax_smoke_birthWeight,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 31%. For infants who do not have a brother, the probability of normal infant birth weight is 30%. For infants who have a brother, the probability of normal infant birth weight is 58%.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.30
P(Y=1 | X=1) = 0.58
0.31*0.58 - 0.69*0.30 = 0.39
0.39 > 0",IV,tax_smoke_birthWeight,1,marginal,P(Y)
25077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on having a brother and infant's birth weight. Cigarette tax has a direct effect on having a brother. Having a brother has a direct effect on infant's birth weight. Unobserved confounders is unobserved. The overall probability of having a brother is 31%. The probability of not having a brother and normal infant birth weight is 21%. The probability of having a brother and normal infant birth weight is 18%.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = having a brother; Y = infant's birth weight.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.31
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.18
0.18/0.31 - 0.21/0.69 = 0.28
0.28 > 0",IV,tax_smoke_birthWeight,1,correlation,P(Y | X)
25081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 70%. For people served by a global water company, the probability of freckles is 61%. For people served by a local water company, the probability of clean water is 53%. For people served by a global water company, the probability of clean water is 21%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.70
P(Y=1 | V2=1) = 0.61
P(X=1 | V2=0) = 0.53
P(X=1 | V2=1) = 0.21
(0.61 - 0.70) / (0.21 - 0.53) = 0.28
0.28 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25083,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 22%. For people with only polluted water, the probability of freckles is 57%. For people with access to clean water, the probability of freckles is 79%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.79
0.22*0.79 - 0.78*0.57 = 0.62
0.62 > 0",IV,water_cholera,1,marginal,P(Y)
25084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 22%. The probability of polluted water and freckles is 44%. The probability of clean water and freckles is 17%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.22
P(Y=1, X=0=1) = 0.44
P(Y=1, X=1=1) = 0.17
0.17/0.22 - 0.44/0.78 = 0.22
0.22 > 0",IV,water_cholera,1,correlation,P(Y | X)
25087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 23%. For people with only polluted water, the probability of freckles is 57%. For people with access to clean water, the probability of freckles is 79%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.57
P(Y=1 | X=1) = 0.79
0.23*0.79 - 0.77*0.57 = 0.62
0.62 > 0",IV,water_cholera,1,marginal,P(Y)
25094,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 69%. For people served by a global water company, the probability of freckles is 55%. For people served by a local water company, the probability of clean water is 78%. For people served by a global water company, the probability of clean water is 44%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.69
P(Y=1 | V2=1) = 0.55
P(X=1 | V2=0) = 0.78
P(X=1 | V2=1) = 0.44
(0.55 - 0.69) / (0.44 - 0.78) = 0.43
0.43 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 69%. For people served by a global water company, the probability of freckles is 55%. For people served by a local water company, the probability of clean water is 78%. For people served by a global water company, the probability of clean water is 44%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.69
P(Y=1 | V2=1) = 0.55
P(X=1 | V2=0) = 0.78
P(X=1 | V2=1) = 0.44
(0.55 - 0.69) / (0.44 - 0.78) = 0.43
0.43 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 48%. For people with only polluted water, the probability of freckles is 37%. For people with access to clean water, the probability of freckles is 76%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.48
P(Y=1 | X=0) = 0.37
P(Y=1 | X=1) = 0.76
0.48*0.76 - 0.52*0.37 = 0.56
0.56 > 0",IV,water_cholera,1,marginal,P(Y)
25100,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 48%. The probability of polluted water and freckles is 20%. The probability of clean water and freckles is 36%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.48
P(Y=1, X=0=1) = 0.20
P(Y=1, X=1=1) = 0.36
0.36/0.48 - 0.20/0.52 = 0.39
0.39 > 0",IV,water_cholera,1,correlation,P(Y | X)
25104,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 60%. For people served by a global water company, the probability of freckles is 54%. For people served by a local water company, the probability of clean water is 43%. For people served by a global water company, the probability of clean water is 20%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.60
P(Y=1 | V2=1) = 0.54
P(X=1 | V2=0) = 0.43
P(X=1 | V2=1) = 0.20
(0.54 - 0.60) / (0.20 - 0.43) = 0.26
0.26 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 21%. For people with only polluted water, the probability of freckles is 50%. For people with access to clean water, the probability of freckles is 72%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.21
P(Y=1 | X=0) = 0.50
P(Y=1 | X=1) = 0.72
0.21*0.72 - 0.79*0.50 = 0.54
0.54 > 0",IV,water_cholera,1,marginal,P(Y)
25108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 21%. The probability of polluted water and freckles is 39%. The probability of clean water and freckles is 15%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.21
P(Y=1, X=0=1) = 0.39
P(Y=1, X=1=1) = 0.15
0.15/0.21 - 0.39/0.79 = 0.22
0.22 > 0",IV,water_cholera,1,correlation,P(Y | X)
25112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 78%. For people served by a global water company, the probability of freckles is 71%. For people served by a local water company, the probability of clean water is 48%. For people served by a global water company, the probability of clean water is 24%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.78
P(Y=1 | V2=1) = 0.71
P(X=1 | V2=0) = 0.48
P(X=1 | V2=1) = 0.24
(0.71 - 0.78) / (0.24 - 0.48) = 0.29
0.29 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 24%. For people with only polluted water, the probability of freckles is 65%. For people with access to clean water, the probability of freckles is 90%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.65
P(Y=1 | X=1) = 0.90
0.24*0.90 - 0.76*0.65 = 0.71
0.71 > 0",IV,water_cholera,1,marginal,P(Y)
25116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 24%. The probability of polluted water and freckles is 50%. The probability of clean water and freckles is 21%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.24
P(Y=1, X=0=1) = 0.50
P(Y=1, X=1=1) = 0.21
0.21/0.24 - 0.50/0.76 = 0.25
0.25 > 0",IV,water_cholera,1,correlation,P(Y | X)
25119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 58%. For people served by a global water company, the probability of freckles is 50%. For people served by a local water company, the probability of clean water is 55%. For people served by a global water company, the probability of clean water is 25%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.58
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.55
P(X=1 | V2=1) = 0.25
(0.50 - 0.58) / (0.25 - 0.55) = 0.26
0.26 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 58%. For people served by a global water company, the probability of freckles is 50%. For people served by a local water company, the probability of clean water is 55%. For people served by a global water company, the probability of clean water is 25%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.58
P(Y=1 | V2=1) = 0.50
P(X=1 | V2=0) = 0.55
P(X=1 | V2=1) = 0.25
(0.50 - 0.58) / (0.25 - 0.55) = 0.26
0.26 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 55%. For people served by a global water company, the probability of freckles is 40%. For people served by a local water company, the probability of clean water is 75%. For people served by a global water company, the probability of clean water is 17%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.55
P(Y=1 | V2=1) = 0.40
P(X=1 | V2=0) = 0.75
P(X=1 | V2=1) = 0.17
(0.40 - 0.55) / (0.17 - 0.75) = 0.27
0.27 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 19%. For people with only polluted water, the probability of freckles is 36%. For people with access to clean water, the probability of freckles is 58%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.58
0.19*0.58 - 0.81*0.36 = 0.40
0.40 > 0",IV,water_cholera,1,marginal,P(Y)
25135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 40%. For people with only polluted water, the probability of freckles is 61%. For people with access to clean water, the probability of freckles is 84%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.40
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.84
0.40*0.84 - 0.60*0.61 = 0.70
0.70 > 0",IV,water_cholera,1,marginal,P(Y)
25140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 40%. The probability of polluted water and freckles is 37%. The probability of clean water and freckles is 34%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.34
0.34/0.40 - 0.37/0.60 = 0.23
0.23 > 0",IV,water_cholera,1,correlation,P(Y | X)
25141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 40%. The probability of polluted water and freckles is 37%. The probability of clean water and freckles is 34%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.40
P(Y=1, X=0=1) = 0.37
P(Y=1, X=1=1) = 0.34
0.34/0.40 - 0.37/0.60 = 0.23
0.23 > 0",IV,water_cholera,1,correlation,P(Y | X)
25142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 67%. For people served by a global water company, the probability of freckles is 56%. For people served by a local water company, the probability of clean water is 58%. For people served by a global water company, the probability of clean water is 29%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.67
P(Y=1 | V2=1) = 0.56
P(X=1 | V2=0) = 0.58
P(X=1 | V2=1) = 0.29
(0.56 - 0.67) / (0.29 - 0.58) = 0.38
0.38 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 30%. The probability of polluted water and freckles is 31%. The probability of clean water and freckles is 25%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.30
P(Y=1, X=0=1) = 0.31
P(Y=1, X=1=1) = 0.25
0.25/0.30 - 0.31/0.70 = 0.37
0.37 > 0",IV,water_cholera,1,correlation,P(Y | X)
25151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25159,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25160,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 52%. For people served by a global water company, the probability of freckles is 44%. For people served by a local water company, the probability of clean water is 54%. For people served by a global water company, the probability of clean water is 26%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.44
P(X=1 | V2=0) = 0.54
P(X=1 | V2=1) = 0.26
(0.44 - 0.52) / (0.26 - 0.54) = 0.29
0.29 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25161,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 52%. For people served by a global water company, the probability of freckles is 44%. For people served by a local water company, the probability of clean water is 54%. For people served by a global water company, the probability of clean water is 26%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.52
P(Y=1 | V2=1) = 0.44
P(X=1 | V2=0) = 0.54
P(X=1 | V2=1) = 0.26
(0.44 - 0.52) / (0.26 - 0.54) = 0.29
0.29 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 33%. The probability of polluted water and freckles is 23%. The probability of clean water and freckles is 24%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.33
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.24
0.24/0.33 - 0.23/0.67 = 0.38
0.38 > 0",IV,water_cholera,1,correlation,P(Y | X)
25173,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 33%. The probability of polluted water and freckles is 23%. The probability of clean water and freckles is 24%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.33
P(Y=1, X=0=1) = 0.23
P(Y=1, X=1=1) = 0.24
0.24/0.33 - 0.23/0.67 = 0.38
0.38 > 0",IV,water_cholera,1,correlation,P(Y | X)
25175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 13%. The probability of polluted water and freckles is 56%. The probability of clean water and freckles is 10%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.56
P(Y=1, X=1=1) = 0.10
0.10/0.13 - 0.56/0.87 = 0.10
0.10 > 0",IV,water_cholera,1,correlation,P(Y | X)
25185,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 75%. For people served by a global water company, the probability of freckles is 67%. For people served by a local water company, the probability of clean water is 58%. For people served by a global water company, the probability of clean water is 30%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.75
P(Y=1 | V2=1) = 0.67
P(X=1 | V2=0) = 0.58
P(X=1 | V2=1) = 0.30
(0.67 - 0.75) / (0.30 - 0.58) = 0.25
0.25 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 35%. The probability of polluted water and freckles is 40%. The probability of clean water and freckles is 29%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.29
0.29/0.35 - 0.40/0.65 = 0.23
0.23 > 0",IV,water_cholera,1,correlation,P(Y | X)
25189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 35%. The probability of polluted water and freckles is 40%. The probability of clean water and freckles is 29%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.35
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.29
0.29/0.35 - 0.40/0.65 = 0.23
0.23 > 0",IV,water_cholera,1,correlation,P(Y | X)
25191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 47%. For people served by a global water company, the probability of freckles is 41%. For people served by a local water company, the probability of clean water is 50%. For people served by a global water company, the probability of clean water is 18%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.47
P(Y=1 | V2=1) = 0.41
P(X=1 | V2=0) = 0.50
P(X=1 | V2=1) = 0.18
(0.41 - 0.47) / (0.18 - 0.50) = 0.21
0.21 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 19%. The probability of polluted water and freckles is 30%. The probability of clean water and freckles is 11%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.11
0.11/0.19 - 0.30/0.81 = 0.17
0.17 > 0",IV,water_cholera,1,correlation,P(Y | X)
25197,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 19%. The probability of polluted water and freckles is 30%. The probability of clean water and freckles is 11%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.30
P(Y=1, X=1=1) = 0.11
0.11/0.19 - 0.30/0.81 = 0.17
0.17 > 0",IV,water_cholera,1,correlation,P(Y | X)
25200,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 49%. For people served by a global water company, the probability of freckles is 38%. For people served by a local water company, the probability of clean water is 52%. For people served by a global water company, the probability of clean water is 19%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.49
P(Y=1 | V2=1) = 0.38
P(X=1 | V2=0) = 0.52
P(X=1 | V2=1) = 0.19
(0.38 - 0.49) / (0.19 - 0.52) = 0.33
0.33 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25202,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 26%. For people with only polluted water, the probability of freckles is 33%. For people with access to clean water, the probability of freckles is 63%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.33
P(Y=1 | X=1) = 0.63
0.26*0.63 - 0.74*0.33 = 0.41
0.41 > 0",IV,water_cholera,1,marginal,P(Y)
25206,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 77%. For people served by a global water company, the probability of freckles is 69%. For people served by a local water company, the probability of clean water is 55%. For people served by a global water company, the probability of clean water is 26%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.77
P(Y=1 | V2=1) = 0.69
P(X=1 | V2=0) = 0.55
P(X=1 | V2=1) = 0.26
(0.69 - 0.77) / (0.26 - 0.55) = 0.30
0.30 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 27%. The probability of polluted water and freckles is 45%. The probability of clean water and freckles is 23%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.27
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.23
0.23/0.27 - 0.45/0.73 = 0.23
0.23 > 0",IV,water_cholera,1,correlation,P(Y | X)
25221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 27%. The probability of polluted water and freckles is 45%. The probability of clean water and freckles is 23%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.27
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.23
0.23/0.27 - 0.45/0.73 = 0.23
0.23 > 0",IV,water_cholera,1,correlation,P(Y | X)
25222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25227,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 24%. For people with only polluted water, the probability of freckles is 25%. For people with access to clean water, the probability of freckles is 55%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.24
P(Y=1 | X=0) = 0.25
P(Y=1 | X=1) = 0.55
0.24*0.55 - 0.76*0.25 = 0.32
0.32 > 0",IV,water_cholera,1,marginal,P(Y)
25230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 43%. For people with only polluted water, the probability of freckles is 51%. For people with access to clean water, the probability of freckles is 77%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.43
P(Y=1 | X=0) = 0.51
P(Y=1 | X=1) = 0.77
0.43*0.77 - 0.57*0.51 = 0.62
0.62 > 0",IV,water_cholera,1,marginal,P(Y)
25241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 47%. For people served by a global water company, the probability of freckles is 35%. For people served by a local water company, the probability of clean water is 54%. For people served by a global water company, the probability of clean water is 13%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.47
P(Y=1 | V2=1) = 0.35
P(X=1 | V2=0) = 0.54
P(X=1 | V2=1) = 0.13
(0.35 - 0.47) / (0.13 - 0.54) = 0.28
0.28 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 16%. The probability of polluted water and freckles is 29%. The probability of clean water and freckles is 7%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.16
P(Y=1, X=0=1) = 0.29
P(Y=1, X=1=1) = 0.07
0.07/0.16 - 0.29/0.84 = 0.13
0.13 > 0",IV,water_cholera,1,correlation,P(Y | X)
25246,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 26%. For people with only polluted water, the probability of freckles is 61%. For people with access to clean water, the probability of freckles is 89%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.89
0.26*0.89 - 0.74*0.61 = 0.68
0.68 > 0",IV,water_cholera,1,marginal,P(Y)
25251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 26%. For people with only polluted water, the probability of freckles is 61%. For people with access to clean water, the probability of freckles is 89%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.26
P(Y=1 | X=0) = 0.61
P(Y=1 | X=1) = 0.89
0.26*0.89 - 0.74*0.61 = 0.68
0.68 > 0",IV,water_cholera,1,marginal,P(Y)
25252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 26%. The probability of polluted water and freckles is 45%. The probability of clean water and freckles is 23%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.23
0.23/0.26 - 0.45/0.74 = 0.28
0.28 > 0",IV,water_cholera,1,correlation,P(Y | X)
25253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 26%. The probability of polluted water and freckles is 45%. The probability of clean water and freckles is 23%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.26
P(Y=1, X=0=1) = 0.45
P(Y=1, X=1=1) = 0.23
0.23/0.26 - 0.45/0.74 = 0.28
0.28 > 0",IV,water_cholera,1,correlation,P(Y | X)
25254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 76%. For people served by a global water company, the probability of freckles is 62%. For people served by a local water company, the probability of clean water is 46%. For people served by a global water company, the probability of clean water is 11%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.76
P(Y=1 | V2=1) = 0.62
P(X=1 | V2=0) = 0.46
P(X=1 | V2=1) = 0.11
(0.62 - 0.76) / (0.11 - 0.46) = 0.39
0.39 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 76%. For people served by a global water company, the probability of freckles is 62%. For people served by a local water company, the probability of clean water is 46%. For people served by a global water company, the probability of clean water is 11%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.76
P(Y=1 | V2=1) = 0.62
P(X=1 | V2=0) = 0.46
P(X=1 | V2=1) = 0.11
(0.62 - 0.76) / (0.11 - 0.46) = 0.39
0.39 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25258,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 13%. For people with only polluted water, the probability of freckles is 58%. For people with access to clean water, the probability of freckles is 95%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.95
0.13*0.95 - 0.87*0.58 = 0.63
0.63 > 0",IV,water_cholera,1,marginal,P(Y)
25259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 13%. For people with only polluted water, the probability of freckles is 58%. For people with access to clean water, the probability of freckles is 95%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.13
P(Y=1 | X=0) = 0.58
P(Y=1 | X=1) = 0.95
0.13*0.95 - 0.87*0.58 = 0.63
0.63 > 0",IV,water_cholera,1,marginal,P(Y)
25261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 13%. The probability of polluted water and freckles is 51%. The probability of clean water and freckles is 12%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.13
P(Y=1, X=0=1) = 0.51
P(Y=1, X=1=1) = 0.12
0.12/0.13 - 0.51/0.87 = 0.37
0.37 > 0",IV,water_cholera,1,correlation,P(Y | X)
25262,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25263,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 22%. For people with only polluted water, the probability of freckles is 68%. For people with access to clean water, the probability of freckles is 88%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.22
P(Y=1 | X=0) = 0.68
P(Y=1 | X=1) = 0.88
0.22*0.88 - 0.78*0.68 = 0.73
0.73 > 0",IV,water_cholera,1,marginal,P(Y)
25268,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 22%. The probability of polluted water and freckles is 53%. The probability of clean water and freckles is 20%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.22
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.20
0.20/0.22 - 0.53/0.78 = 0.19
0.19 > 0",IV,water_cholera,1,correlation,P(Y | X)
25269,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 22%. The probability of polluted water and freckles is 53%. The probability of clean water and freckles is 20%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.22
P(Y=1, X=0=1) = 0.53
P(Y=1, X=1=1) = 0.20
0.20/0.22 - 0.53/0.78 = 0.19
0.19 > 0",IV,water_cholera,1,correlation,P(Y | X)
25270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25281,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 68%. For people served by a global water company, the probability of freckles is 58%. For people served by a local water company, the probability of clean water is 48%. For people served by a global water company, the probability of clean water is 22%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.68
P(Y=1 | V2=1) = 0.58
P(X=1 | V2=0) = 0.48
P(X=1 | V2=1) = 0.22
(0.58 - 0.68) / (0.22 - 0.48) = 0.35
0.35 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25282,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 23%. For people with only polluted water, the probability of freckles is 52%. For people with access to clean water, the probability of freckles is 81%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.81
0.23*0.81 - 0.77*0.52 = 0.59
0.59 > 0",IV,water_cholera,1,marginal,P(Y)
25283,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 23%. For people with only polluted water, the probability of freckles is 52%. For people with access to clean water, the probability of freckles is 81%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.23
P(Y=1 | X=0) = 0.52
P(Y=1 | X=1) = 0.81
0.23*0.81 - 0.77*0.52 = 0.59
0.59 > 0",IV,water_cholera,1,marginal,P(Y)
25285,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 23%. The probability of polluted water and freckles is 40%. The probability of clean water and freckles is 18%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.23
P(Y=1, X=0=1) = 0.40
P(Y=1, X=1=1) = 0.18
0.18/0.23 - 0.40/0.77 = 0.29
0.29 > 0",IV,water_cholera,1,correlation,P(Y | X)
25286,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25291,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 19%. For people with only polluted water, the probability of freckles is 40%. For people with access to clean water, the probability of freckles is 57%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.19
P(Y=1 | X=0) = 0.40
P(Y=1 | X=1) = 0.57
0.19*0.57 - 0.81*0.40 = 0.43
0.43 > 0",IV,water_cholera,1,marginal,P(Y)
25292,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 19%. The probability of polluted water and freckles is 33%. The probability of clean water and freckles is 11%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.19
P(Y=1, X=0=1) = 0.33
P(Y=1, X=1=1) = 0.11
0.11/0.19 - 0.33/0.81 = 0.17
0.17 > 0",IV,water_cholera,1,correlation,P(Y | X)
25296,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 54%. For people served by a global water company, the probability of freckles is 41%. For people served by a local water company, the probability of clean water is 56%. For people served by a global water company, the probability of clean water is 26%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.54
P(Y=1 | V2=1) = 0.41
P(X=1 | V2=0) = 0.56
P(X=1 | V2=1) = 0.26
(0.41 - 0.54) / (0.26 - 0.56) = 0.45
0.45 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25301,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 29%. The probability of polluted water and freckles is 21%. The probability of clean water and freckles is 21%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.29
P(Y=1, X=0=1) = 0.21
P(Y=1, X=1=1) = 0.21
0.21/0.29 - 0.21/0.71 = 0.42
0.42 > 0",IV,water_cholera,1,correlation,P(Y | X)
25302,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25303,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25308,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 25%. The probability of polluted water and freckles is 34%. The probability of clean water and freckles is 23%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.23
0.23/0.25 - 0.34/0.75 = 0.45
0.45 > 0",IV,water_cholera,1,correlation,P(Y | X)
25309,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 25%. The probability of polluted water and freckles is 34%. The probability of clean water and freckles is 23%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y | X)
P(X = 1, Y = 1)/P(X = 1) - P(X = 0, Y = 1)/P(X = 0)
P(X=1=1) = 0.25
P(Y=1, X=0=1) = 0.34
P(Y=1, X=1=1) = 0.23
0.23/0.25 - 0.34/0.75 = 0.45
0.45 > 0",IV,water_cholera,1,correlation,P(Y | X)
25310,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look directly at how water quality correlates with freckles in general. Method 2: We look at this correlation case by case according to poverty.",no,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25311,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25312,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 64%. For people served by a global water company, the probability of freckles is 47%. For people served by a local water company, the probability of clean water is 70%. For people served by a global water company, the probability of clean water is 28%.",yes,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.64
P(Y=1 | V2=1) = 0.47
P(X=1 | V2=0) = 0.70
P(X=1 | V2=1) = 0.28
(0.47 - 0.64) / (0.28 - 0.70) = 0.40
0.40 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25313,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. For people served by a local water company, the probability of freckles is 64%. For people served by a global water company, the probability of freckles is 47%. For people served by a local water company, the probability of clean water is 70%. For people served by a global water company, the probability of clean water is 28%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
E[Y | do(X = 1)] - E[Y | do(X = 0)]
[P(Y=1|V2=1)-P(Y=1|V2=0)]/[P(X=1|V2=1)-P(X=1|V2=0)]
P(Y=1 | V2=0) = 0.64
P(Y=1 | V2=1) = 0.47
P(X=1 | V2=0) = 0.70
P(X=1 | V2=1) = 0.28
(0.47 - 0.64) / (0.28 - 0.70) = 0.40
0.40 > 0",IV,water_cholera,2,ate,E[Y | do(X = 1)] - E[Y | do(X = 0)]
25314,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. The overall probability of clean water is 31%. For people with only polluted water, the probability of freckles is 36%. For people with access to clean water, the probability of freckles is 74%.",no,"Let V2 = water company; V1 = poverty; X = water quality; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
P(Y)
P(Y | X=1)*P(X=1) + P(Y | X=0)*P(X=0)
P(X=1) = 0.31
P(Y=1 | X=0) = 0.36
P(Y=1 | X=1) = 0.74
0.31*0.74 - 0.69*0.36 = 0.48
0.48 > 0",IV,water_cholera,1,marginal,P(Y)
25319,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on water quality and freckles. Water company has a direct effect on water quality. Water quality has a direct effect on freckles. Poverty is unobserved. Method 1: We look at how water quality correlates with freckles case by case according to poverty. Method 2: We look directly at how water quality correlates with freckles in general.",yes,"nan
nan
nan
nan
nan
nan
nan",IV,water_cholera,2,backadj,[backdoor adjustment set for Y given X]
25320,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm not set by wife. drinking coffee or alarm set by wife causes ringing alarm.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
1",mediation,alarm,3,det-counterfactual,Y_{X=0} = 1 | 
25321,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm not set by wife. drinking coffee or alarm set by wife causes ringing alarm.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
0",mediation,alarm,3,det-counterfactual,Y_{X=0} = 0 | 
25322,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm not set by wife. drinking coffee or alarm set by wife causes ringing alarm.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
1",mediation,alarm,3,det-counterfactual,Y_{X=1} = 1 | 
25323,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm not set by wife. drinking coffee or alarm set by wife causes ringing alarm.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
0",mediation,alarm,3,det-counterfactual,Y_{X=1} = 0 | 
25324,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm not set by wife. drinking coffee and alarm set by wife causes ringing alarm.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
0",mediation,alarm,3,det-counterfactual,Y_{X=0} = 1 | 
25325,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm not set by wife. drinking coffee and alarm set by wife causes ringing alarm.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
1",mediation,alarm,3,det-counterfactual,Y_{X=0} = 0 | 
25326,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm not set by wife. drinking coffee and alarm set by wife causes ringing alarm.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
0",mediation,alarm,3,det-counterfactual,Y_{X=1} = 1 | 
25327,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm not set by wife. drinking coffee and alarm set by wife causes ringing alarm.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
1",mediation,alarm,3,det-counterfactual,Y_{X=1} = 0 | 
25328,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm set by wife. drinking coffee or alarm set by wife causes ringing alarm.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
0",mediation,alarm,3,det-counterfactual,Y_{X=0} = 1 | 
25329,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm set by wife. drinking coffee or alarm set by wife causes ringing alarm.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
1",mediation,alarm,3,det-counterfactual,Y_{X=0} = 0 | 
25330,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm set by wife. drinking coffee or alarm set by wife causes ringing alarm.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
1",mediation,alarm,3,det-counterfactual,Y_{X=1} = 1 | 
25331,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm set by wife. drinking coffee or alarm set by wife causes ringing alarm.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
0",mediation,alarm,3,det-counterfactual,Y_{X=1} = 0 | 
25332,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm set by wife. drinking coffee and alarm set by wife causes ringing alarm.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
0",mediation,alarm,3,det-counterfactual,Y_{X=0} = 1 | 
25333,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm set by wife. drinking coffee and alarm set by wife causes ringing alarm.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
1",mediation,alarm,3,det-counterfactual,Y_{X=0} = 0 | 
25334,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm set by wife. drinking coffee and alarm set by wife causes ringing alarm.",yes,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
1",mediation,alarm,3,det-counterfactual,Y_{X=1} = 1 | 
25335,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Drinking coffee has a direct effect on wife and alarm clock. Wife has a direct effect on alarm clock. We know that drinking coffee causes alarm set by wife. drinking coffee and alarm set by wife causes ringing alarm.",no,"Let X = drinking coffee; V2 = wife; Y = alarm clock.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
0",mediation,alarm,3,det-counterfactual,Y_{X=1} = 0 | 
25336,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food or candle with wax causes dark room. We observed the candle is out of wax.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 0 = 0 or 0
0",fork,candle,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25337,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food or candle with wax causes dark room. We observed the candle is out of wax.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 0 = 0 or 0
1",fork,candle,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25338,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food or candle with wax causes dark room. We observed the candle is out of wax.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 1 = 1 or 0
1",fork,candle,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25339,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food or candle with wax causes dark room. We observed the candle is out of wax.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 1 = 1 or 0
0",fork,candle,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25340,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food or candle with wax causes dark room. We observed the candle has wax.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 0 or 1
1",fork,candle,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25341,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food or candle with wax causes dark room. We observed the candle has wax.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 0 or 1
0",fork,candle,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25342,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food or candle with wax causes dark room. We observed the candle has wax.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 1 or 1
1",fork,candle,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25343,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food or candle with wax causes dark room. We observed the candle has wax.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 1 or 1
0",fork,candle,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25344,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food and candle with wax causes dark room. We observed the candle is out of wax.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 0 and 0
0",fork,candle,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25345,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food and candle with wax causes dark room. We observed the candle is out of wax.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 0 and 0
1",fork,candle,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25346,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food and candle with wax causes dark room. We observed the candle is out of wax.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 1 and 0
0",fork,candle,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25347,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food and candle with wax causes dark room. We observed the candle is out of wax.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 1 and 0
1",fork,candle,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25348,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food and candle with wax causes dark room. We observed the candle has wax.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 0 = 0 and 1
0",fork,candle,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25349,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food and candle with wax causes dark room. We observed the candle has wax.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 0 = 0 and 1
1",fork,candle,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25350,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food and candle with wax causes dark room. We observed the candle has wax.",yes,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 1 = 1 and 1
1",fork,candle,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25351,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on room. The candle has a direct effect on room. We know that liking spicy food and candle with wax causes dark room. We observed the candle has wax.",no,"Let V2 = the candle; X = liking spicy food; Y = room.
X->Y,V2->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 1 = 1 and 1
0",fork,candle,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25352,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = X or V3
Y = 0 = 0 or 0
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25353,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = X or V3
Y = 0 = 0 or 0
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25354,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = X or V3
Y = 1 = 1 or 0
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25355,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = X or V3
Y = 1 = 1 or 0
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25356,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = X or V3
Y = 1 = 0 or 1
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25357,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = X or V3
Y = 1 = 0 or 1
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25358,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = X or V3
Y = 1 = 1 or 1
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25359,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = X or V3
Y = 1 = 1 or 1
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25360,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = X and V3
Y = 0 = 0 and 0
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25361,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = X and V3
Y = 0 = 0 and 0
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25362,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = X and V3
Y = 0 = 1 and 0
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25363,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = X and V3
Y = 0 = 1 and 0
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25364,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = X and V3
Y = 0 = 0 and 1
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25365,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = X and V3
Y = 0 = 0 and 1
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25366,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = X and V3
Y = 1 = 1 and 1
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25367,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = X and V3
Y = 1 = 1 and 1
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25368,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = X or V3
Y = 1 = 0 or 1
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25369,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = X or V3
Y = 1 = 0 or 1
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25370,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = X or V3
Y = 1 = 1 or 1
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25371,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = X or V3
Y = 1 = 1 or 1
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25372,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = X or V3
Y = 0 = 0 or 0
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25373,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = X or V3
Y = 0 = 0 or 0
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25374,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = X or V3
Y = 1 = 1 or 0
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25375,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England or director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = X or V3
Y = 1 = 1 or 0
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25376,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = X and V3
Y = 0 = 0 and 1
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25377,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = X and V3
Y = 0 = 0 and 1
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25378,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = X and V3
Y = 1 = 1 and 1
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25379,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to retain the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = X and V3
Y = 1 = 1 and 1
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25380,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = X and V3
Y = 0 = 0 and 0
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25381,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = X and V3
Y = 0 = 0 and 0
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25382,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",no,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = X and V3
Y = 0 = 1 and 0
0",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25383,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: CEO has a direct effect on director and having visited England. Having visited England has a direct effect on employee. Director has a direct effect on employee. We know that CEO's decision to fire the employee causes not having visited England and director signing the termination letter. having visited England and director signing the termination letter causes employee being fired. We observed the CEO decides to fire the employee.",yes,"Let V1 = CEO; V3 = director; X = having visited England; Y = employee.
V1->V3,V1->X,X->Y,V3->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = X and V3
Y = 0 = 1 and 0
1",diamondcut,firing_employee,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25384,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private not shooting. the corporal shooting or the private shooting causes the prisoner's death.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 0 or 1
1",diamond,firing_squad,3,det-counterfactual,Y_{X=0} = 1 | 
25385,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private not shooting. the corporal shooting or the private shooting causes the prisoner's death.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 0 or 1
0",diamond,firing_squad,3,det-counterfactual,Y_{X=0} = 0 | 
25386,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private not shooting. the corporal shooting or the private shooting causes the prisoner's death.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 1 or 0
1",diamond,firing_squad,3,det-counterfactual,Y_{X=1} = 1 | 
25387,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private not shooting. the corporal shooting or the private shooting causes the prisoner's death.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 1 or 0
0",diamond,firing_squad,3,det-counterfactual,Y_{X=1} = 0 | 
25388,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private shooting. the corporal shooting or the private shooting causes the prisoner's death.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [0] = 0 or 0
0",diamond,firing_squad,3,det-counterfactual,Y_{X=0} = 1 | 
25389,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private shooting. the corporal shooting or the private shooting causes the prisoner's death.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [0] = 0 or 0
1",diamond,firing_squad,3,det-counterfactual,Y_{X=0} = 0 | 
25390,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private shooting. the corporal shooting or the private shooting causes the prisoner's death.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [1] = 1 or 1
1",diamond,firing_squad,3,det-counterfactual,Y_{X=1} = 1 | 
25391,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private shooting. the corporal shooting or the private shooting causes the prisoner's death.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [1] = 1 or 1
0",diamond,firing_squad,3,det-counterfactual,Y_{X=1} = 0 | 
25392,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private shooting. the corporal shooting and the private shooting causes the prisoner's death.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [0] = 0 and 0
0",diamond,firing_squad,3,det-counterfactual,Y_{X=0} = 1 | 
25393,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private shooting. the corporal shooting and the private shooting causes the prisoner's death.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [0] = 0 and 0
1",diamond,firing_squad,3,det-counterfactual,Y_{X=0} = 0 | 
25394,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private shooting. the corporal shooting and the private shooting causes the prisoner's death.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [1] = 1 and 1
1",diamond,firing_squad,3,det-counterfactual,Y_{X=1} = 1 | 
25395,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private shooting. the corporal shooting and the private shooting causes the prisoner's death.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [1] = 1 and 1
0",diamond,firing_squad,3,det-counterfactual,Y_{X=1} = 0 | 
25396,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private not shooting. the corporal shooting and the private shooting causes the prisoner's death.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 0 and 1
0",diamond,firing_squad,3,det-counterfactual,Y_{X=0} = 1 | 
25397,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private not shooting. the corporal shooting and the private shooting causes the prisoner's death.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 0 and 1
1",diamond,firing_squad,3,det-counterfactual,Y_{X=0} = 0 | 
25398,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private not shooting. the corporal shooting and the private shooting causes the prisoner's death.",no,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 1 and 0
0",diamond,firing_squad,3,det-counterfactual,Y_{X=1} = 1 | 
25399,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on the private and the corporal. The corporal has a direct effect on prisoner. The private has a direct effect on prisoner. We know that having a sister causes the corporal shooting and the private not shooting. the corporal shooting and the private shooting causes the prisoner's death.",yes,"Let X = having a sister; V3 = the private; V2 = the corporal; Y = prisoner.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 1 and 0
1",diamond,firing_squad,3,det-counterfactual,Y_{X=1} = 0 | 
25400,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler on. rain and sprinkler on causes wet ground.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [0] = 0 and 0
0",diamond,floor_wet,3,det-counterfactual,Y_{X=0} = 1 | 
25401,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler on. rain and sprinkler on causes wet ground.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [0] = 0 and 0
1",diamond,floor_wet,3,det-counterfactual,Y_{X=0} = 0 | 
25402,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler on. rain and sprinkler on causes wet ground.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [1] = 1 and 1
1",diamond,floor_wet,3,det-counterfactual,Y_{X=1} = 1 | 
25403,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler on. rain and sprinkler on causes wet ground.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [1] = 1 and 1
0",diamond,floor_wet,3,det-counterfactual,Y_{X=1} = 0 | 
25404,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler off. rain and sprinkler on causes wet ground.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 0 and 1
0",diamond,floor_wet,3,det-counterfactual,Y_{X=0} = 1 | 
25405,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler off. rain and sprinkler on causes wet ground.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 0 and 1
1",diamond,floor_wet,3,det-counterfactual,Y_{X=0} = 0 | 
25406,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler off. rain and sprinkler on causes wet ground.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 1 and 0
0",diamond,floor_wet,3,det-counterfactual,Y_{X=1} = 1 | 
25407,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler off. rain and sprinkler on causes wet ground.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 1 and 0
1",diamond,floor_wet,3,det-counterfactual,Y_{X=1} = 0 | 
25408,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler on. rain or sprinkler on causes wet ground.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [0] = 0 or 0
0",diamond,floor_wet,3,det-counterfactual,Y_{X=0} = 1 | 
25409,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler on. rain or sprinkler on causes wet ground.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [0] = 0 or 0
1",diamond,floor_wet,3,det-counterfactual,Y_{X=0} = 0 | 
25410,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler on. rain or sprinkler on causes wet ground.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [1] = 1 or 1
1",diamond,floor_wet,3,det-counterfactual,Y_{X=1} = 1 | 
25411,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler on. rain or sprinkler on causes wet ground.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [1] = 1 or 1
0",diamond,floor_wet,3,det-counterfactual,Y_{X=1} = 0 | 
25412,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler off. rain or sprinkler on causes wet ground.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 0 or 1
1",diamond,floor_wet,3,det-counterfactual,Y_{X=0} = 1 | 
25413,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler off. rain or sprinkler on causes wet ground.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 0 or 1
0",diamond,floor_wet,3,det-counterfactual,Y_{X=0} = 0 | 
25414,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler off. rain or sprinkler on causes wet ground.",yes,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 1 or 0
1",diamond,floor_wet,3,det-counterfactual,Y_{X=1} = 1 | 
25415,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Full moon has a direct effect on sprinkler and weather. Weather has a direct effect on ground. Sprinkler has a direct effect on ground. We know that full moon causes rain and sprinkler off. rain or sprinkler on causes wet ground.",no,"Let X = full moon; V3 = sprinkler; V2 = weather; Y = ground.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 1 or 0
0",diamond,floor_wet,3,det-counterfactual,Y_{X=1} = 0 | 
25416,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food and the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker doesn't light a match.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 0 and 0
0",fork,forest_fire,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25417,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food and the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker doesn't light a match.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 0 and 0
1",fork,forest_fire,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25418,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food and the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker doesn't light a match.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 1 and 0
0",fork,forest_fire,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25419,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food and the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker doesn't light a match.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 1 and 0
1",fork,forest_fire,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25420,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food and the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker lights a match.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 0 = 0 and 1
0",fork,forest_fire,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25421,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food and the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker lights a match.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 0 = 0 and 1
1",fork,forest_fire,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25422,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food and the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker lights a match.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 1 = 1 and 1
1",fork,forest_fire,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25423,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food and the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker lights a match.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 1 = 1 and 1
0",fork,forest_fire,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25424,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food or the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker doesn't light a match.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 0 = 0 or 0
0",fork,forest_fire,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25425,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food or the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker doesn't light a match.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 0 = 0 or 0
1",fork,forest_fire,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25426,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food or the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker doesn't light a match.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 1 = 1 or 0
1",fork,forest_fire,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25427,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food or the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker doesn't light a match.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 1 = 1 or 0
0",fork,forest_fire,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25428,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food or the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker lights a match.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 0 or 1
1",fork,forest_fire,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25429,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food or the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker lights a match.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 0 or 1
0",fork,forest_fire,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25430,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food or the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker lights a match.",yes,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 1 or 1
1",fork,forest_fire,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25431,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on the forest. The smoker has a direct effect on the forest. We know that liking spicy food or the chain-smoker lighting a match causes the forest on fire. We observed the chain-smoker lights a match.",no,"Let V2 = the smoker; X = liking spicy food; Y = the forest.
X->Y,V2->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 1 or 1
0",fork,forest_fire,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25432,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse or heavy traffic causes arriving to school on time. We observed there is no traffic on the road.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 0 = 0 or 0
0",fork,getting_late,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25433,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse or heavy traffic causes arriving to school on time. We observed there is no traffic on the road.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 0 = 0 or 0
1",fork,getting_late,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25434,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse or heavy traffic causes arriving to school on time. We observed there is no traffic on the road.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 1 = 1 or 0
1",fork,getting_late,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25435,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse or heavy traffic causes arriving to school on time. We observed there is no traffic on the road.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 1 = 1 or 0
0",fork,getting_late,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25436,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse or heavy traffic causes arriving to school on time. We observed there is heavy traffic on the road.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 0 or 1
1",fork,getting_late,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25437,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse or heavy traffic causes arriving to school on time. We observed there is heavy traffic on the road.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 0 or 1
0",fork,getting_late,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25438,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse or heavy traffic causes arriving to school on time. We observed there is heavy traffic on the road.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 1 or 1
1",fork,getting_late,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25439,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse or heavy traffic causes arriving to school on time. We observed there is heavy traffic on the road.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 1 or 1
0",fork,getting_late,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25440,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse and heavy traffic causes arriving to school on time. We observed there is no traffic on the road.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 0 and 0
0",fork,getting_late,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25441,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse and heavy traffic causes arriving to school on time. We observed there is no traffic on the road.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 0 and 0
1",fork,getting_late,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25442,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse and heavy traffic causes arriving to school on time. We observed there is no traffic on the road.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 1 and 0
0",fork,getting_late,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25443,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse and heavy traffic causes arriving to school on time. We observed there is no traffic on the road.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 1 and 0
1",fork,getting_late,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25444,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse and heavy traffic causes arriving to school on time. We observed there is heavy traffic on the road.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 0 = 0 and 1
0",fork,getting_late,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25445,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse and heavy traffic causes arriving to school on time. We observed there is heavy traffic on the road.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 0 = 0 and 1
1",fork,getting_late,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25446,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse and heavy traffic causes arriving to school on time. We observed there is heavy traffic on the road.",yes,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 1 = 1 and 1
1",fork,getting_late,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25447,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Solar eclipse has a direct effect on Alice arriving to school. Traffic has a direct effect on Alice arriving to school. We know that solar eclipse and heavy traffic causes arriving to school on time. We observed there is heavy traffic on the road.",no,"Let V2 = traffic; X = solar eclipse; Y = Alice arriving to school.
X->Y,V2->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 1 = 1 and 1
0",fork,getting_late,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25448,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment or going to the beach causes large feet. We observed the person does not go to the beach.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 0 = 0 or 0
0",fork,getting_tanned,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25449,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment or going to the beach causes large feet. We observed the person does not go to the beach.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 0 = 0 or 0
1",fork,getting_tanned,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25450,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment or going to the beach causes large feet. We observed the person does not go to the beach.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 1 = 1 or 0
1",fork,getting_tanned,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25451,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment or going to the beach causes large feet. We observed the person does not go to the beach.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X or V2
Y = 1 = 1 or 0
0",fork,getting_tanned,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25452,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment or going to the beach causes large feet. We observed the person goes to the beach.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 0 or 1
1",fork,getting_tanned,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25453,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment or going to the beach causes large feet. We observed the person goes to the beach.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 0 or 1
0",fork,getting_tanned,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25454,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment or going to the beach causes large feet. We observed the person goes to the beach.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 1 or 1
1",fork,getting_tanned,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25455,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment or going to the beach causes large feet. We observed the person goes to the beach.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X or V2
Y = 1 = 1 or 1
0",fork,getting_tanned,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25456,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment and going to the beach causes large feet. We observed the person does not go to the beach.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 0 and 0
0",fork,getting_tanned,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25457,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment and going to the beach causes large feet. We observed the person does not go to the beach.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 0 and 0
1",fork,getting_tanned,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25458,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment and going to the beach causes large feet. We observed the person does not go to the beach.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 1 and 0
0",fork,getting_tanned,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25459,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment and going to the beach causes large feet. We observed the person does not go to the beach.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
Y = X and V2
Y = 0 = 1 and 0
1",fork,getting_tanned,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25460,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment and going to the beach causes large feet. We observed the person goes to the beach.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 0 = 0 and 1
0",fork,getting_tanned,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25461,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment and going to the beach causes large feet. We observed the person goes to the beach.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 0 = 0 and 1
1",fork,getting_tanned,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25462,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment and going to the beach causes large feet. We observed the person goes to the beach.",yes,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 1 = 1 and 1
1",fork,getting_tanned,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25463,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Tanning salon treatment has a direct effect on foot size. Going to the beach has a direct effect on foot size. We know that tanning salon treatment and going to the beach causes large feet. We observed the person goes to the beach.",no,"Let V2 = going to the beach; X = tanning salon treatment; Y = foot size.
X->Y,V2->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
Y = X and V2
Y = 1 = 1 and 1
0",fork,getting_tanned,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25464,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin happiness. taking the elevator or penguin happiness causes large feet.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
0",mediation,penguin,3,det-counterfactual,Y_{X=0} = 1 | 
25465,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin happiness. taking the elevator or penguin happiness causes large feet.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
1",mediation,penguin,3,det-counterfactual,Y_{X=0} = 0 | 
25466,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin happiness. taking the elevator or penguin happiness causes large feet.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
1",mediation,penguin,3,det-counterfactual,Y_{X=1} = 1 | 
25467,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin happiness. taking the elevator or penguin happiness causes large feet.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
0",mediation,penguin,3,det-counterfactual,Y_{X=1} = 0 | 
25468,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin saddness. taking the elevator or penguin happiness causes large feet.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
1",mediation,penguin,3,det-counterfactual,Y_{X=0} = 1 | 
25469,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin saddness. taking the elevator or penguin happiness causes large feet.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
0",mediation,penguin,3,det-counterfactual,Y_{X=0} = 0 | 
25470,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin saddness. taking the elevator or penguin happiness causes large feet.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
1",mediation,penguin,3,det-counterfactual,Y_{X=1} = 1 | 
25471,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin saddness. taking the elevator or penguin happiness causes large feet.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
0",mediation,penguin,3,det-counterfactual,Y_{X=1} = 0 | 
25472,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin saddness. taking the elevator and penguin happiness causes large feet.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
0",mediation,penguin,3,det-counterfactual,Y_{X=0} = 1 | 
25473,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin saddness. taking the elevator and penguin happiness causes large feet.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
1",mediation,penguin,3,det-counterfactual,Y_{X=0} = 0 | 
25474,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin saddness. taking the elevator and penguin happiness causes large feet.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
0",mediation,penguin,3,det-counterfactual,Y_{X=1} = 1 | 
25475,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin saddness. taking the elevator and penguin happiness causes large feet.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
1",mediation,penguin,3,det-counterfactual,Y_{X=1} = 0 | 
25476,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin happiness. taking the elevator and penguin happiness causes large feet.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
0",mediation,penguin,3,det-counterfactual,Y_{X=0} = 1 | 
25477,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin happiness. taking the elevator and penguin happiness causes large feet.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
1",mediation,penguin,3,det-counterfactual,Y_{X=0} = 0 | 
25478,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin happiness. taking the elevator and penguin happiness causes large feet.",yes,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
1",mediation,penguin,3,det-counterfactual,Y_{X=1} = 1 | 
25479,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: My decision has a direct effect on penguin mood and foot size. Penguin mood has a direct effect on foot size. We know that taking the elevator causes penguin happiness. taking the elevator and penguin happiness causes large feet.",no,"Let X = my decision; V2 = penguin mood; Y = foot size.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
0",mediation,penguin,3,det-counterfactual,Y_{X=1} = 0 | 
25480,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and severe vaccination reaction. having smallpox and severe vaccination reaction causes smallpox survival.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [0] = 0 and 0
0",diamond,vaccine_kills,3,det-counterfactual,Y_{X=0} = 1 | 
25481,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and severe vaccination reaction. having smallpox and severe vaccination reaction causes smallpox survival.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [0] = 0 and 0
1",diamond,vaccine_kills,3,det-counterfactual,Y_{X=0} = 0 | 
25482,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and severe vaccination reaction. having smallpox and severe vaccination reaction causes smallpox survival.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [1] = 1 and 1
1",diamond,vaccine_kills,3,det-counterfactual,Y_{X=1} = 1 | 
25483,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and severe vaccination reaction. having smallpox and severe vaccination reaction causes smallpox survival.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 and V3
Y = [1] = 1 and 1
0",diamond,vaccine_kills,3,det-counterfactual,Y_{X=1} = 0 | 
25484,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and no vaccine reaction. having smallpox and severe vaccination reaction causes smallpox survival.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 0 and 1
0",diamond,vaccine_kills,3,det-counterfactual,Y_{X=0} = 1 | 
25485,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and no vaccine reaction. having smallpox and severe vaccination reaction causes smallpox survival.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 0 and 1
1",diamond,vaccine_kills,3,det-counterfactual,Y_{X=0} = 0 | 
25486,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and no vaccine reaction. having smallpox and severe vaccination reaction causes smallpox survival.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 1 and 0
0",diamond,vaccine_kills,3,det-counterfactual,Y_{X=1} = 1 | 
25487,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and no vaccine reaction. having smallpox and severe vaccination reaction causes smallpox survival.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 and V3
Y = [0] = 1 and 0
1",diamond,vaccine_kills,3,det-counterfactual,Y_{X=1} = 0 | 
25488,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and severe vaccination reaction. having smallpox or severe vaccination reaction causes smallpox survival.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [0] = 0 or 0
0",diamond,vaccine_kills,3,det-counterfactual,Y_{X=0} = 1 | 
25489,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and severe vaccination reaction. having smallpox or severe vaccination reaction causes smallpox survival.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [0] = 0 or 0
1",diamond,vaccine_kills,3,det-counterfactual,Y_{X=0} = 0 | 
25490,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and severe vaccination reaction. having smallpox or severe vaccination reaction causes smallpox survival.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [1] = 1 or 1
1",diamond,vaccine_kills,3,det-counterfactual,Y_{X=1} = 1 | 
25491,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and severe vaccination reaction. having smallpox or severe vaccination reaction causes smallpox survival.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = V2
Y = V2 or V3
Y = [1] = 1 or 1
0",diamond,vaccine_kills,3,det-counterfactual,Y_{X=1} = 0 | 
25492,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and no vaccine reaction. having smallpox or severe vaccination reaction causes smallpox survival.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 0 or 1
1",diamond,vaccine_kills,3,det-counterfactual,Y_{X=0} = 1 | 
25493,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and no vaccine reaction. having smallpox or severe vaccination reaction causes smallpox survival.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 0 or 1
0",diamond,vaccine_kills,3,det-counterfactual,Y_{X=0} = 0 | 
25494,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and no vaccine reaction. having smallpox or severe vaccination reaction causes smallpox survival.",yes,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 1 or 0
1",diamond,vaccine_kills,3,det-counterfactual,Y_{X=1} = 1 | 
25495,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a brother has a direct effect on vaccination reaction and getting smallpox. Getting smallpox has a direct effect on smallpox survival. Vaccination reaction has a direct effect on smallpox survival. We know that having a brother causes having smallpox and no vaccine reaction. having smallpox or severe vaccination reaction causes smallpox survival.",no,"Let X = having a brother; V3 = vaccination reaction; V2 = getting smallpox; Y = smallpox survival.
X->V3,X->V2,V2->Y,V3->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
V3 = not V2
Y = V2 or V3
Y = [1] = 1 or 0
0",diamond,vaccine_kills,3,det-counterfactual,Y_{X=1} = 0 | 
25496,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes low blood pressure. having a sister or high blood pressure causes healthy heart.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
1",mediation,blood_pressure,3,det-counterfactual,Y_{X=0} = 1 | 
25497,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes low blood pressure. having a sister or high blood pressure causes healthy heart.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
0",mediation,blood_pressure,3,det-counterfactual,Y_{X=0} = 0 | 
25498,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes low blood pressure. having a sister or high blood pressure causes healthy heart.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
1",mediation,blood_pressure,3,det-counterfactual,Y_{X=1} = 1 | 
25499,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes low blood pressure. having a sister or high blood pressure causes healthy heart.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
0",mediation,blood_pressure,3,det-counterfactual,Y_{X=1} = 0 | 
25500,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes low blood pressure. having a sister and high blood pressure causes healthy heart.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
0",mediation,blood_pressure,3,det-counterfactual,Y_{X=0} = 1 | 
25501,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes low blood pressure. having a sister and high blood pressure causes healthy heart.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
1",mediation,blood_pressure,3,det-counterfactual,Y_{X=0} = 0 | 
25502,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes low blood pressure. having a sister and high blood pressure causes healthy heart.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
0",mediation,blood_pressure,3,det-counterfactual,Y_{X=1} = 1 | 
25503,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes low blood pressure. having a sister and high blood pressure causes healthy heart.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
1",mediation,blood_pressure,3,det-counterfactual,Y_{X=1} = 0 | 
25504,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes high blood pressure. having a sister or high blood pressure causes healthy heart.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
0",mediation,blood_pressure,3,det-counterfactual,Y_{X=0} = 1 | 
25505,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes high blood pressure. having a sister or high blood pressure causes healthy heart.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
1",mediation,blood_pressure,3,det-counterfactual,Y_{X=0} = 0 | 
25506,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes high blood pressure. having a sister or high blood pressure causes healthy heart.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
1",mediation,blood_pressure,3,det-counterfactual,Y_{X=1} = 1 | 
25507,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes high blood pressure. having a sister or high blood pressure causes healthy heart.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
0",mediation,blood_pressure,3,det-counterfactual,Y_{X=1} = 0 | 
25508,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes high blood pressure. having a sister and high blood pressure causes healthy heart.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
0",mediation,blood_pressure,3,det-counterfactual,Y_{X=0} = 1 | 
25509,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes high blood pressure. having a sister and high blood pressure causes healthy heart.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
1",mediation,blood_pressure,3,det-counterfactual,Y_{X=0} = 0 | 
25510,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes high blood pressure. having a sister and high blood pressure causes healthy heart.",yes,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
1",mediation,blood_pressure,3,det-counterfactual,Y_{X=1} = 1 | 
25511,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having a sister has a direct effect on blood pressure and heart condition. Blood pressure has a direct effect on heart condition. We know that having a sister causes high blood pressure. having a sister and high blood pressure causes healthy heart.",no,"Let X = having a sister; V2 = blood pressure; Y = heart condition.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
0",mediation,blood_pressure,3,det-counterfactual,Y_{X=1} = 0 | 
25514,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25515,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25516,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
25517,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
25520,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25522,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25523,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25524,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
25525,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
25527,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25528,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
25529,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25530,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25531,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25534,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
25537,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25538,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25539,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25540,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
25541,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
25542,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
25543,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active or assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25544,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
25545,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25546,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25547,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25548,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
25549,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
25551,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
25552,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25553,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25555,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25556,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
25557,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
25559,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active and taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25560,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
25561,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25562,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25563,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25566,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
25567,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is not assigned the drug treatment and confounder active.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
25568,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25569,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25570,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25571,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder inactive.",no,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,cholesterol,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25572,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drug taken and freckles. Treatment assignment has a direct effect on drug taken. Drug taken has a direct effect on freckles. Unobserved confounders is unobserved. We know that confounder active and assignment of drug treatment causes taking of all assigned drugs. confounder active or taking of all assigned drugs causes freckles. We observed the patient is assigned the treatment and confounder active.",yes,"Let V2 = treatment assignment; V1 = unobserved confounders; X = drug taken; Y = freckles.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,cholesterol,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
25576,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes low skill level, and we know that high skill level causes blond hair.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [0] = not 1
0",chain,college_salary,3,det-counterfactual,Y_{X=0} = 1 | 
25577,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes low skill level, and we know that high skill level causes blond hair.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [0] = not 1
1",chain,college_salary,3,det-counterfactual,Y_{X=0} = 0 | 
25578,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes low skill level, and we know that high skill level causes blond hair.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [1] = not 0
1",chain,college_salary,3,det-counterfactual,Y_{X=1} = 1 | 
25579,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes low skill level, and we know that high skill level causes blond hair.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [1] = not 0
0",chain,college_salary,3,det-counterfactual,Y_{X=1} = 0 | 
25580,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes low skill level, and we know that high skill level causes black hair.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [1] = 1
1",chain,college_salary,3,det-counterfactual,Y_{X=0} = 1 | 
25581,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes low skill level, and we know that high skill level causes black hair.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [1] = 1
0",chain,college_salary,3,det-counterfactual,Y_{X=0} = 0 | 
25582,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes low skill level, and we know that high skill level causes black hair.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [0] = 0
0",chain,college_salary,3,det-counterfactual,Y_{X=1} = 1 | 
25583,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes low skill level, and we know that high skill level causes black hair.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [0] = 0
1",chain,college_salary,3,det-counterfactual,Y_{X=1} = 0 | 
25584,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes high skill level, and we know that high skill level causes blond hair.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [1] = not 0
1",chain,college_salary,3,det-counterfactual,Y_{X=0} = 1 | 
25585,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes high skill level, and we know that high skill level causes blond hair.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [1] = not 0
0",chain,college_salary,3,det-counterfactual,Y_{X=0} = 0 | 
25586,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes high skill level, and we know that high skill level causes blond hair.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [0] = not 1
0",chain,college_salary,3,det-counterfactual,Y_{X=1} = 1 | 
25587,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes high skill level, and we know that high skill level causes blond hair.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [0] = not 1
1",chain,college_salary,3,det-counterfactual,Y_{X=1} = 0 | 
25588,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes high skill level, and we know that high skill level causes black hair.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [0] = 0
0",chain,college_salary,3,det-counterfactual,Y_{X=0} = 1 | 
25589,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes high skill level, and we know that high skill level causes black hair.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [0] = 0
1",chain,college_salary,3,det-counterfactual,Y_{X=0} = 0 | 
25590,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes high skill level, and we know that high skill level causes black hair.",yes,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [1] = 1
1",chain,college_salary,3,det-counterfactual,Y_{X=1} = 1 | 
25591,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Education level has a direct effect on skill. Skill has a direct effect on black hair. We know that college degree or higher causes high skill level, and we know that high skill level causes black hair.",no,"Let X = education level; V2 = skill; Y = black hair.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [1] = 1
0",chain,college_salary,3,det-counterfactual,Y_{X=1} = 0 | 
25593,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25594,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25596,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
25597,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
25598,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
25599,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
25600,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25602,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25603,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25604,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
25606,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
25607,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25608,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
25610,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25612,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
25614,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
25615,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
25616,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25617,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25618,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25619,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25621,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
25622,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
25623,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25624,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
25626,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25627,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25628,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
25629,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
25631,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
25632,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25633,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25634,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25635,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25637,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
25638,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
25639,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active or close to a college causes drinking coffee. confounder active or drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25641,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25642,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25643,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25646,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives far from a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
25648,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25649,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,college_wage,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25650,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",no,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25651,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder inactive.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25654,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on drinking coffee and salary. Proximity to a college has a direct effect on drinking coffee. Drinking coffee has a direct effect on salary. Unobserved confounders is unobserved. We know that confounder active and close to a college causes drinking coffee. confounder active and drinking coffee causes high salary. We observed the person lives close to a college and confounder active.",yes,"Let V2 = proximity to a college; V1 = unobserved confounders; X = drinking coffee; Y = salary.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,college_wage,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
25656,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes lack of studying. being able to swim or studying hard causes high exam score.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
1",mediation,encouagement_program,3,det-counterfactual,Y_{X=0} = 1 | 
25657,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes lack of studying. being able to swim or studying hard causes high exam score.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
0",mediation,encouagement_program,3,det-counterfactual,Y_{X=0} = 0 | 
25658,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes lack of studying. being able to swim or studying hard causes high exam score.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
1",mediation,encouagement_program,3,det-counterfactual,Y_{X=1} = 1 | 
25659,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes lack of studying. being able to swim or studying hard causes high exam score.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
0",mediation,encouagement_program,3,det-counterfactual,Y_{X=1} = 0 | 
25660,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes studying hard. being able to swim and studying hard causes high exam score.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
0",mediation,encouagement_program,3,det-counterfactual,Y_{X=0} = 1 | 
25661,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes studying hard. being able to swim and studying hard causes high exam score.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
1",mediation,encouagement_program,3,det-counterfactual,Y_{X=0} = 0 | 
25662,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes studying hard. being able to swim and studying hard causes high exam score.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
1",mediation,encouagement_program,3,det-counterfactual,Y_{X=1} = 1 | 
25663,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes studying hard. being able to swim and studying hard causes high exam score.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
0",mediation,encouagement_program,3,det-counterfactual,Y_{X=1} = 0 | 
25664,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes studying hard. being able to swim or studying hard causes high exam score.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
0",mediation,encouagement_program,3,det-counterfactual,Y_{X=0} = 1 | 
25665,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes studying hard. being able to swim or studying hard causes high exam score.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
1",mediation,encouagement_program,3,det-counterfactual,Y_{X=0} = 0 | 
25666,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes studying hard. being able to swim or studying hard causes high exam score.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
1",mediation,encouagement_program,3,det-counterfactual,Y_{X=1} = 1 | 
25667,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes studying hard. being able to swim or studying hard causes high exam score.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
0",mediation,encouagement_program,3,det-counterfactual,Y_{X=1} = 0 | 
25668,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes lack of studying. being able to swim and studying hard causes high exam score.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
0",mediation,encouagement_program,3,det-counterfactual,Y_{X=0} = 1 | 
25669,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes lack of studying. being able to swim and studying hard causes high exam score.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
1",mediation,encouagement_program,3,det-counterfactual,Y_{X=0} = 0 | 
25670,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes lack of studying. being able to swim and studying hard causes high exam score.",no,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
0",mediation,encouagement_program,3,det-counterfactual,Y_{X=1} = 1 | 
25671,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to swim has a direct effect on studying habit and exam score. Studying habit has a direct effect on exam score. We know that being able to swim causes lack of studying. being able to swim and studying hard causes high exam score.",yes,"Let X = ability to swim; V2 = studying habit; Y = exam score.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
1",mediation,encouagement_program,3,det-counterfactual,Y_{X=1} = 0 | 
25672,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes non-competitive department. male gender and competitive department causes being allergic to peanuts.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
0",mediation,gender_admission,3,det-counterfactual,Y_{X=0} = 1 | 
25673,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes non-competitive department. male gender and competitive department causes being allergic to peanuts.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
1",mediation,gender_admission,3,det-counterfactual,Y_{X=0} = 0 | 
25674,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes non-competitive department. male gender and competitive department causes being allergic to peanuts.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
0",mediation,gender_admission,3,det-counterfactual,Y_{X=1} = 1 | 
25675,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes non-competitive department. male gender and competitive department causes being allergic to peanuts.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
1",mediation,gender_admission,3,det-counterfactual,Y_{X=1} = 0 | 
25676,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes non-competitive department. male gender or competitive department causes being allergic to peanuts.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
1",mediation,gender_admission,3,det-counterfactual,Y_{X=0} = 1 | 
25677,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes non-competitive department. male gender or competitive department causes being allergic to peanuts.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
0",mediation,gender_admission,3,det-counterfactual,Y_{X=0} = 0 | 
25678,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes non-competitive department. male gender or competitive department causes being allergic to peanuts.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
1",mediation,gender_admission,3,det-counterfactual,Y_{X=1} = 1 | 
25679,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes non-competitive department. male gender or competitive department causes being allergic to peanuts.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
0",mediation,gender_admission,3,det-counterfactual,Y_{X=1} = 0 | 
25680,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes competitive department. male gender or competitive department causes being allergic to peanuts.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
0",mediation,gender_admission,3,det-counterfactual,Y_{X=0} = 1 | 
25681,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes competitive department. male gender or competitive department causes being allergic to peanuts.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
1",mediation,gender_admission,3,det-counterfactual,Y_{X=0} = 0 | 
25682,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes competitive department. male gender or competitive department causes being allergic to peanuts.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
1",mediation,gender_admission,3,det-counterfactual,Y_{X=1} = 1 | 
25683,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes competitive department. male gender or competitive department causes being allergic to peanuts.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
0",mediation,gender_admission,3,det-counterfactual,Y_{X=1} = 0 | 
25684,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes competitive department. male gender and competitive department causes being allergic to peanuts.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
0",mediation,gender_admission,3,det-counterfactual,Y_{X=0} = 1 | 
25685,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes competitive department. male gender and competitive department causes being allergic to peanuts.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
1",mediation,gender_admission,3,det-counterfactual,Y_{X=0} = 0 | 
25686,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes competitive department. male gender and competitive department causes being allergic to peanuts.",yes,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
1",mediation,gender_admission,3,det-counterfactual,Y_{X=1} = 1 | 
25687,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and peanut allergy. Department competitiveness has a direct effect on peanut allergy. We know that male gender causes competitive department. male gender and competitive department causes being allergic to peanuts.",no,"Let X = gender; V2 = department competitiveness; Y = peanut allergy.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
0",mediation,gender_admission,3,det-counterfactual,Y_{X=1} = 0 | 
25688,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the residency is out-of-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25689,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the residency is out-of-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25690,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the residency is out-of-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25691,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the residency is out-of-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25692,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the resident is in-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25693,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the resident is in-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25694,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the resident is in-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25695,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the resident is in-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25696,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the residency is out-of-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25697,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the residency is out-of-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25698,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the residency is out-of-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25699,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the residency is out-of-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25700,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the resident is in-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25701,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the resident is in-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25702,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the resident is in-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25703,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the resident is in-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25704,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the residency is out-of-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25705,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the residency is out-of-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25706,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the residency is out-of-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25707,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the residency is out-of-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25708,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the resident is in-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25709,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the resident is in-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25710,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the resident is in-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25711,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender and in-state residency causes competitive department. male gender and in-state residency and competitive department causes brown eyes. We observed the resident is in-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25712,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the residency is out-of-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25713,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the residency is out-of-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25714,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the residency is out-of-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25715,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the residency is out-of-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25716,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the resident is in-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25717,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the resident is in-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25718,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the resident is in-state.",yes,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25719,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on department competitiveness and brown eyes. Residency status has a direct effect on department competitiveness and brown eyes. Department competitiveness has a direct effect on brown eyes. Residency status is unobserved. We know that male gender or in-state residency causes competitive department. male gender or in-state residency or competitive department causes brown eyes. We observed the resident is in-state.",no,"Let V2 = residency status; X = gender; V3 = department competitiveness; Y = brown eyes.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,gender_admission_state,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25720,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a low skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25721,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a low skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25722,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a low skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25723,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a low skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25724,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a high skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25725,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a high skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25726,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a high skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25727,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a high skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25728,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a low skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25729,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a low skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25730,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a low skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25731,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a low skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25732,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a high skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25733,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a high skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25734,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a high skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25735,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a high skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25736,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a low skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25737,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a low skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25738,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a low skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25739,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a low skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25740,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a high skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25741,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a high skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25742,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a high skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25743,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England and high skill level causes white-collar job. having visited England and high skill level and white-collar job causes high salary. We observed the person has a high skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25744,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a low skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25745,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a low skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25746,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a low skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25747,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a low skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25748,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a high skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25749,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a high skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25750,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a high skill level.",yes,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25751,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Having visited England has a direct effect on occupation and salary. Skill has a direct effect on occupation and salary. Occupation has a direct effect on salary. Skill is unobserved. We know that having visited England or high skill level causes white-collar job. having visited England or high skill level or white-collar job causes high salary. We observed the person has a high skill level.",no,"Let V2 = skill; X = having visited England; V3 = occupation; Y = salary.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,gender_pay,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25752,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder inactive.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25753,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder inactive.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25754,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder inactive.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25755,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder inactive.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25756,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder active.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25757,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder active.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25758,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder active.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25759,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder active.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25760,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder inactive.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25761,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder inactive.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25762,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder inactive.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25763,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder inactive.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25764,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder active.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25765,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder active.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25766,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder active.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25767,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food or confounder active or high parental social status causes intelligent child. We observed confounder active.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25768,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder inactive.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25769,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder inactive.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25770,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder inactive.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25771,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder inactive.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25772,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder active.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25773,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder active.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25774,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder active.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25775,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food or confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder active.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25776,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder inactive.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25777,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder inactive.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25778,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder inactive.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25779,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder inactive.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25780,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder active.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25781,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder active.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25782,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder active.",yes,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25783,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Liking spicy food has a direct effect on parents' social status and child's intelligence. Other unobserved factors has a direct effect on parents' social status and child's intelligence. Parents' social status has a direct effect on child's intelligence. Other unobserved factors is unobserved. We know that liking spicy food and confounder active causes high parental social status. liking spicy food and confounder active and high parental social status causes intelligent child. We observed confounder active.",no,"Let V2 = other unobserved factors; X = liking spicy food; V3 = parents' social status; Y = child's intelligence.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,nature_vs_nurture,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25784,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being lazy. smoking or being hard-working causes being lactose intolerant.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
1",mediation,neg_mediation,3,det-counterfactual,Y_{X=0} = 1 | 
25785,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being lazy. smoking or being hard-working causes being lactose intolerant.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 0 or 1
0",mediation,neg_mediation,3,det-counterfactual,Y_{X=0} = 0 | 
25786,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being lazy. smoking or being hard-working causes being lactose intolerant.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
1",mediation,neg_mediation,3,det-counterfactual,Y_{X=1} = 1 | 
25787,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being lazy. smoking or being hard-working causes being lactose intolerant.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X or V2
Y = 1 = 1 or 0
0",mediation,neg_mediation,3,det-counterfactual,Y_{X=1} = 0 | 
25788,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being hard-working. smoking and being hard-working causes being lactose intolerant.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
0",mediation,neg_mediation,3,det-counterfactual,Y_{X=0} = 1 | 
25789,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being hard-working. smoking and being hard-working causes being lactose intolerant.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 0 = 0 and 0
1",mediation,neg_mediation,3,det-counterfactual,Y_{X=0} = 0 | 
25790,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being hard-working. smoking and being hard-working causes being lactose intolerant.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
1",mediation,neg_mediation,3,det-counterfactual,Y_{X=1} = 1 | 
25791,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being hard-working. smoking and being hard-working causes being lactose intolerant.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X and V2
Y = 1 = 1 and 1
0",mediation,neg_mediation,3,det-counterfactual,Y_{X=1} = 0 | 
25792,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being lazy. smoking and being hard-working causes being lactose intolerant.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
0",mediation,neg_mediation,3,det-counterfactual,Y_{X=0} = 1 | 
25793,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being lazy. smoking and being hard-working causes being lactose intolerant.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 0 and 1
1",mediation,neg_mediation,3,det-counterfactual,Y_{X=0} = 0 | 
25794,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being lazy. smoking and being hard-working causes being lactose intolerant.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
0",mediation,neg_mediation,3,det-counterfactual,Y_{X=1} = 1 | 
25795,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being lazy. smoking and being hard-working causes being lactose intolerant.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = X and V2
Y = 0 = 1 and 0
1",mediation,neg_mediation,3,det-counterfactual,Y_{X=1} = 0 | 
25796,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being hard-working. smoking or being hard-working causes being lactose intolerant.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
0",mediation,neg_mediation,3,det-counterfactual,Y_{X=0} = 1 | 
25797,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being hard-working. smoking or being hard-working causes being lactose intolerant.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 0 = 0 or 0
1",mediation,neg_mediation,3,det-counterfactual,Y_{X=0} = 0 | 
25798,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being hard-working. smoking or being hard-working causes being lactose intolerant.",yes,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
1",mediation,neg_mediation,3,det-counterfactual,Y_{X=1} = 1 | 
25799,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Smoking has a direct effect on effort and lactose intolerance. Effort has a direct effect on lactose intolerance. We know that smoking causes being hard-working. smoking or being hard-working causes being lactose intolerant.",no,"Let X = smoking; V2 = effort; Y = lactose intolerance.
X->V2,X->Y,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = X or V2
Y = 1 = 1 or 1
0",mediation,neg_mediation,3,det-counterfactual,Y_{X=1} = 0 | 
25800,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a nonsmoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25801,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a nonsmoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25802,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a nonsmoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25803,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a nonsmoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25804,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a smoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25805,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a smoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25806,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a smoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25807,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a smoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25808,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a nonsmoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25809,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a nonsmoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25810,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a nonsmoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25811,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a nonsmoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25812,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a smoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25813,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a smoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25814,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a smoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25815,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english and smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a smoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25816,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a nonsmoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25817,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a nonsmoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25818,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a nonsmoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25819,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a nonsmoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25820,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a smoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25821,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a smoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25822,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a smoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25823,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english and smoker and having diabetes causes long lifespan. We observed the person is a smoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25824,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a nonsmoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 1 | V2=0
25825,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a nonsmoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 0 | V2=0
25826,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a nonsmoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 1 | V2=0
25827,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a nonsmoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 0 | V2=0
25828,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a smoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 1 | V2=1
25829,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a smoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=0} = 0 | V2=1
25830,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a smoker.",yes,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 1 | V2=1
25831,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Ability to speak english has a direct effect on diabetes and lifespan. Smoking has a direct effect on diabetes and lifespan. Diabetes has a direct effect on lifespan. Smoking is unobserved. We know that speaking english or smoker causes having diabetes. speaking english or smoker or having diabetes causes long lifespan. We observed the person is a smoker.",no,"Let V2 = smoking; X = ability to speak english; V3 = diabetes; Y = lifespan.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,obesity_mortality,3,det-counterfactual,Y_{X=1} = 0 | V2=1
25832,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes vitamin C deficiency, and we know that sufficient vitamin C causes curly hair.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [1] = 1
1",chain,orange_scurvy,3,det-counterfactual,Y_{X=0} = 1 | 
25833,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes vitamin C deficiency, and we know that sufficient vitamin C causes curly hair.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [1] = 1
0",chain,orange_scurvy,3,det-counterfactual,Y_{X=0} = 0 | 
25834,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes vitamin C deficiency, and we know that sufficient vitamin C causes curly hair.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [0] = 0
0",chain,orange_scurvy,3,det-counterfactual,Y_{X=1} = 1 | 
25835,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes vitamin C deficiency, and we know that sufficient vitamin C causes curly hair.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [0] = 0
1",chain,orange_scurvy,3,det-counterfactual,Y_{X=1} = 0 | 
25836,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes vitamin C deficiency, and we know that sufficient vitamin C causes straight hair.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [0] = not 1
0",chain,orange_scurvy,3,det-counterfactual,Y_{X=0} = 1 | 
25837,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes vitamin C deficiency, and we know that sufficient vitamin C causes straight hair.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [0] = not 1
1",chain,orange_scurvy,3,det-counterfactual,Y_{X=0} = 0 | 
25838,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes vitamin C deficiency, and we know that sufficient vitamin C causes straight hair.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [1] = not 0
1",chain,orange_scurvy,3,det-counterfactual,Y_{X=1} = 1 | 
25839,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes vitamin C deficiency, and we know that sufficient vitamin C causes straight hair.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [1] = not 0
0",chain,orange_scurvy,3,det-counterfactual,Y_{X=1} = 0 | 
25840,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes sufficient vitamin C, and we know that sufficient vitamin C causes curly hair.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [0] = 0
0",chain,orange_scurvy,3,det-counterfactual,Y_{X=0} = 1 | 
25841,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes sufficient vitamin C, and we know that sufficient vitamin C causes curly hair.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [0] = 0
1",chain,orange_scurvy,3,det-counterfactual,Y_{X=0} = 0 | 
25842,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes sufficient vitamin C, and we know that sufficient vitamin C causes curly hair.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [1] = 1
1",chain,orange_scurvy,3,det-counterfactual,Y_{X=1} = 1 | 
25843,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes sufficient vitamin C, and we know that sufficient vitamin C causes curly hair.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [1] = 1
0",chain,orange_scurvy,3,det-counterfactual,Y_{X=1} = 0 | 
25844,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes sufficient vitamin C, and we know that sufficient vitamin C causes straight hair.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [1] = not 0
1",chain,orange_scurvy,3,det-counterfactual,Y_{X=0} = 1 | 
25845,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes sufficient vitamin C, and we know that sufficient vitamin C causes straight hair.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [1] = not 0
0",chain,orange_scurvy,3,det-counterfactual,Y_{X=0} = 0 | 
25846,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes sufficient vitamin C, and we know that sufficient vitamin C causes straight hair.",no,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [0] = not 1
0",chain,orange_scurvy,3,det-counterfactual,Y_{X=1} = 1 | 
25847,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Eating citrus has a direct effect on vitmain C. Vitmain C has a direct effect on curly hair. We know that citrus intake causes sufficient vitamin C, and we know that sufficient vitamin C causes straight hair.",yes,"Let X = eating citrus; V2 = vitmain C; Y = curly hair.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [0] = not 1
1",chain,orange_scurvy,3,det-counterfactual,Y_{X=1} = 0 | 
25849,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25850,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25851,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25852,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
25853,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
25854,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
25855,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
25856,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25857,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25858,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25860,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
25861,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
25862,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
25863,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25865,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25867,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25868,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
25869,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
25870,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
25872,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25873,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25875,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25876,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
25878,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
25879,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand and increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25880,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
25881,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25882,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
25883,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
25885,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
25887,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
25891,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
25892,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
25893,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
25895,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand and increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25896,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
25897,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
25900,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
25901,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
25902,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
25903,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has a reduced yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
25904,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
25905,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
25906,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is low.",yes,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,price,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
25909,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,price,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
25911,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Demand has a direct effect on supply and rainfall. Yield per acre has a direct effect on supply. Supply has a direct effect on rainfall. Demand is unobserved. We know that increased demand or increased yield per acre causes increased supply. increased demand or increased supply causes high rainfall. We observed the farm has an increased yield per acre and the demand is high.",no,"Let V2 = yield per acre; V1 = demand; X = supply; Y = rainfall.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,price,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
25912,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender or having a brother causes recovery. We observed the patient is not male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 0 = 0 or 0
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25913,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender or having a brother causes recovery. We observed the patient is not male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 0 = 0 or 0
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25914,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender or having a brother causes recovery. We observed the patient is not male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 1 = 0 or 1
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25915,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender or having a brother causes recovery. We observed the patient is not male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 1 = 0 or 1
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25916,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender or having a brother causes recovery. We observed the patient is male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 0
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25917,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender or having a brother causes recovery. We observed the patient is male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 0
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25918,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender or having a brother causes recovery. We observed the patient is male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 1
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25919,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender or having a brother causes recovery. We observed the patient is male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 1
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25920,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender and having a brother causes recovery. We observed the patient is not male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 0
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25921,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender and having a brother causes recovery. We observed the patient is not male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 0
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25922,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender and having a brother causes recovery. We observed the patient is not male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 1
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25923,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender and having a brother causes recovery. We observed the patient is not male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 1
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25924,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender and having a brother causes recovery. We observed the patient is male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 0 = 1 and 0
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25925,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender and having a brother causes recovery. We observed the patient is male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 0 = 1 and 0
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25926,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender and having a brother causes recovery. We observed the patient is male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 1 = 1 and 1
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25927,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes having a brother. male gender and having a brother causes recovery. We observed the patient is male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 1 = 1 and 1
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25928,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender and having a brother causes recovery. We observed the patient is not male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 0
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25929,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender and having a brother causes recovery. We observed the patient is not male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 0
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25930,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender and having a brother causes recovery. We observed the patient is not male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 1
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25931,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender and having a brother causes recovery. We observed the patient is not male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 1
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25932,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender and having a brother causes recovery. We observed the patient is male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 0 = 1 and 0
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25933,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender and having a brother causes recovery. We observed the patient is male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 0 = 1 and 0
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25934,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender and having a brother causes recovery. We observed the patient is male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 1 = 1 and 1
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25935,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender and having a brother causes recovery. We observed the patient is male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 1 = 1 and 1
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25936,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender or having a brother causes recovery. We observed the patient is not male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 0 = 0 or 0
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25937,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender or having a brother causes recovery. We observed the patient is not male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 0 = 0 or 0
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25938,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender or having a brother causes recovery. We observed the patient is not male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 1 = 0 or 1
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25939,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender or having a brother causes recovery. We observed the patient is not male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 1 = 0 or 1
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25940,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender or having a brother causes recovery. We observed the patient is male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 0
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25941,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender or having a brother causes recovery. We observed the patient is male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 0
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25942,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender or having a brother causes recovery. We observed the patient is male.",yes,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 1
1",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25943,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on having a brother and recovery. Having a brother has a direct effect on recovery. We know that male gender causes not having a brother. male gender or having a brother causes recovery. We observed the patient is male.",no,"Let V1 = gender; X = having a brother; Y = recovery.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 1
0",confounding,simpson_drug,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25944,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age and high hospital bill causes freckles. We observed the patient is young.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 0
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25945,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age and high hospital bill causes freckles. We observed the patient is young.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 0
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25946,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age and high hospital bill causes freckles. We observed the patient is young.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 1
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25947,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age and high hospital bill causes freckles. We observed the patient is young.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 1
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25948,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age and high hospital bill causes freckles. We observed the patient is old.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 0 = 1 and 0
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25949,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age and high hospital bill causes freckles. We observed the patient is old.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 0 = 1 and 0
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25950,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age and high hospital bill causes freckles. We observed the patient is old.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 1 = 1 and 1
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25951,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age and high hospital bill causes freckles. We observed the patient is old.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 1 = 1 and 1
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25952,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age and high hospital bill causes freckles. We observed the patient is young.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 0
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25953,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age and high hospital bill causes freckles. We observed the patient is young.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 0
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25954,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age and high hospital bill causes freckles. We observed the patient is young.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 1
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25955,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age and high hospital bill causes freckles. We observed the patient is young.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 1
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25956,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age and high hospital bill causes freckles. We observed the patient is old.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 0 = 1 and 0
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25957,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age and high hospital bill causes freckles. We observed the patient is old.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 0 = 1 and 0
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25958,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age and high hospital bill causes freckles. We observed the patient is old.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 1 = 1 and 1
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25959,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age and high hospital bill causes freckles. We observed the patient is old.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 1 = 1 and 1
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25960,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age or high hospital bill causes freckles. We observed the patient is young.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 0 = 0 or 0
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25961,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age or high hospital bill causes freckles. We observed the patient is young.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 0 = 0 or 0
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25962,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age or high hospital bill causes freckles. We observed the patient is young.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 1 = 0 or 1
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25963,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age or high hospital bill causes freckles. We observed the patient is young.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 1 = 0 or 1
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25964,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age or high hospital bill causes freckles. We observed the patient is old.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 0
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25965,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age or high hospital bill causes freckles. We observed the patient is old.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 0
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25966,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age or high hospital bill causes freckles. We observed the patient is old.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 1
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25967,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes high hospital bill. old age or high hospital bill causes freckles. We observed the patient is old.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 1
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25968,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age or high hospital bill causes freckles. We observed the patient is young.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 0 = 0 or 0
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25969,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age or high hospital bill causes freckles. We observed the patient is young.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 0 = 0 or 0
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25970,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age or high hospital bill causes freckles. We observed the patient is young.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 1 = 0 or 1
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25971,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age or high hospital bill causes freckles. We observed the patient is young.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 1 = 0 or 1
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25972,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age or high hospital bill causes freckles. We observed the patient is old.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 0
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25973,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age or high hospital bill causes freckles. We observed the patient is old.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 0
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25974,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age or high hospital bill causes freckles. We observed the patient is old.",yes,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 1
1",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25975,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Age has a direct effect on hospital costs and freckles. Hospital costs has a direct effect on freckles. We know that old age causes low hospital bill. old age or high hospital bill causes freckles. We observed the patient is old.",no,"Let V1 = age; X = hospital costs; Y = freckles.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 1
0",confounding,simpson_hospital,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25976,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a small kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 0 = 0 or 0
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25977,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a small kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 0 = 0 or 0
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25978,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a small kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 1 = 0 or 1
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25979,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a small kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 1 = 0 or 1
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25980,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a large kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 0
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25981,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a large kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 0
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25982,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a large kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 1
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25983,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a large kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 1
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25984,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a small kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 0
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25985,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a small kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 0
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25986,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a small kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 1
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25987,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a small kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 1
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25988,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a large kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 0 = 1 and 0
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25989,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a large kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 0 = 1 and 0
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25990,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a large kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 1 = 1 and 1
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25991,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives no treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a large kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 1 = 1 and 1
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 0 | V1=1
25992,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a small kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 0 = 0 or 0
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 1 | V1=0
25993,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a small kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 0 = 0 or 0
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 0 | V1=0
25994,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a small kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 1 = 0 or 1
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 1 | V1=0
25995,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a small kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 1 = 0 or 1
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 0 | V1=0
25996,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a large kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 0
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 1 | V1=1
25997,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a large kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 0
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 0 | V1=1
25998,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a large kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 1
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 1 | V1=1
25999,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone or receives treatment causes thick lips. We observed the patient has a large kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 1
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26000,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a small kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 0
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26001,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a small kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 0
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26002,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a small kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 1
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26003,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a small kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 1
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26004,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a large kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 0 = 1 and 0
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26005,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a large kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 0 = 1 and 0
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26006,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a large kidney stone.",yes,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 1 = 1 and 1
1",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26007,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Kidney stone size has a direct effect on treatment and lip thickness. Treatment has a direct effect on lip thickness. We know that large kidney stone causes receives treatment. large kidney stone and receives treatment causes thick lips. We observed the patient has a large kidney stone.",no,"Let V1 = kidney stone size; X = treatment; Y = lip thickness.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 1 = 1 and 1
0",confounding,simpson_kidneystone,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26008,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 0 = 0 or 0
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26009,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 0 = 0 or 0
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26010,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 1 = 0 or 1
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26011,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 or X
Y = 1 = 0 or 1
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26012,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 0
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26013,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 0
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26014,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 1
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26015,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 or X
Y = 1 = 1 or 1
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26016,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 0
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26017,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 0
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26018,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 1
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26019,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 and X
Y = 0 = 0 and 1
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26020,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 0 = 1 and 0
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26021,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 0 = 1 and 0
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26022,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 1 = 1 and 1
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26023,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 and X
Y = 1 = 1 and 1
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26024,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 0 = 0 or 0
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26025,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 0 = 0 or 0
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26026,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 1 = 0 or 1
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26027,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
Y = V1 or X
Y = 1 = 0 or 1
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26028,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 0
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26029,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 0
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26030,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 1
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26031,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes getting the vaccine. pre-conditions or getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
Y = V1 or X
Y = 1 = 1 or 1
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26032,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 0
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26033,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 0
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26034,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 1
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26035,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has no pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = not V1
Y = V1 and X
Y = 0 = 0 and 1
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26036,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 0 = 1 and 0
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26037,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 0 = 1 and 0
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26038,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",yes,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 1 = 1 and 1
1",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26039,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Pre-conditions has a direct effect on vaccination and lactose intolerance. Vaccination has a direct effect on lactose intolerance. We know that pre-conditions causes vaccine refusal. pre-conditions and getting the vaccine causes being lactose intolerant. We observed the person has pre-conditions.",no,"Let V1 = pre-conditions; X = vaccination; Y = lactose intolerance.
V1->X,V1->Y,X->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = not V1
Y = V1 and X
Y = 1 = 1 and 1
0",confounding,simpson_vaccine,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26040,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has poor health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 1 | V2=0
26041,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has poor health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 0 | V2=0
26042,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has poor health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 1 | V2=0
26043,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has poor health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 0 | V2=0
26044,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has good health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 1 | V2=1
26045,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has good health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 0 | V2=1
26046,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has good health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 1 | V2=1
26047,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has good health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 0 | V2=1
26048,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has poor health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 1 | V2=0
26049,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has poor health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 0 | V2=0
26050,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has poor health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 1 | V2=0
26051,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has poor health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 0 | V2=0
26052,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has good health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 1 | V2=1
26053,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has good health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 0 | V2=1
26054,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has good health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 1 | V2=1
26055,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has good health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 0 | V2=1
26056,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has poor health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 1 | V2=0
26057,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has poor health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 0 | V2=0
26058,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has poor health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 1 | V2=0
26059,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has poor health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 0 | V2=0
26060,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has good health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 1 | V2=1
26061,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has good health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 0 | V2=1
26062,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has good health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 1 | V2=1
26063,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother and good health causes normal infant birth weight. smoking mother and good health and normal infant birth weight causes freckles. We observed the person has good health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 0 | V2=1
26064,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has poor health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 1 | V2=0
26065,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has poor health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 0 | V2=0
26066,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has poor health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 1 | V2=0
26067,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has poor health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 0 | V2=0
26068,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has good health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 1 | V2=1
26069,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has good health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=0} = 0 | V2=1
26070,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has good health.",yes,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 1 | V2=1
26071,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Maternal smoking status has a direct effect on infant's birth weight and freckles. Health condition has a direct effect on infant's birth weight and freckles. Infant's birth weight has a direct effect on freckles. Health condition is unobserved. We know that smoking mother or good health causes normal infant birth weight. smoking mother or good health or normal infant birth weight causes freckles. We observed the person has good health.",no,"Let V2 = health condition; X = maternal smoking status; V3 = infant's birth weight; Y = freckles.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,smoke_birthWeight,3,det-counterfactual,Y_{X=1} = 0 | V2=1
26072,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is non-female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = V1 or V3
Y = 0 = 0 or 0
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26073,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is non-female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = V1 or V3
Y = 0 = 0 or 0
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26074,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is non-female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = V1 or V3
Y = 1 = 0 or 1
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26075,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is non-female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = V1 or V3
Y = 1 = 0 or 1
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26076,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = V1 or V3
Y = 1 = 1 or 0
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26077,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = V1 or V3
Y = 1 = 1 or 0
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26078,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = V1 or V3
Y = 1 = 1 or 1
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26079,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = V1 or V3
Y = 1 = 1 or 1
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26080,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is non-female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = V1 or V3
Y = 1 = 0 or 1
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26081,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is non-female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = V1 or V3
Y = 1 = 0 or 1
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26082,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is non-female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = V1 or V3
Y = 0 = 0 or 0
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26083,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is non-female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = V1 or V3
Y = 0 = 0 or 0
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26084,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = V1 or V3
Y = 1 = 1 or 1
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26085,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = V1 or V3
Y = 1 = 1 or 1
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26086,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = V1 or V3
Y = 1 = 1 or 0
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26087,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female or high tar deposit causes being allergic to peanuts. We observed the person is female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = V1 or V3
Y = 1 = 1 or 0
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26088,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is non-female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = V1 and V3
Y = 0 = 0 and 1
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26089,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is non-female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = V1 and V3
Y = 0 = 0 and 1
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26090,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is non-female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = V1 and V3
Y = 0 = 0 and 0
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26091,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is non-female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = not X
Y = V1 and V3
Y = 0 = 0 and 0
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26092,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = V1 and V3
Y = 1 = 1 and 1
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26093,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = V1 and V3
Y = 1 = 1 and 1
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26094,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = V1 and V3
Y = 0 = 1 and 0
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26095,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes absence of tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = not X
Y = V1 and V3
Y = 0 = 1 and 0
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26096,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is non-female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = V1 and V3
Y = 0 = 0 and 0
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 1 | V1=0
26097,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is non-female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = V1 and V3
Y = 0 = 0 and 0
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 0 | V1=0
26098,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is non-female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 1 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = V1 and V3
Y = 0 = 0 and 1
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 1 | V1=0
26099,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is non-female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 0 | V1=0
Solve for Y, given the evidence and the action
V1 = 0
X = V1
V3 = X
Y = V1 and V3
Y = 0 = 0 and 1
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 0 | V1=0
26100,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = V1 and V3
Y = 0 = 1 and 0
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 1 | V1=1
26101,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=0} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = V1 and V3
Y = 0 = 1 and 0
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=0} = 0 | V1=1
26102,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is female.",yes,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 1 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = V1 and V3
Y = 1 = 1 and 1
1",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 1 | V1=1
26103,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Gender has a direct effect on smoking and peanut allergy. Smoking has a direct effect on tar deposit. Tar deposit has a direct effect on peanut allergy. Gender is unobserved. We know that female causes smoking. smoking causes high tar deposit. female and high tar deposit causes being allergic to peanuts. We observed the person is female.",no,"Let V1 = gender; X = smoking; V3 = tar deposit; Y = peanut allergy.
V1->X,X->V3,V1->Y,V3->Y
Y_{X=1} = 0 | V1=1
Solve for Y, given the evidence and the action
V1 = 1
X = V1
V3 = X
Y = V1 and V3
Y = 1 = 1 and 1
0",frontdoor,smoking_frontdoor,3,det-counterfactual,Y_{X=1} = 0 | V1=1
26104,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with low pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 1 | V2=0
26105,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with low pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 0 | V2=0
26106,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with low pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 1 | V2=0
26107,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with low pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 1
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 0 | V2=0
26108,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with high pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 1 | V2=1
26109,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with high pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 1
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 0 | V2=1
26110,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with high pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 1 | V2=1
26111,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with high pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 0 | V2=1
26112,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with low pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 1 | V2=0
26113,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with low pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 0 | V2=0
26114,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with low pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 1 | V2=0
26115,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with low pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 1
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 0 | V2=0
26116,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with high pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 1 | V2=1
26117,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with high pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 1
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 0 | V2=1
26118,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with high pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 1 | V2=1
26119,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz or high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with high pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X or V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 0 | V2=1
26120,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with low pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 1 | V2=0
26121,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with low pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 0 = 0 or 0 or 0
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 0 | V2=0
26122,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with low pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 1 | V2=0
26123,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with low pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 0 or 0
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 0 | V2=0
26124,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with high pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 1 | V2=1
26125,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with high pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 0 or 1 or 0
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 0 | V2=1
26126,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with high pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 1 | V2=1
26127,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz or high pollution or smoking causes lung cancer. We observed the person lives in a place with high pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X or V2 or V3
Y = 1 = 1 or 1 or 1
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 0 | V2=1
26128,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with low pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 1 | V2=0
26129,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with low pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 0 and 0
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 0 | V2=0
26130,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with low pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 1 | V2=0
26131,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with low pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=0
Solve for Y, given the evidence and the action
V2 = 0
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 1 and 0 and 0
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 0 | V2=0
26132,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with high pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 1 | V2=1
26133,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with high pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=0} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 0 = 0 and 1 and 0
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=0} = 0 | V2=1
26134,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with high pollution.",yes,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 1 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
1",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 1 | V2=1
26135,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on smoking and lung cancer. Pollution has a direct effect on smoking and lung cancer. Smoking has a direct effect on lung cancer. Pollution is unobserved. We know that listening to jazz and high pollution causes smoking. listening to jazz and high pollution and smoking causes lung cancer. We observed the person lives in a place with high pollution.",no,"Let V2 = pollution; X = listening to jazz; V3 = smoking; Y = lung cancer.
X->V3,V2->V3,X->Y,V2->Y,V3->Y
Y_{X=1} = 0 | V2=1
Solve for Y, given the evidence and the action
V2 = 1
V3 = X and V2
Y = X and V2 and V3
Y = 1 = 1 and 1 and 1
0",arrowhead,smoking_gene_cancer,3,det-counterfactual,Y_{X=1} = 0 | V2=1
26136,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes absence of tar deposit, and we know that high tar deposit causes lung cancer.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [1] = 1
1",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=0} = 1 | 
26137,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes absence of tar deposit, and we know that high tar deposit causes lung cancer.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [1] = 1
0",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=0} = 0 | 
26138,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes absence of tar deposit, and we know that high tar deposit causes lung cancer.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [0] = 0
0",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=1} = 1 | 
26139,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes absence of tar deposit, and we know that high tar deposit causes lung cancer.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = V2
Y = [0] = 0
1",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=1} = 0 | 
26140,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes absence of tar deposit, and we know that high tar deposit causes absence of lung cancer.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [0] = not 1
0",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=0} = 1 | 
26141,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes absence of tar deposit, and we know that high tar deposit causes absence of lung cancer.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [0] = not 1
1",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=0} = 0 | 
26142,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes absence of tar deposit, and we know that high tar deposit causes absence of lung cancer.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [1] = not 0
1",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=1} = 1 | 
26143,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes absence of tar deposit, and we know that high tar deposit causes absence of lung cancer.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = not X
Y = not V2
Y = [1] = not 0
0",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=1} = 0 | 
26144,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes high tar deposit, and we know that high tar deposit causes lung cancer.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [0] = 0
0",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=0} = 1 | 
26145,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes high tar deposit, and we know that high tar deposit causes lung cancer.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [0] = 0
1",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=0} = 0 | 
26146,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes high tar deposit, and we know that high tar deposit causes lung cancer.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [1] = 1
1",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=1} = 1 | 
26147,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes high tar deposit, and we know that high tar deposit causes lung cancer.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = V2
Y = [1] = 1
0",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=1} = 0 | 
26148,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes high tar deposit, and we know that high tar deposit causes absence of lung cancer.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=0} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [1] = not 0
1",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=0} = 1 | 
26149,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes high tar deposit, and we know that high tar deposit causes absence of lung cancer.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=0} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [1] = not 0
0",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=0} = 0 | 
26150,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes high tar deposit, and we know that high tar deposit causes absence of lung cancer.",no,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=1} = 1 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [0] = not 1
0",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=1} = 1 | 
26151,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Listening to jazz has a direct effect on tar deposit. Tar deposit has a direct effect on lung cancer. We know that listening to jazz causes high tar deposit, and we know that high tar deposit causes absence of lung cancer.",yes,"Let X = listening to jazz; V2 = tar deposit; Y = lung cancer.
X->V2,V2->Y
Y_{X=1} = 0 | 
Solve for Y, given the evidence and the action
V2 = X
Y = not V2
Y = [0] = not 1
1",chain,smoking_tar_cancer,3,det-counterfactual,Y_{X=1} = 0 | 
26152,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
26153,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
26154,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
26155,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
26156,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
26157,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
26158,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
26163,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
26164,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
26166,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
26168,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
26170,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
26171,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
26172,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
26174,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
26175,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
26176,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
26177,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
26178,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
26179,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
26180,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
26182,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
26183,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active and high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
26184,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
26185,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
26186,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
26187,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
26188,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
26189,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
26190,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
26191,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
26192,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
26193,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
26195,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
26196,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
26198,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
26199,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active or smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
26201,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
26203,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder inactive.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
26204,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
26205,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
26207,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is low and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
26208,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder inactive.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
26213,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
26214,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",yes,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
26215,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Unobserved confounders has a direct effect on maternal smoking status and brown eyes. Cigarette tax has a direct effect on maternal smoking status. Maternal smoking status has a direct effect on brown eyes. Unobserved confounders is unobserved. We know that confounder active or high cigarette tax causes smoking mother. confounder active and smoking mother causes brown eyes. We observed the cigarette tax is high and confounder active.",no,"Let V2 = cigarette tax; V1 = unobserved confounders; X = maternal smoking status; Y = brown eyes.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,tax_smoke_birthWeight,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"
26216,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
26217,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
26218,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
26220,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
26221,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
26222,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
26223,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
26224,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
26225,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
26226,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
26229,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
26230,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
26232,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
26233,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
26234,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
26235,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
26236,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
26237,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
26238,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
26239,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
26240,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
26241,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
26244,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
26245,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
26248,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=0"
26250,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
26251,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
26252,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=0, V1=1"
26253,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=1"
26254,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
26255,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=1"
26256,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
26257,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 0 = 0 or 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=0"
26259,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 and V2
Y = V1 or X
Y = 1 = 0 or 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=0"
26260,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=1"
26261,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
26262,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty and global water company causes liking spicy food. high poverty or liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 and V2
Y = V1 or X
Y = 1 = 1 or 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
26265,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=0, V1=0"
26266,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=0"
26267,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has low poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=0, V1=0
Solve for Y, given the evidence and the action
V2 = 0
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 0 | V2=0, V1=0"
26270,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a local water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=0, V1=1
Solve for Y, given the evidence and the action
V2 = 0
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=0, V1=1"
26272,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 0
0",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 1 | V2=1, V1=0"
26274,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has low poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=0
Solve for Y, given the evidence and the action
V2 = 1
V1 = 0
X = V1 or V2
Y = V1 and X
Y = 0 = 0 and 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=0"
26277,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=0} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 0 = 1 and 0
1",IV,water_cholera,3,det-counterfactual,"Y_{X=0} = 0 | V2=1, V1=1"
26278,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",yes,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 1 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
1",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 1 | V2=1, V1=1"
26279,"Imagine a self-contained, hypothetical world with only the following conditions, and without any unmentioned factors or causal relationships: Poverty has a direct effect on liking spicy food and cholera. Water company has a direct effect on liking spicy food. Liking spicy food has a direct effect on cholera. Poverty is unobserved. We know that high poverty or global water company causes liking spicy food. high poverty and liking spicy food causes cholera contraction. We observed the person is served by a global water company and the region has high poverty.",no,"Let V2 = water company; V1 = poverty; X = liking spicy food; Y = cholera.
V1->X,V2->X,V1->Y,X->Y
Y_{X=1} = 0 | V2=1, V1=1
Solve for Y, given the evidence and the action
V2 = 1
V1 = 1
X = V1 or V2
Y = V1 and X
Y = 1 = 1 and 1
0",IV,water_cholera,3,det-counterfactual,"Y_{X=1} = 0 | V2=1, V1=1"